Individual differences |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
In statistics, a confidence interval (CI) is an interval estimate of a population parameter. Instead of estimating the parameter by a single value, an interval likely to include the parameter is given. How likely the interval is to contain the parameter is determined by the confidence level or confidence coefficient. Increasing the desired confidence level will widen the confidence interval.
Confidence intervals are used to indicate the reliability of an estimate. For example, a CI can be used to describe how reliable survey results are. All other things being equal, a survey result with a small CI is more reliable than a result with a large CI.
More specifically, for a given associated proportion p (or confidence level), a CI for a population parameter is an interval that is calculated from a random sample of an underlying population such that, if the sampling was repeated numerous times and the confidence interval recalculated from each sample according to the same method, a proportion p of the confidence intervals would contain the population parameter in question. In unusual cases, a confidence set may consist of a collection several separate intervals, which may include semi-infinite intervals, and it is possible that an outcome of a confidence-interval calculation could be the set of all values from minus infinity to plus infinity.
Confidence intervals are the most prevalent form of interval estimation. Interval estimates may be contrasted with point estimates and have the advantage over these as summaries of a dataset in that more information is conveyed – not just a "best estimate" of a parameter but an indication of the accuracy with which the parameter is known.
Confidence intervals play a similar role in frequentist statistics to the credibility interval in Bayesian statistics. However, confidence intervals and credibility intervals are not only mathematically different; they have radically different interpretations.
The concept of a confidence interval for a single quantity can be generalised to be able to deal with several quantities simultaneously, in which case they are called confidence regions. Such regions can indicate not only the extent of likely estimation errors but can also reveal whether (for example) if the estimate for one quantity is too large then the other is also likely to be too large.
In modern applied practice, confidence intervals are often stated at the 95% level. However, when presented graphically, confidence intervals or confidence regions may be shown for several confidence levels, for example 50%, 90% and 99%.
CI's as random intervals
Confidence intervals are constructed on the basis of a given dataset: x denotes the set of observations in the dataset, and X is used when considering the outcomes that might have been observed from the same population, where X is treated as a random variable whose observed outcome is X = x. A confidence interval is specified by a pair of functions u(.) and v(.) and the confidence interval for the given data set is defined as the interval (u(x), v(x)). To complete the definition of a confidence interval, there needs to be a clear understanding of the quantity for which the CI provides an interval estimate. Suppose this quantity is w. The property of the rules u(.) and v(.) that makes the interval (u(x),v(x)) closest to what a confidence interval for w would be, relates to the properties of the set of random intervals given by (u(X),v(X)): that is treating the end-points as random variables. This property is the coverage probability or the probability c that the random interval includes w,
Here the endpoints U = u(X) and V = v(X) are statistics (i.e., observable random variables) which are derived from values in the dataset. The random interval is (U, V).
Confidence intervals for inference
For the above to provide a viable means to statistical inference, something further is required: a tie between the quantity being estimated and the probability distribution of the outcome X. Suppose that this probability distribution is characterised by the unobservable parameter θ, which is a quantity to be estimated, and by other unobservable parameters φ which are not of immediate interest. These other quantities φ in which there is no immediate interest are called nuisance parameters, as statistical theory still needs to find some way to deal with them.
The definition of a confidence interval for θ is, for a given α,
- for all
The number (sometimes reported as a percentage (100%·)) is called the confidence level or confidence coefficient. Here is used to indicate the probability when the random variable X has the distribution characterised by . An important part of this specification is that the random interval (U, V) covers the unknown value θ with a high probability no matter what the true value of θ actually is.
Note that here need not refer to an explicitly given parameterised family of distributions, although it often does. Just as the random variable X notionally corresponds to other possible realisations of x from the same population or from the same version of reality, the parameters indicate that we need to consider other versions of reality in which the distribution of X might have different characteristics.
Intervals for random outcomes
Confidence intervals can be defined for random quantities as well as for fixed quantities as in the above. See prediction interval. For this, consider an additional single-valued random variable Y which may or may not be statistically dependent on X. Then the rule for for constructing the interval(u(x), v(x)) provides a confidence interval for the as-yet-to-be observed value y of Y if
- for all
Here is used to indicate the probability over the joint distribution of the random variables (X,Y) when this is characterised by parameters .
Approximate confidence intervals
For non-standard applications it is sometimes not possible to find rules for constructing confidence intervals that have exactly the required properties. But practically useful intervals can still be found. The coverage probability for a random interval is defined by
and the rule for constructing the interval may be accepted as providing a confidence interval if
- for all
to an acceptable level of approximation.
Comparison to Bayesian interval estimates
A Bayesian interval estimate is called a credible interval. Using much of the same notation as above, the definition of a credible interval for the unknown true value of θ is, for a given α,
Here Θ is used to emhasize that the unknown value of is being treated as a random variable. The definitions of the two types of intervals may be compared as follows.
- The definition of a confidence interval involves probabilities calculated from the distribution of X for given (or conditional on these values) and the condition needs to hold for all values of .
- The definition of a credible interval involves probabilities calculated from the distribution of Θ conditional on the observed values of X=x and marginalised (or averaged) over the values of , where this last quantity is the random variable corresponding to the uncertainty about the nuisance parameters in .
Note that the treatment of the nuisance parameters above is often omitted from discussions comparing confidence and credible intervals but it is markedly different between the two cases.
In some simple standard cases, the intervals produced as confidence and credible intervals from the same data set can be identical. They are always very different if moderate or strong prior information is included in the Bayesian analysis.
When applying fairly standard statistical procedures, there will often be fairly standard ways of constructing confidence intervals. These will have been devised so as to meet certain desirable properties, which will hold given that the assumptions on which the procedure rely are true. In non-standard applications, the same desirable properties would be sought. These desirable properties may be described as: validity, optimality and invariance. Of these "validity" is most important, followed closely by "optimality". "Invariance" may be considered as a property of the method of derivation of a confidence interval rather than of the rule for constructing the interval.
- Validity. This means that the nominal coverage probability (confidence level) of the confidence interval should hold, either exactly or to a good approximation.
- Optimality. This means that the rule for constructing the confidence interval should make as much use of the information in the data-set as possible. Recall that one could throw away half of a dataset and still be able to derive a valid confidence interval. One way of assessing optimality is by the length of the interval, so that a rule for constructing a confidence interval is judged better than another if it leads to intervals whose widths are typically shorter.
- Invariance. In many applications the quantity being estimated might not be tightly defined as such. For example, a survey might result in an estimate of the median income in a population, but it might equally be considered as providing an estimate of the logarithm of the median income, given that this is a common scale for presenting graphical results. It would be desirable that the method used for constructing a confidence interval for the median income would give equivalent results when applied to constructing a confidence interval for the logarithm of the median income: specifically the values at the ends of the latter interval would be the logarithms of the values at the ends of former interval.
Methods of derivation
For non-standard applications, there are several routes that might be taken to derive a rule for the construction of confidence intervals. Established rules for standard procedures might be justified or explained via several of these routes. Typically a rule for constructing confidence intervals is closely tied to a particular way of finding a point estimate of the quantity being considered.
- Sample statistics
- This is closely related to the method of moments for estimation. A simple example arises where the quantity to be estimated is the mean, in which case an natural estimate is the sample mean. The usual arguments indicate that the sample variance can be used to estimate the variance of the sample mean. A naive confidence interval for the true mean can be constructed centred on the sample mean with a width which is a multiple of the square root of the sample variance.
- Likelihood theory
- Where estimates are constructed using the maximum likelihood principle, the theory for this provides two ways of constructing confidence intervals or confidence regions for the estimates.
- Estimating equations
- The estimation approach here can be considered as both a generalisation of the method of moments and a generalisation of the maximum likelihood approach. There are corresponding generalisations of the results of maximum likelihood theory that allow confidence intervals to be constructed based on estimates derived from estimating equations.
- Via significance testing
- If significance tests are available for general values of a parameter, then confidence intervals/regions can be constructed by including in the 100p% confidence region all those points for which the significance test of the null hypothesis that the true value is the given value is not rejected at a significance level of (1-p).
A machine fills cups with margarine, and is supposed to be adjusted so that the mean content of the cups is close to 250 grams of margarine. Of course it is not possible to fill every cup with exactly 250 grams of margarine. Hence the weight of the filling can be considered to be a random variable X. The distribution of X is assumed here to be a normal distribution with unknown expectation μ and (for the sake of simplicity) known standard deviation σ = 2.5 grams. To check if the machine is adequately adjusted, a sample of n = 25 cups of margarine is chosen at random and the cups weighed. The weights of margarine are , a random sample from X.
To get an impression of the expectation μ, it is sufficient to give an estimate. The appropriate estimator is the sample mean:
The sample shows actual weights , with mean:
If we take another sample of 25 cups, we could easily expect to find values like 250.4 or 251.1 grams. A sample mean value of 280 grams however would be extremely rare if the mean content of the cups is in fact close to 250g. There is a whole interval around the observed value 250.2 of the sample mean within which, if the whole population mean actually takes a value in this range, the observed data would not be considered particularly unusual. Such an interval is called a confidence interval for the parameter μ. How do we calculate such an interval? The endpoints of the interval have to be calculated from the sample, so they are statistics, functions of the sample and hence random variables themselves.
In our case we may determine the endpoints by considering that the sample mean from a normally distributed sample is also normally distributed, with the same expectation μ, but with standard error (grams). By standardizing we get a random variable
dependent on μ, but with a standard normal distribution independent of the parameter μ to be estimated. Hence it is possible to find numbers −z and z, independent of μ, where Z lies in between with probability 1 − α, a measure of how confident we want to be. We take 1 − α = 0.95. So we have:
The number z follows from:
This might be interpreted as: with probability 0.95 to one we will choose a confidence interval in which we will meet the parameter μ between the stochastic endpoints, but that does not mean that possibility of meeting parameter μ in confidence interval is 95% :
Every time the measurements are repeated, there will be another value for the mean of the sample. In 95% of the cases μ will be between the endpoints calculated from this mean, but in 5% of the cases it will not be. The actual confidence interval is calculated by entering the measured weights in the formula. Our 0.95 confidence interval becomes:
This interval has fixed endpoints, where μ might be in between (or not). There is no probability of such an event. We cannot say: "with probability (1 − α) the parameter μ lies in the confidence interval." We only know that by repetition in 100(1 − α) % of the cases μ will be in the calculated interval. In 100α % of the cases however it doesn't. And unfortunately we don't know in which of the cases this happens. That's why we say: with confidence level 100(1 − α) % μ lies in the confidence interval."
The following picture shows 50 realisations of a confidence interval for μ.
Observation of the sample means we choose from the population of all realisations. There the probability is 95% we end up having chosen an interval that contains the parameter. After realisation we just have our chosen interval. As seen from the picture there was a fair chance we choose an interval containing μ; however we may be unlucky and have picked the wrong one. We'll never know; we're stuck with our interval.
has a Student's t-distribution with n − 1 degrees of freedom. Note that the distribution of T does not depend on the values of the unobservable parameters μ and σ2; i.e., it is a pivotal quantity. If c is the 95th percentile of this distribution, then
(Note: "95th" and "0.9" are correct in the preceding expressions. There is a 5% chance that T will be less than −c and a 5% chance that it will be larger than +c. Thus, the probability that T will be between −c and +c is 90%.)
and we have a theoretical (stochastic) 90% confidence interval for μ.
After observing the sample we find values for and s for S, from which we compute the confidence interval
an interval with fixed numbers as endpoints, of which we can no more say there is a certain probability it contains the parameter μ. Either μ is in this interval or isn't.
Meaning and interpretation
Confidence intervals in measurement
The results of measurements are often accompanied by confidence intervals. For instance, suppose a scale is known to yield the actual mass of an object plus a normally distributed random error with mean 0 and known standard deviation σ. If we weigh 100 objects of known mass on this scale and report the values ±σ, then we can expect to find that around 68% of the reported ranges include the actual mass.
If we wish to report values with a smaller standard error value, then we repeat the measurement n times and average the results. Then the 68.2% confidence interval is . For example, repeating the measurement 100 times reduces the confidence interval to 1/10 of the original width.
Note that when we report a 68.2% confidence interval (usually termed standard error) as v ± σ, this does not mean that the true mass has a 68.2% chance of being in the reported range. In fact, the true mass is either in the range or not. How can a value outside the range be said to have any chance of being in the range? Rather, our statement means that 68.2% of the ranges we report using ± σ are likely to include the true mass.
This is not just a quibble. Under the incorrect interpretation, each of the 100 measurements described above would be specifying a different range, and the true mass supposedly has a 68% chance of being in each and every range. Also, it supposedly has a 32% chance of being outside each and every range. If two of the ranges happen to be disjoint, the statements are obviously inconsistent. Say one range is 1 to 2, and the other is 2 to 3. Supposedly, the true mass has a 68% chance of being between 1 and 2, but only a 32% chance of being less than 2 or more than 3. The incorrect interpretation reads more into the statement than is meant.
On the other hand, under the correct interpretation, each and every statement we make is really true, because the statements are not about any specific range. We could report that one mass is 10.2 ± 0.1 grams, while really it is 10.6 grams, and not be lying. But if we report fewer than 1000 values and more than two of them are that far off, we will have some explaining to do.
It is also possible to estimate a confidence interval without knowing the standard deviation of the random error. This is done using the t distribution, or by using non-parametric resampling methods such as the bootstrap, which do not require that the error have a normal distribution.
How to understand confidence intervals
For users of frequentist methods, various interpretations of a confidence interval can be given.
- The confidence interval can be expressed in terms of samples (or repeated samples): "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time."
- The explanation of a confidence interval can amount to something like: "The confidence interval represents values for the population parameter for which the difference between the parameter and the observed estimate is not statistically significant at the 10% level". In fact, this relates to one particular way in which a confidence interval may be constructed.
- The probability associated with a confidence interval may also be considered from a pre-experiment point of view, in the same context in which arguments for the random allocation of treatments to study items are made. Here the experimenter sets out the way in which they intend to calculate a confidence interval and know, before they do the actual experiment, that the interval they will end up calculating has a certain chance of covering the true but unknown value. This is very similar to the "repeated sample" interpretation above, except that it avoids relying on considering hypothetical repeats of a sampling procedure that may not be repeatable in any meaningful sense.
Critics of frequentist methods dislike at least the first two of the three interpretations given above. Users of Bayesian methods, if they produced an interval estimate, would by contrast want to say "My degree of belief that the parameter is in fact in this interval is 90%". Disagreements about these issues are not disagreements about solutions to mathematical problems. Rather they are disagreements about the ways in which mathematics is to be applied.
| The factual accuracy of this section is disputed.|
Please see the relevant discussion on the talk page
Confidence levels are typically given alongside statistics resulting from sampling.
In a statement "we are 90% confident that between 35% and 45% of voters favor Candidate A", 90% is our confidence level and 35%-45% is our confidence interval.
It is very tempting to misunderstand this statement in the following way. We used capital letters U and V for random variables; it is conventional to use lower-case letters u and v for their observed values in a particular instance. The misunderstanding is the conclusion that[How to reference and link to summary or text]
so that after the data has been observed, a conditional probability distribution of θ, given the data, is inferred. For example, suppose X is normally distributed with expected value θ and variance 1. (It is grossly unrealistic to take the variance to be known while the expected value must be inferred from the data, but it makes the example simple.) The random variable X is observable. (The random variable X − θ is not observable, since its value depends on θ.) Then X − θ is normally distributed with expectation 0 and variance 1. Given that 90% of the standard normal distribution lies between −1.645 and 1.645, we know:
so the interval from X − 1.645 to X + 1.645 is a 90% confidence interval for θ. But when X = 82 is observed, can we then say that
This conclusion does not follow from the laws of probability because θ is not a "random variable"; i.e., no probability distribution has been assigned to it.[How to reference and link to summary or text] Confidence intervals are generally a frequentist method, i.e., employed by those who interpret "90% probability" as "occurring in 90% of all cases".[How to reference and link to summary or text] Suppose, for example, that θ is the mass of the planet Neptune, and the randomness in our measurement error means that 90% of the time our statement that the mass is between this number and that number will be correct. The mass is not what is random. Therefore, given that we have measured it to be 82 units, we cannot say that in 90% of all cases, the mass is between 82 − 1.645 and 82 + 1.645. There are no such cases; there is, after all, only one planet Neptune.
But if probabilities are construed as degrees of belief rather than as relative frequencies of occurrence of random events, i.e., if we are Bayesians rather than frequentists, can we then say we are 90% sure that the mass is between 82 − 1.645 and 82 + 1.645? Many answers to this question have been proposed, and are philosophically controversial. The answer will not be a mathematical theorem, but a philosophical tenet. Less controversial are Bayesian credible intervals, in which one starts with a prior probability distribution of θ, and finds a posterior probability distribution, which is the conditional probability distribution of θ given the data.
Robust confidence intervals
In the process of weighing 1000 objects, under practical conditions, it is easy to believe that the operator might make a mistake in procedure and so report an incorrect mass (thereby making one type of systematic error). Suppose he has 100 objects and he weighed them all, one at a time, and repeated the whole process ten times. Then he can calculate a sample standard deviation for each object, and look for outliers. Any object with an unusually large standard deviation probably has an outlier in its data. These can be removed by various non-parametric techniques. If he repeated the process only three times, he would simply take the median of the three measurements and use σ to give a confidence interval. The 200 extra weighings served only to detect and correct for operator error and did nothing to improve the confidence interval. With more repetitions, he could use a truncated mean, discarding say the largest and smallest values and averaging the rest. He could then use a bootstrap calculation to determine a confidence interval narrower than that calculated from σ, and so obtain some benefit from a large amount of extra work.
These procedures are robust against procedural errors which are not modeled by the assumption that the balance has a fixed known standard deviation σ. In practical applications where the occasional operator error can occur, or the balance can malfunction, the assumptions behind simple statistical calculations cannot be taken for granted. Before trusting the results of 100 objects weighed just three times each to have confidence intervals calculated from σ, it is necessary to test for and remove a reasonable number of outliers (testing the assumption that the operator is careful and correcting for the fact that he is not perfect), and to test the assumption that the data really have a normal distribution with standard deviation σ.
The theoretical analysis of such an experiment is complicated, but it is easy to set up a spreadsheet which draws random numbers from a normal distribution with standard deviation σ to simulate the situation (use =norminv(rand(),0,σ)). See for example Wittwer, J.W., "Monte Carlo Simulation in Excel: A Practical Guide", June 1, 2004. These techniques also work in Open Office and gnumeric.
After removing obvious outliers, one could subtract the median from the other two values for each object, and examine the distribution of the 200 resulting numbers. It should be normal with mean near zero and standard deviation a little larger than σ. A simple Monte Carlo spreadsheet calculation would reveal typical values for the standard deviation (around 105 to 115% of σ). Or, one could subtract the mean of each triplet from the values, and examine the distribution of 300 values. The mean is identically zero, but the standard deviation should be somewhat smaller (around 75 to 85% of σ).
- See also: Margin of error
An approximate confidence interval for a population mean can be constructed for random variables that are not normally distributed in the population, relying on the central limit theorem, if the sample sizes and counts are big enough. The formulae are identical to the case above (where the sample mean is actually normally distributed about the population mean). The approximation will be quite good with only a few dozen observations in the sample if the probability distribution of the random variable is not too different from the normal distribution (e.g. its cumulative distribution function does not have any discontinuities and its skewness is moderate).
One type of sample mean is the mean of an indicator variable, which takes on the value 1 for true and the value 0 for false. (Statisticians often call indicator variables "dummy variables", but that term is also frequently used by mathematicians for the concept of a bound variable.) The mean of such a variable is equal to the proportion that have the variable equal to one (both in the population and in any sample). Thus, the sample mean for a variable labeled MALE in data is just the proportion of sampled observations who have MALE = 1, i.e. the proportion who are male. This is a useful property of indicator variables, especially for hypothesis testing.
To apply the central limit theorem, one must use a large enough sample. A rough rule of thumb is that one should see at least 5 cases in which the indicator is 1 and at least 5 in which it is 0. Confidence intervals constructed using the above formulae may include negative numbers or numbers greater than 1, but proportions obviously cannot be negative or exceed 1. The probability assigned to negative numbers and numbers greater than 1 is usually small when the sample size is large and the proportion being estimated is not too close to 0 or 1.
Confidence intervals for cases where the method above assigns a substantial probability to (−∞, 0) or to (1, ∞) may be constructed by inverting hypothesis tests. If we think of conducting hypothesis tests over the whole feasible range of parameter values, and including any values for which a single hypothesis test would not reject the null hypothesis that the true value was that value, given our sample value, we can make a confidence interval based on the central limit theorem that does not violate the basic properties of proportions.
On the other hand, sample proportions can only take on a finite number of values, so the central limit theorem and the normal distribution are not the best tools for building a confidence interval. A better method would rely on the binomial distribution or the beta distribution, and there are a number of better methods in widespread use. For details on advantages and disadvantages of each, see:
- "Interval Estimation for a Binomial Proportion", Lawrence D. Brown, T. Tony Cai, Anirban DasGupta, Statistical Science, volume 16, number 2 (May, 2001), pages 101-117.
- Analysis of variance
- Confidence region
- Prediction interval
- Regression analysis
- Segmented regression
- Cumulative frequency
- Bootstrapping (statistics)
- Binomial proportion confidence interval
- ↑ Goldstein, H., & Healey, M.J.R. (1995). "The graphical presentation of a collection of means." Journal of the Royal Statistical Society, 158, 175-77.
- ↑ Zar, J.H. (1984) Biostatistical Analysis. Prentice Hall International, New Jersey. pp 43-45
- Fisher, R.A. (1956) Statistical Methods and Scientific Inference. Oliver and Boyd, Edinburgh. (See p. 32.)
- Freund, J.E. (1962) Mathematical Statistics Prentice Hall, Englewood Cliffs, NJ. (See pp. 227-228.)
- Hacking, I. (1965) Logic of Statistical Inference. Cambridge University Press, Cambridge
- Keeping, E.S. (1962) Introduction to Statistical Inference. D. Van Nostrand, Princeton, NJ.
- Kiefer, J. (1977) "Conditional Confidence Statements and Confidence Estimators (with discussion)" Journal of the American Statistical Association, 72, 789-827.
- Neyman, J. (1937) "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability" Philosophical Transactions of the Royal Society of London A, 236, 333-380. (Seminal work.)
- Robinson, G.K. (1975) "Some Counterexamples to the Theory of Confidence Intervals." Biometrika, 62, 155-161.
- Abelson, R. P. (1997). On the surprising longevity of flogged horses: Why there is a case for the significance test: Psychological Science Vol 8(1) Jan 1997, 12-15.
- Aiken, L. R. (1983). An interactive program for testing the significance of various correlation coefficients: Educational and Psychological Measurement Vol 43(1) Spr 1983, 181-182.
- Alf, E. F., Jr., & Graf, R. G. (1999). Asymptotic confidence limits for the difference between two squared multiple correlations: A simplified approach: Psychological Methods Vol 4(1) Mar 1999, 70-75.
- Alf, E. F., & Grossberg, J. M. (1979). The geometric mean: Confidence limits and significance tests: Perception & Psychophysics Vol 26(5) Nov 1979, 419-421.
- Algina, J. (1999). A comparison of methods for constructing confidence intervals for the squared multiple correlation coefficient: Multivariate Behavioral Research Vol 34(4) 1999, 493-504.
- Algina, J., & Keselman, H. J. (2003). Approximate confidence intervals for effect sizes: Educational and Psychological Measurement Vol 63(4) Aug 2003, 537-553.
- Algina, J., Keselman, H. J., & Penfield, R. D. (2006). Confidence Interval Coverage for Cohen's Effect Size Statistic: Educational and Psychological Measurement Vol 66(6) Dec 2006, 945-960.
- Algina, J., & Moulder, B. C. (2001). Sample sizes for confidence intervals on the increase in the squared multiple correlation coefficient: Educational and Psychological Measurement Vol 61(4) Aug 2001, 633-649.
- Anderson, A. J. (2003). Utility of a dynamic termination criterion in the ZEST adaptive threshold method: Vision Research Vol 43(2) Jan 2003, 165-170.
- Andrade, A. G., & Scalco, M. Z. (1989). Concepts of validity and confidence in an instrument for evaluating treatment for alcoholics: Jornal Brasileiro de Psiquiatria Vol 38(1) Jan-Feb 1989, 41-45.
- Aoshima, M., & Mukhopadhyay, N. (1998). Fixed-Width Simultaneous Confidence Intervals for Multinormal Means in Several Intraclass Correlation Models: Journal of Multivariate Analysis Vol 66(1) Jul 1998, 46-63.
- Appel, V., & Kipnis, D. (1954). The use of levels of confidence in item analysis: Journal of Applied Psychology Vol 38(4) Aug 1954, 256-259.
- Atkinson, L. (1990). Standard errors of prediction for the Vineland Adaptive Behavior Scales: Journal of School Psychology Vol 28(4) Win 1990, 355-359.
- Attorresi, H. F., Aguerri, M. E., Lozzia, G. S., & Galibert, M. S. (2004). Confidence intervals or true scores. Their assumptions made explicit: Interdisciplinaria Revista de Psicologia y Ciencias Afines Vol 21(1) 2004, 29-51.
- Baranski, J. V., & Petrusic, W. M. (1994). The calibration and resolution of confidence in perceptual judgments: Perception & Psychophysics Vol 55(4) Apr 1994, 412-428.
- Barchard, K. A., & Hakstian, A. R. (1997). The robustness of confidence intervals for coefficient alpha under violation of the assumption of essential parallelism: Multivariate Behavioral Research Vol 32(2) 1997, 169-191.
- Bedrick, E. J. (1991). Approximate confidence intervals for the correlation from data in two-by-two tables: British Journal of Mathematical and Statistical Psychology Vol 44(2) Nov 1991, 369-378.
- Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers Misunderstand Confidence Intervals and Standard Error Bars: Psychological Methods Vol 10(4) Dec 2005, 389-396.
- Bell, J. F. (1986). Simultaneous confidence intervals for the linear functions of expected mean squares used in generalizability theory: Journal of Educational Statistics Vol 11(3) Fal 1986, 197-205.
- Berger, M. P. (1977). STP: A subroutine for simultaneous test procedures and confidence intervals: Behavior Research Methods & Instrumentation Vol 9(4) Aug 1977, 385.
- Bergstrom, B. A., & Lunz, M. E. (1992). Confidence in pass/fail decisions for computer adaptive and paper and pencil examinations: Evaluation & the Health Professions Vol 15(4) Dec 1992, 453-464.
- Bernbach, H. A. (1972). Confidence ratings for individual items in recall: Psychological Review Vol 79(6) Nov 1972, 536-537.
- Berry, K. J., & Mielke, P. W. (1976). Large sample confidence limits for Goodman and Kruskal's proportional prediction measure TAU-sub(b): Educational and Psychological Measurement Vol 36(3) Fal 1976, 747-751.
- Berry, K. J., & Mielke, P. W., Jr. (1996). Exact confidence limits for population proportions based on the negative hypergeometric probability distribution: Perceptual and Motor Skills Vol 83(3, Pt 2) Dec 1996, 1216-1218.
- Berry, K. J., Mielke, P. W., & Helmericks, S. G. (1988). Exact confidence limits for proportions: Educational and Psychological Measurement Vol 48(3) Fal 1988, 713-716.
- Bieliauskas, L. A., Fastenau, P. S., Lacy, M. A., & Roper, B. L. (1997). Use of the odds ratio to translate neuropsychological test scores into real-world outcomes: From statistical significance to clinical significance: Journal of Clinical and Experimental Neuropsychology Vol 19(6) Dec 1997, 889-896.
- Bird, K. D. (2002). Confidence intervals for effect sizes in analysis of variance: Educational and Psychological Measurement Vol 62(2) Apr 2002, 197-226.
- Bivens, H., & Slotnick, B. (2000). Decrement in the horizontal-vertical illusion: Are subjects aware of their increased accuracy? : Perceptual and Motor Skills Vol 90(2) Apr 2000, 403-412.
- Blackhouse, G., Briggs, A. H., & O'Brien, B. J. (2002). A note on the estimation of confidence intervals for cost-effectiveness when costs and effects are censored: Medical Decision Making Vol 22(2) Mar-Apr 2002, 173-177.
- Blouin, D. C., & Riopelle, A. J. (2005). On Confidence Intervals for Within-Subjects Designs: Psychological Methods Vol 10(4) Dec 2005, 397-412.
- Bobko, P. (1983). An analysis of correlations corrected for attenuation and range restriction: Journal of Applied Psychology Vol 68(4) Nov 1983, 584-589.
- Bobko, P., Sapinkopf, R., & Anderson, N. S. (1978). A lack of confidence about formulae for regression confidence intervals: Teaching of Psychology Vol 5(2) Apr 1978, 102-103.
- Bond, C. F., Jr., & Richardson, K. (2004). Seeing the fisher Z-transformation: Psychometrika Vol 69(2) Jun 2004, 291-303.
- Bonett, D. G. (2006). Robust Confidence Interval for a Ratio of Standard Deviations: Applied Psychological Measurement Vol 30(5) Sep 2006, 432-439.
- Bonett, D. G., & Price, R. M. (2002). Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements: Psychological Methods Vol 7(3) Sep 2002, 370-383.
- Bonett, D. G., & Price, R. M. (2005). Inferential Methods for the Tetrachoric Correlation Coefficient: Journal of Educational and Behavioral Statistics Vol 30(2) Sum 2005, 213-225.
- Borenstein, M. (1994). A note on the use of confidence intervals in psychiatric research: Psychopharmacology Bulletin Vol 30(2) 1994, 235-238.
- Borgmeier, C., & Homer, R. H. (2006). An evaluation of the predictive validity of confidence ratings in identifying functional behavioral assessment hypothesis statements: Journal of Positive Behavior Interventions Vol 8(2) Spr 2006, 100-105.
- Brandstatter, E. (1999). Confidence intervals as an alternative to significance testing: Methods of Psychological Research Vol 4(2) 1999, 33-46.
- Braun, C., Kaiser, S., Kincses, W.-E., & Elbert, T. (1997). Confidence interval of single dipole locations based on EEG data: Brain Topography Vol 10(1) Fal 1997, 31-39.
- Brewer, J. K., & Sindelar, P. T. (1987). Adequate sample size: A priori and post hoc considerations: The Journal of Special Education Vol 21(4) Win 1987-1988, 74-84.
- Brewer, N., & Wells, G. L. (2006). The Confidence-Accuracy Relationship in Eyewitness Identification: Effects of Lineup Instructions, Foil Similarity, and Target-Absent Base Rates: Journal of Experimental Psychology: Applied Vol 12(1) Mar 2006, 11-30.
- Brophy, A. L. (1983). Approximation of probabilities near the median of the F distribution: Educational and Psychological Measurement Vol 43(1) Spr 1983, 177-180.
- Brophy, A. L. (1986). Confidence intervals for true scores and retest scores on clinical tests: Journal of Clinical Psychology Vol 42(6) Nov 1986, 989-991.
- Budescu, D. V. (1980). Approximate confidence intervals for a robust scale parameter: Psychometrika Vol 45(3) Sep 1980, 397-402.
- Budescu, D. V. (2006). Confidence in Aggregation of Opinions from Multiple Sources. New York, NY: Cambridge University Press.
- Budescu, D. V., Erev, I., & Wallsten, T. S. (1997). On the importance of random error in the study of probability judgment: Part I. New theoretical developments: Journal of Behavioral Decision Making Vol 10(3) Sep 1997, 157-171.
- Budescu, D. V., Wallsten, T. S., & Au, W. T. (1997). On the importance of random error in the study of probability judgment: Part II. Applying the stochastic judgment model to detect systematic trends: Journal of Behavioral Decision Making Vol 10(3) Sep 1997, 173-188.
- Burke, C. J. (1954). Further remarks on one-tailed tests: Psychological Bulletin Vol 51(6) Nov 1954, 587-590.
- Capraro, M. M. (2005). An introduction to confidence introduction to confidence intervals for both statistical estimates and effect sizes: Research in the Schools Vol 12(2) Fal 2005, 22-33.
- Capraro, M. M., & Capraro, R. M. (2003). Exploring the APA Fifth Edition Publication Manual's impact on the analytic preferences of journal editorial board members: Educational and Psychological Measurement Vol 63(4) Aug 2003, 554-565.
- Capraro, R. M. (2004). Statistical Significance, Effect Size Reporting, and Confidence Intervals: Best Reporting Strategies: Journal for Research in Mathematics Education Vol 35(1) Jan 2004, 57-62.
- Carr, J. W., Marascuilo, L. A., & Busk, P. (1982). Optimal randomized response models and methods for hypothesis testing: Journal of Educational Statistics Vol 7(4) Win 1982, 295-310.
- Caruso, J. C., & Cliff, N. (1997). Empirical size, coverage, and power of confidence intervals for Spearman's rho: Educational and Psychological Measurement Vol 57(4) Aug 1997, 637-654.
- Castaneda, J. A., & Gil, J. F. (2004). A look at confidence intervals in research: Revista Colombiana de Psiquiatria Vol 33(2) Jun 2004, 193-201.
- Cesarini, D., Sandewall, O., & Johannesson, M. (2006). Confidence interval estimation tasks and the economics of overconfidence: Journal of Economic Behavior & Organization Vol 61(3) Nov 2006, 453-470.
- Chan, W., & Chan, D. W. L. (2004). Bootstrap Standard Error and Confidence Intervals for the Correlation Corrected for Range Restriction: A Simulation Study: Psychological Methods Vol 9(3) Sep 2004, 369-385.
- Chang, Y.-C. I. (2005). Application of Sequential Interval Estimation to Adaptive Mastery Testing: Psychometrika Vol 70(4) Dec 2005, 685-713.
- Charles, E. P. (2005). The Correction for Attenuation Due to Measurement Error: Clarifying Concepts and Creating Confidence Sets: Psychological Methods Vol 10(2) Jun 2005, 206-226.
- Charter, R. A. (1997). Confidence interval procedures for retest, alternative-form, validity, and alpha coefficients: Perceptual and Motor Skills Vol 84(3, Pt 2) Jun 1997, 1488-1490.
- Charter, R. A., & Feldt, L. S. (2002). The importance of reliabiliity as it relates to true score confidence intervals: Measurement and Evaluation in Counseling and Development Vol 35(2) Jul 2002, 104-112.
- Charter, R. A., & Larsen, B. S. (1983). Fisher's z to r: Educational and Psychological Measurement Vol 43(1) Spr 1983, 41-42.
- Charter, R. A., & Lopez, M. N. (2003). MMPI-2: Confidence intervals for random responding to the F, F back and VAIN Scales: Journal of Clinical Psychology Vol 59(9) Sep 2003, 985-991.
- Chen, J. J., & Novick, M. R. (1982). On the use of a cumulative distribution as a utility function in educational or employment selection: Journal of Educational Statistics Vol 7(1) Spr 1982, 19-35.
- Chilcoat, H. D., Munoz, A., Vlahov, D., & Anthony, J. C. (1994). Low power? Use two-dimensional confidence regions as a graphical method for depicting uncertainty: Drug and Alcohol Dependence Vol 36(1) Aug 1994, 39-48.
- Clement, M., Mercier, P., & Pasto, L. (2002). Sample size, confidence, and contingency judgement: Canadian Journal of Experimental Psychology/Revue canadienne de psychologie experimentale Vol 56(2) Jun 2002, 128-137.
- Cohen, L. M., & Forthman, J. H. (1972). CFQ: The first statement of a statistical procedure to determine similarities and differences for behavioral science research: Journal of Psychology: Interdisciplinary and Applied Vol 82(1) Sep 1972, 3-11.
- Cohn, L. D., & Becker, B. J. (2003). How Meta-Analysis Increases Statistical Power: Psychological Methods Vol 8(3) Sep 2003, 243-253.
- Colugnati, F. A. B., Louzada-Neto, F., & de Aguiar Carrazedo Taddei, J. A. (2005). An application of bootstrap resampling method to obtain confidence interval for percentile fatness cutoff points in childhood and adolescence overweight diagnoses: International Journal of Obesity Vol 29(3) Mar 2005, 340-347.
- Convey, J. J. (1975). The application of simultaneous confidence intervals for multinomial populations to an inventory of plans and goals: Florida Journal of Educational Research Vol 17 1975, 1-12.
- Cortina, J. M., & Dunlap, W. P. (1997). On the logic and purpose of significance testing: Psychological Methods Vol 2(2) Jun 1997, 161-172.
- Cowles, M., & Davis, C. (1982). On the origins of the .05 level of statistical significance: American Psychologist Vol 37(5) May 1982, 553-558.
- Cowles, M., & Davis, C. (1992). On the origins of the .05 level of statistical significance. Washington, DC: American Psychological Association.
- Cowles, M., & Davis, C. (2003). On the origins of the .05 level of statistical significance. Washington, DC: American Psychological Association.
- Cravens, D. W., LaForge, R. W., Pickett, G. M., & Young, C. E. (1993). Incorporating a quality improvement perspective into measures of salesperson performance: Journal of Personal Selling & Sales Management Vol 13(1) Win 1993, 1-14.
- Crawford, J. R., & Garthwaite, P. H. (2002). Investigation of the single case in neuropsychology: Confidence limits on the abnormality of test scores and test score differences: Neuropsychologia Vol 40(8) 2002, 1196-1208.
- Crawford, J. R., Garthwaite, P. H., Howell, D. C., & Venneri, A. (2003). Intra-individual measures of association in neuropsychology: Inferential methods for comparing a single case with a control or normative sample: Journal of the International Neuropsychological Society Vol 9(7) Nov 2003, 989-1000.
- Crawford, J. R., & Howell, D. C. (1998). Regression equations in clinical neuropsychology: An evaluation of statistical methods for comparing predicted and obtained scores: Journal of Clinical and Experimental Neuropsychology Vol 20(5) Oct 1998, 755-762.
- Cui, H., & Chen, S. X. (2003). Empirical likelihood confidence region for parameter in the errors-in-variables models: Journal of Multivariate Analysis Vol 84(1) Jan 2003, 101-115.
- Cumming, G. (2007). Inference by eye: Pictures of confidence intervals and thinking about levels of confidence: Teaching Statistics Vol 29(3) Aug 2007, 89-93.
- Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions: Educational and Psychological Measurement Vol 61(4) Aug 2001, 532-574.
- Cumming, G., & Finch, S. (2005). Inference by Eye: Confidence Intervals and How to Read Pictures of Data: American Psychologist Vol 60(2) Feb-Mar 2005, 170-180.
- Cumming, G., Williams, J., & Fidler, F. (2004). Replication and Researchers' Understanding of Confidence Intervals and Standard Error Bars: Understanding Statistics Vol 3(4) 2004, 299-311.
- Curran, P. J., Bollen, K. A., Chen, F., Paxton, P., & Kirby, J. B. (2003). Finite Sampling Properties of the Point Estimates and Confidence Intervals of the RMSEA: Sociological Methods & Research Vol 32(2) Nov 2003, 208-252.
- Curtis, D. A., & Marascuilo, L. A. (1992). Point estimates and confidence intervals for the parameters of the two-sample and matched-pair combined tests for ranks and normal scores: Journal of Experimental Education Vol 60(3) Spr 1992, 243-269.
- Davison, T. C., & Jagacinski, R. J. (1977). Nonparametric analysis of signal detection confidence ratings: Behavior Research Methods & Instrumentation Vol 9(6) Dec 1977, 545-546.
- de Almeida, N. O. (1983). Two "new" classics: Confidence testing and probit item analysis: Arquivos Brasileiros de Psicologia Vol 35(1) Jan-Mar 1983, 93-99.
- de Soete, G. (1982). A note on the use of critical levels and p-values for informative inference: Psychologische Beitrage Vol 24(2) 1982, 296-301.
- de Soete, G., & Vandierendonck, A. (1982). On the use of the jackknife and the bootstrap for estimating a confidence interval for the product-moment correlation coefficient: Psychologica Belgica Vol 22(2) 1982, 87-97.
- Drummond, C., Matwin, S., & Gaffield, C. (2006). Inferring and revising theories with confidence: Analyzing bilingualism in the 1901 Canadian census: Applied Artificial Intelligence Vol 20(1) Jan 2006, 1-33.
- Duhachek, A., & lacobucci, D. (2004). Alpha's Standard Error (ASE): An Accurate and Precise Confidence Interval Estimate: Journal of Applied Psychology Vol 89(5) Oct 2004, 792-808.
- Dumbgen, L. (1998). Perturbation Inequalities and Confidence Sets for Functions of a Scatter Matrix: Journal of Multivariate Analysis Vol 65(1) Apr 1998, 19-35.
- Dunlap, W. P. (1981). An interactive FORTRAN IV program for calculating power, sample size, or detectable differences in means: Behavior Research Methods & Instrumentation Vol 13(6) Dec 1981, 757-759.
- Dunlap, W. P., & Silver, N. C. (1986). Confidence intervals and standard errors for ratios of normal variables: Behavior Research Methods, Instruments & Computers Vol 18(5) Oct 1986, 469-471.
- Dzieciolowski, K. (1993). Methods of inference and analysis of influence in multiresponse nonlinear regression: Dissertation Abstracts International.
- Eberhard-Gran, M., Eskild, A., Tambs, K., Opjordsmoen, S., & Samuelsen, S. O. (2001). Review of validation studies of the Edinburgh Postnatal Depression Scale: Acta Psychiatrica Scandinavica Vol 104(4) Oct 2001, 243-249.
- Echternacht, G. J. (1972). The use of confidence testing in objective tests: Review of Educational Research Vol 42(2) Spr 1972, 217-236.
- Echternacht, G. J., Boldt, R. F., & Sellman, W. S. (1972). Personality influences on confidence test scores: Journal of Educational Measurement Vol 9(3) Fal 1972, 235-241.
- Efron, B. (1988). Bootstrap confidence intervals: Good or bad? : Psychological Bulletin Vol 104(2) Sep 1988, 293-296.
- Estes, W. K. (1997). On the communication of information by displays of standard errors and confidence intervals: Psychonomic Bulletin & Review Vol 4(3) Sep 1997, 330-341.
- Fan, X., & Thompson, B. (2001). Confidence intervals about score reliability coefficients, please: An EPM guidelines editorial: Educational and Psychological Measurement Vol 61(4) Aug 2001, 517-531.
- Faulkner, L. (2003). Beyond the five-user assumption: Benefits of increased sample sizes in usability testing: Behavior Research Methods, Instruments & Computers Vol 35(3) Aug 2003, 379-383.
- Feldt, L. S. (1996). Confidence intervals for the proportion of mastery in criterion-referenced measurement: Journal of Educational Measurement Vol 33(1) Spr 1996, 106-114.
- Ferron, J. (2002). Reconsidering the use of the general linear model with single-case data: Behavior Research Methods, Instruments & Computers Vol 34(3) Aug 2002, 324-331.
- Fidler, F., Faulkner, C., & Cumming, G. (2008). Analyzing and presenting outcomes. New York, NY: Oxford University Press.
- Fidler, F., Thomason, N., Cumming, G., Finch, S., & Leeman, J. (2004). Editors Can Lead Researchers to Confidence Intervals, but Can't Make Them Think: Statistical Reform Lessons From Medicine: Psychological Science Vol 15(2) Mar 2004, 119-126.
- Fidler, F., Thomason, N., Cumming, G., Finch, S., & Leeman, J. (2005). Commentary: Still Much to Learn About Confidence Intervals: Reply to Rouder and Morey (2005): Psychological Science Vol 16(6) Jun 2005, 494-495.
- Fidler, F., & Thompson, B. (2001). Computing correct confidence intervals for ANOVA fixed-and random-effects effect sizes: Educational and Psychological Measurement Vol 61(4) Aug 2001, 575-604.
- Fleischman, A. I. (1980). Confidence intervals for correlation ratios: Educational and Psychological Measurement Vol 40(3) Fal 1980, 659-670.
- Foster, E. K. (2003). METASTATS: Behavioral science statistics for Microsoft Windows and the HP49G programmable calculator: Behavior Research Methods, Instruments & Computers Vol 35(2) May 2003, 325-328.
- Fowler, R. L. (1985). Point estimates and confidence intervals in measures of association: Psychological Bulletin Vol 98(1) Jul 1985, 160-165.
- Fowler, R. L. (1988). Estimating the standardized mean difference in intervention studies: Journal of Educational Statistics Vol 13(4) Win 1988, 337-350.
- Franses, P. H., & Vroomen, B. (2006). Estimating confidence bounds for advertising effect duration intervals: Journal of Advertising Vol 35(2) Sum 2006, 33-37.
- Frick, R. W. (1995). A problem with confidence intervals: American Psychologist Vol 50(12) Dec 1995, 1102-1103.
- Friedland, D. L. (1976). The relationship of scoring procedures based on a confidence testing rationale applied to an objective achievement examination for police officers, to each of eight criteria of job performance, and to measures of selected personality constructs: Dissertation Abstracts International.
- Fuentealba, R. G. (2006). The standard error of measurement and the true score of psychological tests: Some practical recommendations: Terapia Psicologica Vol 24(2) 2006, 117-130.
- Futatsuya, M., & Takahashi, K. (1978). Comparative Monte-Carlo studies on confidence intervals of the mean and standard deviation of a normal distribution from censored samples: Proceedings of the Institute of Statistical Mathematics Vol 25(1) 1978, 11-22.
- Gajewski, B., Hall, M., & Dunton, N. (2007). Summarizing Benchmarks in the National Database of Nursing Quality Indicators Using Bootstrap Confidence Intervals: Research in Nursing & Health Vol 30(1) Feb 2007, 112-119.
- Garcia-Perez, M. A. (2000). Exact finite-sample significance and confidence regions for goodness-of-fit statistics in one-way multinomials: British Journal of Mathematical and Statistical Psychology Vol 53(2) Nov 2000, 193-207.
- Gillett, R. (1989). Confidence interval construction by Stein's method: A practical and economical approach to sample size determination: Journal of Marketing Research Vol 26(2) May 1989, 237-240.
- Gleser, L. J. (1972). On bounds for the average correlation between subtest scores in ipsatively scored tests: Educational and Psychological Measurement Vol 32(3) Fal 1972, 759-765.
- Glutting, J. J., McDermott, P. A., & Stanley, J. C. (1987). Resolving differences among methods of establishing confidence limits for test scores: Educational and Psychological Measurement Vol 47(3) Fal 1987, 607-614.
- Gocka, E. F. (1973). Tolerance intervals vs. confidence intervals: Educational and Psychological Measurement Vol 33(3) Fal 1973, 603-605.
- Gradstein, M. (1986). Maximal correlation between normal and dichotomous variables: Journal of Educational Statistics Vol 11(4) Win 1986, 259-261.
- Graf, R. G., & Alf, E. F., Jr. (1999). Correlations redux: Asymptotic confidence limits for partial and squared multiple correlations: Applied Psychological Measurement Vol 23(2) Jun 1999, 116-119.
- Grayson, D. A. (1998). The frequentist facade and the flight from evidential inference: British Journal of Psychology Vol 89(2) May 1998, 325-345.
- Gullickson, A., & Hopkins, K. (1976). Interval estimation of correlation coefficients corrected for restriction of range: Educational and Psychological Measurement Vol 36(1) Spr 1976, 9-25.
- Hakstian, A. R., Whalen, T. E., & Rank, A. D. (1980). Confidence intervals for maximized alpha coefficients: An evaluation of Joe and Woodward's procedures and an alternative method: Multivariate Behavioral Research Vol 15(1) Jan 1980, 99-108.
- Hand, J., Jannarone, R. J., Laughlin, J. E., & Hand, M. R. (1985). Developing an estimate of the lower bound of a confidence ratio for statistical decisions: Perceptual and Motor Skills Vol 61(2) Oct 1985, 599-602.
- Hand, J., & McCarter, R. E. (1975). Two sources of univariate confidence intervals: Psychological Reports Vol 37(1) Aug 1975, 167-169.
- Hanson, S. J. (1978). Confidence intervals for nonlinear regression: A BASIC program: Behavior Research Methods & Instrumentation Vol 10(3) Jun 1978, 437-441.
- Hedges, L. V., Cooper, H., & Bushman, B. J. (1992). Testing the null hypothesis in meta-analysis: A comparison of combined probability and confidence interval procedures: Psychological Bulletin Vol 111(1) Jan 1992, 188-194.
- Hedges, L. V., & Vevea, J. L. (1998). Fixed- and random-effects models in meta-analysis: Psychological Methods Vol 3(4) Dec 1998, 486-504.
- Henson, R. K. (2004). Expanding Reliability Generalization: Confidence Intervals and Charter's Combined Reliability Coefficient: Perceptual and Motor Skills Vol 99(3,Part1) Dec 2004, 818-820.
- Henson, R. K. (2006). Book Review: Beyond Significance Testing: Reforming Data Analysis Methods in Behavioral Research: Applied Psychological Measurement Vol 30(5) Sep 2006, 452-455.
- Hess, M. R., Hogarty, K. Y., Ferron, J. M., & Kromrey, J. D. (2007). Interval Estimates of Multivariate Effect Sizes: Coverage and Interval Width Estimates Under Variance Heterogeneity and Nonnormality: Educational and Psychological Measurement Vol 67(1) Feb 2007, 21-40.
- Hilliker, G., & Thyer, B. A. (1985). Confidence intervals for statistical inference in single-subject research: A BASIC program: Behavioral Engineering Vol 9(3) 1985, 88-93.
- Hintzman, D. L. (1972). Confidence ratings in recall: A reanalysis: Psychological Review Vol 79(6) Nov 1972, 531-535.
- Hole, A. R. (2007). A comparison of approaches to estimating confidence intervals for willingness to pay measures: Health Economics Vol 16(8) Aug 2007, 827-840.
- Hsu, L. M. (1980). A chi-squared/d.f. test for interaction in two-treatment repeated measurements designs: Educational and Psychological Measurement Vol 40(2) Sum 1980, 291-299.
- Hubert, L. J. (1972). A note on the restriction of range for Pearson product-moment correlation coefficients: Educational and Psychological Measurement Vol 32(3) Fal 1972, 767-770.
- Huwang, L. (1995). Interval Estimation in Structural Errors-in-Variables Model with Partial Replication: Journal of Multivariate Analysis Vol 55(2) Nov 1995, 230-245.
- Iacobucci, D., & Duhachek, A. (2003). Advancing alpha: Measuring reliability with confidence: Journal of Consumer Psychology Vol 13(4) 2003, 478-487.
- Jarjoura, D. (1985). Tolerance intervals for true scores: Journal of Educational Statistics Vol 10(1) Spr 1985, 1-17.
- Jiang, H. (2005). Confidence measures for speech recognition: A survey: Speech Communication Vol 45(4) Apr 2005, 455-470.
- Juslin, P., Olsson, H., & Bjorkman, M. (1997). Brunswikian and Thurstonian origins of bias in probability assessment: On the interpretation of stochastic components of judgment: Journal of Behavioral Decision Making Vol 10(3) Sep 1997, 189-209.
- Juslin, P., Wennerholm, P., & Olsson, H. (1999). Format dependence in subjective probability calibration: Journal of Experimental Psychology: Learning, Memory, and Cognition Vol 25(4) Jul 1999, 1038-1052.
- Kehle, T. J., Bray, M. A., Chafouleas, S. M., & Kawano, T. (2007). Lack of statistical significance: Psychology in the Schools Vol 44(5) May 2007, 417-422.
- Kelley, K. (2005). The Effects of Nonnormal Distributions on Confidence Intervals Around the Standardized Mean Difference: Bootstrap and Parametric Confidence Intervals: Educational and Psychological Measurement Vol 65(1) Feb 2005, 51-69.
- Kelley, K. (2007). Methods for the Behavioral, Educational, and Social Sciences: An R package: Behavior Research Methods Vol 39(4) Nov 2007, 979-984.
- Kempf, W. (1992). A pragmatic approach to statistical theories of psychological test scores: Zeitschrift fur Differentielle und Diagnostische Psychologie Vol 13(4) 1992, 269-275.
- Keselman, H. J., Othman, A. R., Wilcox, R. R., & Fradette, K. (2004). The New and Improved Two-Sample t Test: Psychological Science Vol 15(1) Jan 2004, 47-51.
- Kirk, R. E., & Natanegara, F. (2001). Three programs for computing Dunn-Sidak values: Psychological Reports Vol 88(3,Pt2) Jun 2001, 1067-1070.
- Klauer, K. C. (1991). Exact and best confidence intervals for the ability parameter of the Rasch model: Psychometrika Vol 56(3) Sep 1991, 535-547.
- Klayman, J., Soll, J. B., Juslin, P., & Winman, A. (2006). Subjective Confidence and the Sampling of Knowledge. New York, NY: Cambridge University Press.
- Kline, R. B. (2004). Changing Times. Washington, DC: American Psychological Association.
- Kraemer, H. C. (1983). Theory of estimation and testing of effect sizes: Use in meta-analysis: Journal of Educational Statistics Vol 8(2) Sum 1983, 93-101.
- Lambert, Z. V., Wildt, A. R., & Durand, R. M. (1991). Approximating confidence intervals for factor loadings: Multivariate Behavioral Research Vol 26(3) 1991, 421-434.
- Lecoutre, B., & Charron, C. (2000). Bayesian procedures for prediction analysis of implication hypotheses in 2x2 contingency tables: Journal of Educational and Behavioral Statistics Vol 25(2) Sum 2000, 185-201.
- Lee, J., & Fung, K. P. (1993). Confidence interval of the kappa coefficient by bootstrap resampling: Psychiatry Research Vol 49(1) Oct 1993, 97-98.
- Lienert, G. A. (1956). A statistical concept for precise and efficient interpretation of test-profiles: Zeitschrift fur Experimentelle und Angewandte Psychologie 4 1956, 319-333.
- Lin, M.-h., & Hsiung, C. A. (1992). Four bootstrap confidence intervals for the binomial-error model: Psychometrika Vol 57(4) Dec 1992, 499-520.
- Lindell, M. K., & St. Clair, J. B. (1980). Tukknife: A jackknife supplement to canned statistical packages: Educational and Psychological Measurement Vol 40(3) Fal 1980, 751-754.
- Long, J. D. (1999). A confidence interval for ordinal multiple regression weights: Psychological Methods Vol 4(3) Sep 1999, 315-330.
- Long, J. D., & Cliff, N. (1997). Confidence intervals for Kendall's tau: British Journal of Mathematical and Statistical Psychology Vol 50(1) May 1997, 31-41.
- Lui, K.-J., Cumberland, W. G., Mayer, J. A., & Eckhardt, L. (1999). Interval estimation for the intraclass correlation in Dirichlet-multinomial data: Psychometrika Vol 64(3) Sep 1999, 355-369.
- Lumsden, E. A. (1977). A simple and reliable method for assessing partial knowledge with objective tests: Journal of Instructional Psychology Vol 4(1) Win 1977, 7-21.
- Lunneborg, C. E. (1986). Confidence intervals for a quantile contrast: Application of the bootstrap: Journal of Applied Psychology Vol 71(3) Aug 1986, 451-456.
- Lunneborg, C. E. (2001). Random assignment of available cases: Bootstrap standard errors and confidence intervals: Psychological Methods Vol 6(4) Dec 2001, 402-412.
- Lutz, J. G. (1974). A computer program for Hotelling's T2 for single or related samples with optional post-hoc and contrasting univariate analyses: Educational and Psychological Measurement Vol 34(3) Fal 1974, 699-701.
- MacKinnon, D. P., Fritz, M. S., Williams, J., & Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODLIN: Behavior Research Methods Vol 39(3) Aug 2007, 384-389.
- MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding and suppression effect: Prevention Science Vol 1(4) Dec 2000, 173-181.
- MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods: Multivariate Behavioral Research Vol 39(1) Jan 2004, 99-128.
- Macmillan, N. A., Rotello, C. M., & Miller, J. O. (2004). The sampling distributions of Gaussian ROC statistics: Perception & Psychophysics Vol 66(3) Apr 2004, 406-421.
- Malmberg, K. J. (2002). On the form of ROCs constructed from confidence ratings: Journal of Experimental Psychology: Learning, Memory, and Cognition Vol 28(2) Mar 2002, 380-387.
- Maloney, L. T. (1990). Confidence intervals for the parameters of psychometric functions: Perception & Psychophysics Vol 47(2) Feb 1990, 127-134.
- Maravelakis, P. E., Perakis, M., Psarakis, S., & Panaretos, J. (2003). The Use of Indices in Surveys: Quality & Quantity: International Journal of Methodology Vol 37(1) Feb 2003, 1-19.
- Maris, E. (1998). On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation: Psychometrika Vol 63(1) Mar 1998, 65-71.
- Masson, M. E. J. (2004). Correction to Masson and Loftus (2003): Canadian Journal of Experimental Psychology/Revue canadienne de psychologie experimentale Vol 58(4) Dec 2004, 289.
- Masson, M. E. J., & Loftus, G. R. (2003). Using confidence intervals for graphically based data interpretation: Canadian Journal of Experimental Psychology/Revue canadienne de psychologie experimentale Vol 57(3) Sep 2003, 203-220.
- May, K. (2003). A note on the use of confidence intervals: Understanding Statistics Vol 2(2) Apr 2003, 133-135.
- McGowan, A. S. (2003). New and Practical Sections in the Journal of Counseling & Development: Information for the Prospective Author and the Readership: Journal of Counseling & Development Vol 81(4) Fal 2003, 387-388.
- McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients: Psychological Methods Vol 1(1) Mar 1996, 30-46.
- McGraw, K. O., & Wong, S. P. (1996). "Forming inferences about some intraclass correlations coefficients": Correction: Psychological Methods Vol 1(4) Dec 1996, 390.
- McKeague, I. W., & Zhao, Y. (2005). Comparing distribution functions via empirical likelihood: The International Journal of Biostatistics Vol 1(1) 2005, 1-18.
- McKenzie, D. P., Vida, S., Mackinnon, A. J., Onghena, P., & et al. (1997). Accurate confidence intervals for measures of test performance: Psychiatry Research Vol 69(2-3) Mar 1997, 207-209.
- Meighan, M. (1977). Estimating the reliability of observational data with nonparametric confidence intervals: Revista Mexicana de Analisis de la Conducta Vol 3(2) Dec 1977, 181-186.
- Mendoza, J. L., Hart, D. E., & Powell, A. (1991). A bootstrap confidence interval based on a correlation corrected for range restriction: Multivariate Behavioral Research Vol 26(2) Apr 1991, 255-269.
- Mendoza, J. L., Stafford, K. L., & Stauffer, J. M. (2000). Large-sample confidence intervals for validity and reliability coefficients: Psychological Methods Vol 5(3) Sep 2000, 356-369.
- Meyer-Bahlburg, H. F. (1972). On the significance of the biserial tau coefficient: Psychologische Beitrage Vol 14(2) 1972, 292-297.
- Millsap, R. E. (1988). Tolerance intervals: Alternatives to credibility intervals in validity generalization research: Applied Psychological Measurement Vol 12(1) Mar 1988, 27-32.
- Mix, R. (1986). Confidence intervals instead of tests of significance? : Psychologische Beitrage Vol 28(3-4) 1986, 397-399.
- Montori, V. M., Kleinbart, J., Newman, T. B., Keitz, S., Wyer, P. C., Moyer, V., et al. (2004). Tips for learners of evidence-based medicine: 2. Measures of precision (confidence intervals): Canadian Medical Association Journal Vol 171(6) Sep 2004, 611-615.
- Morris, S. B., & Lobsenz, R. E. (2000). Significance tests and confidence intervals for the adverse impact ratio: Personnel Psychology Vol 53(1) Spr 2000, 89-111.
- Mossman, D. (2000). The meaning of malingering data: Further applications of Bayes' theorem: Behavioral Sciences & the Law Vol 18(6) 2000, 761-779.
- Mukhopadhyay, N. (1999). Second-Order Properties of a Two-Stage Fixed-Size Confidence Region for the Mean Vector of a Multivariate Normal Distribution: Journal of Multivariate Analysis Vol 68(2) Feb 1999, 250-263.
- Munley, P. H. (1991). Confidence intervals for the MMPI-2: Journal of Personality Assessment Vol 57(1) Aug 1991, 52-60.
- Munoz Delgado, A. (1978). Reduction of confidence intervals: Revista de Psicologia General y Aplicada Vol 33(150) Jan-Feb 1978, 71-78.
- Nelson, M. W., Bloomfield, R., Hales, J. W., & Libby, R. (2001). The effect of information strength and weight on behavior in financial markets: Organizational Behavior and Human Decision Processes Vol 86(2) Nov 2001, 168-196.
- Nijsse, M. (1990). An evaluation of two techniques for constructing confidence intervals for the squared multiple correlation coefficient: Psychological Reports 67(3, Pt 2) Dec 1990, 1107-1116.
- No authorship, i. (2008). "Confidence intervals for gamma-family measures of ordinal association": Correction: Psychological Methods Vol 13(1) Mar 2008, 72-73.
- O' de Almeida, N. (1987). Confidence testing in evaluations of dissertations and performance: Arquivos Brasileiros de Psicologia Vol 39(3) Jul-Sep 1987, 85-95.
- Olsson, H., & Winman, A. (1996). Underconfidence in sensory discrimination: The interaction between experimental setting and response strategies: Perception & Psychophysics Vol 58(3) Apr 1996, 374-382.
- Olsson, N. (2000). A comparison of correlation, calibration, and diagnosticity as measures of the confidence-accuracy relationship in witness identification: Journal of Applied Psychology Vol 85(4) Aug 2000, 504-511.
- Onwuegbuzie, A. J., & Daniel, L. G. (2002). A framework for reporting and interpreting internal consistency reliability estimates: Measurement and Evaluation in Counseling and Development Vol 35(2) Jul 2002, 89-103.
- Onwuegbuzie, A. J., & Daniel, L. G. (2002). Uses and misuses of the correlation coefficient: Research in the Schools Vol 9(1) Spr 2002, 73-90.
- Onwuegbuzie, A. J., & Daniel, L. G. (2004). Reliability Generalization: The Importance of Considering Sample Specificity, Confidence Intervals, and Subgroup Differences: Research in the Schools Vol 11(1) Spr 2004, 60-71.
- Paap, K. R., Chun, E., & Vonnahme, P. (1999). Discrete threshold versus continuous strength models of perceptual recognition: Canadian Journal of Experimental Psychology/Revue canadienne de psychologie experimentale Vol 53(4) Dec 1999, 277-293.
- Palachek, A. D., & Schucany, W. R. (1984). On approximate confidence intervals for measures of concordance: Psychometrika Vol 49(1) Mar 1984, 133-141.
- Peladeau, N., & Lacouture, Y. (1993). SIMSTAT: Bootstrap computer simulation and statistical program for IBM personal computers: Behavior Research Methods, Instruments & Computers Vol 25(3) Aug 1993, 410-413.
- Penfield, R. D. (2003). A score method of constructing asymmetric confidence intervals for the mean of a rating scale item: Psychological Methods Vol 8(2) Jun 2003, 149-163.
- Penfield, R. D., & Miller, J. M. (2004). Improving Content Validation Studies Using an Asymmetric Confidence Interval for the Mean of Expert Ratings: Applied Measurement in Education Vol 17(4) Oct 2004, 359-370.
- Pituch, K. A., Stapleton, L. M., & Kang, J. Y. (2006). A Comparison of Single Sample and Bootstrap Methods to Assess Mediation in Cluster Randomized Trials: Multivariate Behavioral Research Vol 41(3) 2006, 367-400.
- Pituch, K. A., Whittaker, T. A., & Stapleton, L. M. (2005). A Comparison of Methods to Test for Mediation in Multisite Experiments: Multivariate Behavioral Research Vol 40(1) Jan 2005, 1-23.
- Raffin, M. J., & Thornton, A. R. (1980). Confidence levels for differences between speech-discrimination scores: Journal of Speech & Hearing Research Vol 23(1) Mar 1980, 5-18.
- Ramsay, J. O. (1978). Confidence regions for multidimensional scaling analysis: Psychometrika Vol 43(2) Jun 1978, 145-160.
- Rasmussen, J. L. (1987). Estimating correlation coefficients: Bootstrap and parametric approaches: Psychological Bulletin Vol 101(1) Jan 1987, 136-139.
- Rasmussen, J. L. (1988). "Bootstrap confidence intervals: Good or bad": Comments on Efron (1988) and Strube (1988) and further evaluation: Psychological Bulletin Vol 104(2) Sep 1988, 297-299.
- Raykov, T. (2001). Approximate confidence interval for difference in fit of structural equation models: Structural Equation Modeling Vol 8(3) 2001, 458-469.
- Raykov, T. (2002). Automated procedure for obtaining standard error and confidence interval for scale reliability: Understanding Statistics Vol 1(2) Apr 2002, 75-84.
- Raykov, T., & Penev, S. (1998). Nested structural equation models: Noncentrality and power of restriction test: Structural Equation Modeling Vol 5(3) 1998, 229-246.
- Raykov, T., & Penev, S. (2002). Interval estimation of latent correlations in structural equation models with a priori restricted parameters: Understanding Statistics Vol 1(3) Jul 2002, 139-155.
- Reeb, M. (1972). Nomographs for the significance of the difference between percentages: Educational and Psychological Measurement Vol 32(3) Fal 1972, 715-723.
- Reid, J. B. (1980). An investigation of factors underlying the utility of confidence testing procedures: Dissertation Abstracts International.
- Riopelle, A. J. (2000). Are effect sizes and confidence levels problems for or solutions to the null hypothesis test? : Journal of General Psychology Vol 127(2) Apr 2000, 198-216.
- Rippey, R. M., & Voytovich, A. E. (1985). Anomalous responses on confidence-scored tests: Evaluation & the Health Professions Vol 8(1) Mar 1985, 109-119.
- Rivest, L.-P., & Wells, M. T. (2001). A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring: Journal of Multivariate Analysis Vol 79(1) Oct 2001, 138-155.
- Rodger, R. S. (1973). Confidence intervals for multiple comparisons and the misuse of the Bonferroni inequality: British Journal of Mathematical and Statistical Psychology Vol 26(1) May 1973, 58-60.
- Rodriguez-Campos, M. C. (1999). On Confidence Intervals in Nonparametric Binary Regression via Edgeworth Expansions: Journal of Multivariate Analysis Vol 69(2) May 1999, 218-241.
- Rogers, W. T. (1976). Jackknifing disattenuated correlations: Psychometrika Vol 41(1) Mar 1976, 121-133.
- Rosen, G. A. (2004). A Review of Score Reliability: Contemporary Thinking on Reliability Issues: Journal of Educational and Behavioral Statistics Vol 29(2) Sum 2004, 257-259.
- Rouder, J. N., & Morey, R. D. (2005). Relational and Arelational Confidence Intervals: A Comment on Fidler, Thomason, Cumming, Finch, and Leeman (2004): Psychological Science Vol 16(1) Jan 2005, 77-79.
- Rueda, C., Salvador, B., & Fernandez, M. A. (1997). Simultaneous Estimation in a Restricted Linear Model: Journal of Multivariate Analysis Vol 61(1) Apr 1997, 61-66.
- Ryan, J. J. (1999). Two types of tables for use with the seven-subtest short forms of the WAIS-III: Journal of Psychoeducational Assessment Vol 17(2) Jun 1999, 145-151.
- Sancho, J.-L., Pierson, W. E., Ulug, B., Figueiras-Vidal, A. R., & Ahalt, S. C. (2000). Class separability estimation and incremental learning using boundary methods: Neurocomputing: An International Journal Vol 35 Nov 2000, 3-26.
- Sapp, M. (2004). Confidence Intervals Within Hypnosis Research: Sleep and Hypnosis Vol 6(4) 2004, 169-176.
- Schaeffer, M. S., & Levitt, E. E. (1956). Concerning Kendall's tau, a nonparametric correlation coefficient: Psychological Bulletin Vol 53(4) Jul 1956, 338-346.
- Schulte, A. C., & Borich, G. D. (1988). False confidence in intervals: Inaccuracies in reporting confidence intervals: Psychology in the Schools Vol 25(4) Oct 1988, 405-412.
- Seaman, M. A., & Serlin, R. C. (1998). Equivalence confidence intervals for two-group comparisons of means: Psychological Methods Vol 3(4) Dec 1998, 403-411.
- Seo, T., Kikuchi, J., & Koizumi, K. (2006). On simultaneous confidence intervals for all contrasts in the means of the intraclass correlation model with missing data: Journal of Multivariate Analysis Vol 97(9) Oct 2006, 1976-1983.
- Serlin, R. C. (1993). Confidence intervals and the scientific method: A case for Holm on the range: Journal of Experimental Education Vol 61(4) Sum 1993, 350-360.
- Shaffer, J. P. (2002). Multiplicity, directional (Type III) errors, and the Null Hypothesis: Psychological Methods Vol 7(3) Sep 2002, 356-369.
- Sievers, W. (1990). Bootstrap confidence intervals and bootstrap acceptance ranges of procedures for testing hypotheses: Zeitschrift fur Experimentelle und Angewandte Psychologie Vol 37(1) 1990, 85-123.
- Sievers, W. (1996). Standard and bootstrap confidence intervals for the correlation coefficient: British Journal of Mathematical and Statistical Psychology Vol 49(2) Nov 1996, 381-396.
- Silcocks, P. (1994). Estimating confidence limits on a standardised mortality ratio when the expected number is not error free: Journal of Epidemiology & Community Health Vol 48(3) Jun 1994, 313-317.
- Silcocks, P. (1995). "Estimating confidence limits on a standardised mortality ratio when the expected number is not error free": Corrigendum: Journal of Epidemiology & Community Health Vol 49(2) Apr 1995, 224.
- Silver, S. J., & Clampit, M. K. (1991). Corrected confidence intervals for quotients on the WISC--R, by level of quotient: Psychology in the Schools Vol 28(1) Jan 1991, 9-14.
- Silverstein, A. B. (1989). Confidence intervals for test scores and significance tests for test score differences: A comparison of methods: Journal of Clinical Psychology Vol 45(5, Mono Suppl) Sep 1989, 828-832.
- Smith, P. L. (1982). A confidence interval approach for variance component estimates in the context of generalizability theory: Educational and Psychological Measurement Vol 42(2) Sum 1982, 459-466.
- Smithson, M. (2001). Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals: Educational and Psychological Measurement Vol 61(4) Aug 2001, 605-632.
- Spiegel, D. K. (1986). Small sample confidence bounds on measures of agreement or confusion matrices: Multivariate Behavioral Research Vol 21(3) Jul 1986, 299-307.
- Sprock, J. (2003). Dimensional versus categorical classification of prototypic and nonprototypic cases of personality disorder: Journal of Clinical Psychology Vol 59(9) Sep 2003, 992-1014.
- Spruill, J. (1988). Two types of tables for use with the Stanford Binet Intelligence Scale: Fourth Edition: Journal of Psychoeducational Assessment Vol 6(1) Mar 1988, 78-86.
- Steiger, J. H. (2004). Beyond the F Test: Effect Size Confidence Intervals and Tests of Close Fit in the Analysis of Variance and Contrast Analysis: Psychological Methods Vol 9(2) Jun 2004, 164-182.
- Stelzl, I. (1972). The usefulness of the Rasch model: Psychologische Beitrage Vol 14(2) 1972, 298-310.
- Stevens, J. P. (1973). Step-down analysis and simultaneous confidence intervals in MANOVA: Multivariate Behavioral Research Vol 8(3) Jul 1973, 391-402.
- Strube, M. J. (1988). Bootstrap Type I error rates for the correlation coefficient: An examination of alternate procedures: Psychological Bulletin Vol 104(2) Sep 1988, 290-292.
- Su, Y.-H., Sheu, C.-F., & Wang, W.-C. (2007). Computing confidence intervals of item fit statistics in the family of Rasch models using the bootstrap method: Journal of Applied Measurement Vol 8(2) 2007, 190-203.
- Szatrowski, T. H. (1982). Testing and estimation in the block compound symmetry problem: Journal of Educational Statistics Vol 7(1) Spr 1982, 3-18.
- Takahashi, A. (1998). The relationship of the proportion correct in recognition and the confidence rating: Japanese Journal of Psychology Vol 69(1) Apr 1998, 9-14.
- Thissen, D., & Wainer, H. (1990). Confidence envelopes for item response theory: Journal of Educational Statistics Vol 15(2) Sum 1990, 113-128.
- Thomas, D. R., Zhu, P., & Decady, Y. J. (2007). Point estimates and confidence intervals for variable importance in multiple linear regression: Journal of Educational and Behavioral Statistics Vol 32(1) Mar 2007, 61-91.
- Thompson, B. (2006). Research Synthesis: Effect Sizes. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Thompson, B. (2007). Effect sizes, confidence intervals, and confidence intervals for effect sizes: Psychology in the Schools Vol 44(5) May 2007, 423-432.
- Thompson, B., Diamond, K. E., McWilliam, R., Snyder, P., & Snyder, S. W. (2005). Evaluating the Quality of Evidence From Correlational Research for Evidence-Based Practice: Exceptional Children Vol 71(2) Win 2005, 181-194.
- Thompson, W. B. (1999). Individual differences in memory-monitoring accuracy: Learning and Individual Differences Vol 11(4) 1999, 365-376.
- Thornton, A. R., & Raffin, M. J. (1978). Speech-discrimination scores modeled as a binomial variable: Journal of Speech & Hearing Research Vol 21(3) Sep 1978, 507-518.
- Tittmar, H. G. (1987). Concerning the probability of our confidence in statistics: Alcohol and Alcoholism Vol 22(2) 1987, 99-101.
- Torres, F., Hurtado, L. F., Garcia, F., Sanchis, E., & Segarra, E. (2005). Error handling in a stochastic dialog system through confidence measures: Speech Communication Vol 45(3) Mar 2005, 211-229.
- Tryon, W. W. (2001). Evaluating statistical difference, equivalence, and indeterminancy using inferential confidence intervals: An integrated alternative method of conducting null hypothesis statistical tests: Psychological Methods Vol 6(4) Dec 2001, 371-386.
- Turpin, A., & McKendrick, A. M. (2005). Observer-based rather than population-based confidence limits for determining probability of change in visual fields: Vision Research Vol 45(25-26) Nov 2005, 3277-3289.
- Udolf, R., & Raymond, B. (1973). Multivariate analysis of variance and confidence levels: American Psychologist Vol 28(12) Dec 1973, 1139-1140.
- Vacha-Haase, T., Henson, R. K., & Caruso, J. C. (2002). Reliability generalization: Moving toward improved understanding and use of score reliability: Educational and Psychological Measurement Vol 62(4) Aug 2002, 562-569.
- Viechtbauer, W. (2007). Approximate confidence intervals for standardized effect sizes in the two-independent and two-dependent samples design: Journal of Educational and Behavioral Statistics Vol 32(1) Mar 2007, 39-60.
- Visser, I., Raijmakers, M. E. J., & Molenaar, P. C. M. (2000). Confidence intervals for hidden Markov model parameters: British Journal of Mathematical and Statistical Psychology Vol 53(2) Nov 2000, 317-327.
- Walker, B., & Erdman, A. (1984). Childbirth education programs: The relationship between confidence and knowledge: Birth: Issues in Perinatal Care & Education Vol 11(2) Sum 1984, 103-108.
- Wang, M. C., & Silver, N. C. (1994). A MicrosoftReg. FORTRAN 77 program for determining the confidence interval around the estimate of the population correlation coefficicent for the vote-counting method: Educational and Psychological Measurement Vol 54(1) Spr 1994, 105-109.
- Weinberg, S. L., Carroll, J. D., & Cohen, H. S. (1984). Confidence regions for INDSCAL using the jackknife and bootstrap techniques: Psychometrika Vol 49(4) Dec 1984, 475-491.
- Wesner, M. F., Pokorny, J., Shevell, S. K., & Smith, V. C. (1991). Foveal cone detection statistics in color-normals and dichromats: Vision Research Vol 31(6) 1991, 1021-1037.
- Whitener, E. M. (1990). Confusion of confidence intervals and credibility intervals in meta-analysis: Journal of Applied Psychology Vol 75(3) Jun 1990, 315-321.
- Wilcox, R. R. (1987). Confidence intervals for true scores under an answer-until-correct scoring procedure: Journal of Educational Measurement Vol 24(3) Fal 1987, 263-269.
- Wilcox, R. R. (1994). Computing confidence intervals for the slope of the biweight midregression and Winsorized regression lines: British Journal of Mathematical and Statistical Psychology Vol 47(2) Nov 1994, 355-372.
- Wilcox, R. R. (1996). Confidence intervals for two robust regression lines with a heteroscedastic error term: British Journal of Mathematical and Statistical Psychology Vol 49(1) May 1996, 163-170.
- Wilcox, R. R. (1997). Comparing the slopes of two independent regression lines when there is complete heteroscedasticity: British Journal of Mathematical and Statistical Psychology Vol 50(2) Nov 1997, 309-317.
- Winman, A., Hansson, P., & Juslin, P. (2004). Subjective Probability Intervals: How to Reduce Overconfidence by Interval Evaluation: Journal of Experimental Psychology: Learning, Memory, and Cognition Vol 30(6) Nov 2004, 1167-1175.
- Winman, A., & Juslin, P. (2006). "I'm m/n Confident That I'm Correct": Confidence in Foresight and Hindsight as a Sampling Probability. New York, NY: Cambridge University Press.
- Wolf, B., & Brandt, W. (1982). Estimating the magnitude of effects in analyses of variance and regression analyses: Zeitschrift fur Empirische Padagogik Vol 6(2) 1982, 57-73.
- Wong, S. P., & McGraw, K. O. (1999). Confidence intervals and F tests for intraclass correlations based on three-way random effects models: Educational and Psychological Measurement Vol 59(2) Apr 1999, 270-288.
- Wood, M. (2005). Bootstrapped Confidence Intervals as an Approach to Statistical Inference: Organizational Research Methods Vol 8(4) Oct 2005, 454-470.
- Woods, C. M. (2007). Confidence intervals for gamma-family measures of ordinal association: Psychological Methods Vol 12(2) Jun 2007, 185-204.
- Wouters, L. (1979). An APL function for computing distribution-free confidence limits on the median of a population: Behavior Research Methods & Instrumentation Vol 11(3) Jun 1979, 401.
- Wright, D. B. (2007). Graphing within-subjects confidence intervals using SPSS and S-Plus: Behavior Research Methods Vol 39(1) Feb 2007, 82-85.
- Xu, L. (1999). Bootstrap for dual scaling of rankings. Dissertation Abstracts International: Section B: The Sciences and Engineering.
- Yonge, G. D. (1988). What form of reliability is most appropriate for establishing confidence intervals and for profile analyses? : Psychological Reports Vol 63(1) Aug 1988, 86.
- Yu, J., Krishnamoorthy, K., & Pannala, M. K. (2006). Two-sample inference for normal mean vectors based on monotone missing data: Journal of Multivariate Analysis Vol 97(10) Nov 2006, 2162-2176.
- Zhang, G. (2006). Confidence intervals for root mean square standardized effect size in one-way fixed effects ANOVA. Dissertation Abstracts International: Section B: The Sciences and Engineering.
- Zhang, G., & Browne, M. W. (2006). Bootstrap Fit Testing, Confidence Intervals, and Standard Error Estimation in the Factor Analysis of Polychoric Correlation Matrices: Behaviormetrika Vol 33(1) Jan 2006, 61-74.
- Zhao, Y., & Chen, F. (2008). Empirical likelihood inference for censored median regression model via nonparametric kernel estimation: Journal of Multivariate Analysis Vol 99(2) Feb 2008, 215-231.
- Zhou, Y., & Yip, P. S. F. (1999). A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data: Journal of Multivariate Analysis Vol 69(2) May 1999, 261-280.
- Zou, G. Y. (2007). Toward using confidence intervals to compare correlations: Psychological Methods Vol 12(4) Dec 2007, 399-413.
- The Exploratory Software for Confidence Intervals tutorial programs that run under Excel
- Confidence interval calculators for R-Squares, Regression Coefficients, and Regression Intercepts
- Eric W. Weisstein, Confidence Interval at MathWorld.
- Analytical argumentations of probability and statistics
- Free download of software for segmented linear regression and cumulative frequency analysis with confidence intervals
- CAUSEweb.org Many resources for teaching statistics including Confidence Intervals.
- An interactive introduction to Confidence Intervals
|This page uses Creative Commons Licensed content from Wikipedia (view authors).|