Summary of Statistical Significance Testing

Analysis;
Purpose / Test Hypothesis (HA):
This is your research hypothesis / Null Hypothesis (HO):
This is the hypothesis you test statistically. / Relevant (Test) Statistic / Significance / Probability <= .05;
Interpretation / Significance / Probability > .05;
Interpretation
Note that we can only accept the test hypothesis by rejecting the null hypothesis.
Cross Tabulation:
Tests the RELATIONSHIPS between variables / Variable A is related to Variable B / Variable A is unrelated to Variable B / Chi-Squared
(X2) / Reject HO;
If the sample is a fair, randomly drawn sample, we would only have about 5 chances in 100 or fewer of getting this result.
The two variables are related. / Retain HO;
If the sample is a fair, randomly drawn sample, we would expect to get this finding most of the time. Any apparent relationship is solely attributable to chance.
The two variables are not related
Test of Independent Means / Group 01’s mean score is different from Group 02’s score (the samples are drawn from different populations) / Group 01’s mean score is NO different from Group 02’s score (the samples are drawn from the same population) / t
(critical value of t with 95% confidence = 1.96) / Reject HO;
If the sample is a fair, randomly drawn sample, we would only have about 5 chances in 100 or fewer of finding a difference between our sampleslarge enough to produce a value of t of this size or larger.
The two groups’ means score are different. / Retain HO;
If the sample is a fair, randomly drawn sample, we would conclude that any apparent differences in groups’ mean scores is attributable to chance.
The two groups’ means score areNO different.
Regression / Standardized beta coefficient (ranges from 0 to 1)
Analysis of Variance (3 or more groups) / Meangroup1 ≠ Meangroup2 ≠ Meangroup3 ≠
Meangroup4
etc. / Meangroup1 = Meangroup2 = Meangroup3 =
Meangroup4
etc. / F / Reject HO;
If the sample is a fair, randomly drawn sample, we would only have about 5 chances in 100 or fewer of finding differences among our sample means large enough to produce a value of F of this size or larger.
The groups’ means score are different. / Retain HO;
If the sample is a fair, randomly drawn sample, we would conclude that any apparent differences in groups’ mean scores is attributable to chance.
The groups’ means score areNO different.
Test of a Proportion or Mean / Sample proportion or mean = Population proportion or mean / Sample proportion or mean ≠ Population proportion or mean / Z
(critical value of Z with 95% confidence = 1.96) / Reject HO;
we would only have about 5 chances in 100 of obtaining a proportion or mean different enough from the Population proportion or mean to produce a value of z this size or larger.