Directory to a variety of statistical procedures
| Statistical Procedure | Type of Data Analyzed | Null Hypothesis Tested |
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One-Sample Tests |
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| Chi-square test of Goodness of Fit. | Categorical (nominal-level). | Cases are distributed over categories according theory. |
| Student t test--One Sample. | Interval (continuous). | The sample is drawn from a population having a specific mean. |
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Two Independent-Samples Tests |
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| 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). |
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Two Dependent-Samples Tests |
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| 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. |
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Tests of Relationships (Correlations) |
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| 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). |
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Effect Size Calculators |
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