Statistics Page

Statistical Procedure	Type of Data Analyzed	Null Hypothesis Tested
One-Sample Tests
Chi-square test of Goodness of Fit.	Categorical (nominal-level).	Cases are distributed over categories according theory.
Student t test--One Sample and Dependent Samples.	Interval (continuous).	The sample is drawn from a population having a specific mean.
Two Independent-Samples Tests
Wilcoxon Independent Samples Test	Ordinal (rank-ordered) data.	The two samples are drawn from the same population (the median values of the two samples are identical).
Chi-square Test of Equality of of Distributions (Independence)	Categorical (nominal-level)	This is typically use with cross-tablulated data (i.e. for frequency data than can be cast in two-fold or rows x columns table. The null hypotheses is that the row variable is independent of the column variable.
Mann-Whitney U Test	Ordinal (rank-ordered) data.	The two samples are drawn from the same population (the median values of the two samples are identical).
Student t Test for Independent Samples	Interval (continuous) data collected from two independent groups.	The two samples are drawn from a common population (they have the same mean).
Two Dependent-Samples Tests
Wilcoxon matched pairs signed ranks test	Ordinal or interval (ordered metric scale) {A very powerful test, especially for small samples}	The medium difference (d = x - y) between members of pairs is zero.
McNemar's Test for Matched Pairs	Categorical (nominal-level)	The number of "A followed by B" pairs is equal to the number of "B followed by A" pairs.
Friedman Two-way ANOVA by Ranks	Ordinal (rank-ordered) data, usually ratings of several judges.	The ratings of several judges are not related.
Sign Test	Two sets of ordinal (rank-ordered) data collected on the the same individuals or pairs.	The median scores under the two conditions are identical.
Student t test for dependent samples	Interval (continuous), for either a repeated measures or matched-pairs design.	The mean scores for the two (repeated or paired) observations are identical.

Tests of Relationships (Correlations)
Spearman correlation coefficient	Ordinal	No monotonic relationship between the variables.
Pearson correlation	Interval	No linear relationship between the variables
Comparing two correlation coefficients	Interval for raw data otherwise ordinal or interval	Two correlations are equal (in strength).

Power and Effect Size Calculators
g*Power Power analysis software from the Institut fur Experimentelle Psychologie, University of Dusseldorf.	Power Analysis. Java applets for power and sample size	Statistical Toolkit from DSS Research: A variety of statistical calculators, including power and sample size calculators.
	Web-based Sample Size and Power Calculators