Analytic Statistics
Present appropriate analytic statistics for strength and significance.
For two interacting variables, analytic statistics can show:
Strength: Strength is how strongly the variables interact. The statistic used depends on data type:
a) For both variables interval: Use Pearson's correlation coefficient (r). Squaring this coefficient is interpreted as the percentage of variance shared or explained, e. g. if r = 0.5 in an experiment then only 25% of the variance is explained.
b) For independent variable categorical, dependant variable interval: Use the Eta statistic calculated in Analysis of Variance. Eta squared gives the proportion of variance explained or shared.
c) For both ordinal: Use Gamma
d) For both categorical: Use Phi or Lambda.
Significance: Is how likely the interaction occurred by chance, and is measured as a probability (p), e. g. p < .05 means there is less than a 5% probability the results are just random chance. The significance statistic to use depends on data type:
a) For both variables interval or ordinal: Use a t-test
b) For independent variable categorical, dependant variable interval: Use a t-test for two variables, for more than two variables use an Analysis of Variance (ANOVA) F-test
c) For both categorical: Use Chi-squared.
Strength and significance are different:
A correlation over millions of subjects may be very significant but very weak, e. g. a correlation of r = 0.30 (strength) with only 9% common variance may be highly significant at p < 0.01 (only 1 of 100 such cases are by chance).
- A correlation for a few subjects may be insignificant but very strong, e. g. r = 0.86 but p = 0.06 (ns)
Tags: Valid, Quantitative, Results
Example(s)
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