Significance Testing (Statistical Associates Blue Book Series 18)

Significance Testing: Parametric and Nonparametric

A statistical significance coefficient is the chance that a relationship as strong or stronger than the one observed was due to the chance of random sampling. Thus if a correlation coefficient is significant at exactly the .05 level, this means there is 5% chance that a correlation as strong or stronger than the observed one would result from an unusual random sampling of data when in fact the correlation was zero. There are many, many specific significance tests. Common tests are listed below, but in addition each statistical procedure has associated significance tests which are discussed in the respective Statistical Associates "Blue Book" volumes dealing with each procedure.

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Below is the unformatted table of contents.

Table of Contents

Significance Testing15
Overview15
Types of significance tests15
Parametric tests15
Key Concepts and Terms16
When significance testing applies16
Significance and Type I Errors19
Confidence limits19
Power and Type II Errors20
One-tailed vs. two-tailed tests20
Assumptions of significance testing in general22
Random sampling22
Adequate sample size22
Significance is not importance22
À priori testing23
Appropriate alpha significance level23
Absence of intervening and common anteceding causes23
Frequently asked questions about significance testing in general23
How is significance related to effect size?24
Should I "fail to accept" or should I "reject" the null hypothesis?24
If cases in my sample are weighted, am I getting accurate significance values?24
Is significance the same for multistage random samples as for simple random samples?24
Binomial Test of Significance26
Overview26
Key Concepts and Terms26
Implementing the binomial test in SPSS27
Selections27
Normal approximation of the binomial test30
Assumptions of the binomial test31
Dichotomous distribution31
Data distribution31
Random sampling31
Student's t-Test of Difference of Means32
Overview of the t-test32
SPSS t-test types32
Key Concepts and Terms33
Formula33
Critical value33
Confidence limits34
One-sample t-test34
Example34
Interpretation35
Independent sample t-test35
Example36
Interpretation (with Levene's test)36
The independent samples assumption37
Paired sample t-test for non-independent samples37
Overview37
Example38
Interpretation38
Assumptions for t-tests39
Normal distribution39
Random sampling39
Similar variances39
Dependent/independent samples40
Effect size measures40
Frequently Asked Questions40
What are common alternatives to the t-test?40
What non-parametric test do I use instead of the t-test if my data cannot meet the assumption of normality?41
Normal Curve Tests of Means and Proportions42
Overview42
Key Concepts and Terms42
Deviation scores42
Standard deviation42
Variance43
Standard error43
Confidence limits43
Binomial distribution44
Normal distribution44
Normal curve means tests ("hypothesis tests")46
Confidence interval47
Manual computation of z values for normal curve tests49
Assumptions for normal curve tests50
Interval data51
Sample size should not be small51
Homogeneity of variances51
Random sampling51
Chi-Square Significance Tests52
Overview52
Pearson's chi-square52
Overview52
SPSS output53
Yates correction for continuity56
Crosstabulation control variables and chi-square57
Chi-square goodness-of-fit test58
Likelihood ratio chi-square61
Mantel-Haenszel (linear by linear) chi-square62
Assumptions for chi-square tests63
Random sampling63
Independence64
Known distribution64
Non-directional hypotheses64
Finite values64
Normal distribution of deviations64
Data level64
Frequently asked questions about chi-square65
and 165 more pages of topics on significance testing.