Statistics

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Dependent means/groups

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Association or link in the research design between the sets of scores. Usually occurs in one of three conditions - repeated measures, linked selection, or matching.

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Repeated Measures

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Repeated measures designs collect data on subjects using the same measure on at least two occasions. This often occurs before and after a treatment or when the same research subjects are exposed to two different experimental conditions.

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Linked Selection

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When selection is with the intent to analyze the data together (e.g. parent-child, partners)

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Subject matching

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When you want to control for something (e.g. socioeconomic differences in research subjects). You match on the variable and the scores on the dependent variables are then treated as a pair in the statistical test.

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Statistics for dependent means

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McNemar Test (two samples or times of measurement), Wilcoxon t Test (two samples), Dependent Means t Test (two samples), Friedman ANOVA for Ranks (three or more samples), Simple Repeated Measures ANOVA (three or more samples), and Mixed Factorial ANOVA (at least one factor is linked/correlated).

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Independent means/groups

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No subject overlap across group (can the person be in both groups? e.g. gender)

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Statistics for Independent Means

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chi-square test of independence (two or more groups), Mann-Whitney U Test (two groups), Independent Means t test (two groups), One-Way Between-Groups ANOVA (three or more groups), and Factorial ANOVA (two or more independent variables).

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Nominal Data

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McNemar – two sample/dependent
Chi-Squares – all others

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Nominal – one sample
Dependent variable

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Chi goodness of fit

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Nominal –one sample
DV & IV

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Chi test of independence

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Nominal – two samples
Independent Groups

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Chi test of independence

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Nominal – two samples
Dependent Groups

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McNemar

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Ordinal data- one sample
DV & IV

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Spearman’s r’s

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Ordinal Data – multiple samples
Independent Samples
Two samples

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Mann-Whitney U

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Ordinal Data – multiple samples
Independent Samples
3+ samples

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Kruskal Wallis H

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Ordinal Data – multiple samples
Dependent samples
Two samples

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Wilcoxon T

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Ordinal Data – multiple samples
Dependent samples
3+ samples

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Friedman Anova by Ranks

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Scale Data

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Includes approximate interval, interval and ratio
-group differences or associations between independent and dependent variables

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Scale data – one sample
Dependent variable
Known population sd

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Z test

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Scale data – one sample
Dependent variable
Known population mean

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One-sample t-test

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Scale data – one sample
(1) IV & DV

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Pearsons r
Bivariate regression

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Scale data – one sample
Mulitple IVs & DVs

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Multiple Regression

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Scale Data Multiple Samples
Independent Samples
Two Samples

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Independent t-test

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Scale Data Multiple Samples
Independent Samples
Three Samples

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One-way ANOVA
Factorial ANOVA

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Scale Data Multiple Samples
Dependent Samples
Two Samples

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Dependent t-test

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Scale Data Multiple Samples
Dependent Samples
Three Samples

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Repeated Measures ANOVA
Mixed Factorial ANOVA

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Parametric Assumptions
Kolmogorov-Smirnov Test

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used to determine how likely it is that a sample came from a population that is normally distributed.

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Parametric Assumptions
Levene test

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used to test the assumption of equal variances

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Parametric Assumptions

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A) Interval, ration, approximate interval scale
B) random sampling from a defined population
C) Characteristic is normally distributed in the population
D) Population variance is equal (if two or more groups/variables)

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Violated parametric test assumptions

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A) transform data
B) Use non-parametric statistic

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Parameter

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A value, usually numeric, characteristic of a population
Mu – mean
Sigma – standard deviation
Sigma square – variance

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Parametric tests assume:

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A) populations from which samples are drawn have specific characteristics
B) samples are drawn under certain conditions.

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Nonparametric tests assume:

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A) sampling (random)
B) independence or dependence of samples (varies by test) but make no assumptions about the population.

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one-sample tests

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Z test; t test; Pearson and Spearman correlations; chi-square goodness-of-fit

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Two- sample tests

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("samples" for any statistic that examines differences between groups t test for dependent means)
t test for independent means; one-way ANOVA; Friedman ANOVA; chi-square test of independence

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Type I Error

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Rejecting the null when it is true
Alpha
Usually with one-tailed test

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Type II Error

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Rejecting the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true.
Beta

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Power of test

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1 minus beta
Opposite of type 2 error
increased by increase sample size, alpha, effect magnitude, decreasing random error, use parametric and one-tailed tests.
1-B (inverse of Beta)

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Increasing Power

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A) Increasing alpha, decreases beta and increases power
B) sample size
C) effect size
D) directional –one tailed are more powerful

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Effect size

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The degree of distance between the null hypothesis and alternative hypothesis distributions. The larger the effect size, the easier it is to detect a true difference between the two population means. The effect size is the only factor that influences power that is not under the investigator's control. We estimate the effect size (anticipated difference between our null hypothesis and alternative hypothesis) from the literature.