Parametric Tests

PARAMETRIC TESTS Parametric tests are statistical tests based on assumptions that the sample is representative of the population and that the scores are normally distributed.

Which parametric test should I use? • Make sure parametric tests are appropriate • Know what you want to test. • Determine how many groups or samples are being tested.

Comparing Means If you are: •

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Comparing a single sample mean with that of a hypothetical sample or population Comparing means from the same subjects measured twice Comparing means from two independent groups (if the variances are not significantly different) (if the variances are significantly different) Comparing means from more than two independent groups or samples Comparing means from the same group measured twice (within-subjects design)

Consider using:

single sample t-test

paired t-test

Pooled t-test Separate formula ttest One-way ANOVA Repeated measures ANOVA Repeated measures ANOVA

Testing for Relationships If you are examining the kind and degree of relationship between variables – consider using Pearson’s Coefficient of Correlation

Predicting Values If you wish to predict the value of one variable from the value of another: - Consider using Regression Analysis

Assumptions Underlying t-test The three assumptions underlying the t-test concern the type of data used in the test and the characteristics of the distribution of the variables. • T-test requires at least interval level data for the dependent measure. The independent variable is categorical and contains two levels, that is, you have two mutually exclusive groups of subjects. • The distribution of the dependent variable is normal. • The variances of the dependent variable for the

Paired t-test •

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Compares the means of two related samples Assumptions: Data are randomly sampled Data are repeated measures from the same subjects or data from matched subjects (a significant positive correlation is expected) Data are from a population which is normally distributed.

Comment: Where used appropriately a paired t-test is more powerful than the t-test because variability is reduced.

One-way ANOVA Compares the means of more than two unrelated (independent) samples Assumptions: 4. 5. 6.

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Data are randomly sampled Data are independent Data are from a population that is normally distributed. The standard deviations of the two samples or populations are equal.

Comments: ANOVA on its own does not tell which groups were different, however carrying out repeated tests on pairs of groups increases type I error. Post-hoc (unplanned) multiple comparison tests are designed to reduce type I error to a given

Repeated Measures ANOVA Compares the means of more than related samples. Assumptions: 4. Data are randomly sampled 5. Data are repeated measures on the same subjects, or measures on matched subjects 6. Data are from a population that is normally distributed 7. The standard deviations of the two samples or populations are equal. 8. The data were obtained independently in each group. Comments: • Same as one-way ANOVA • A RM design increases the power of the statistical analysis by

Linear Regression Describes the “best fit” line through the data points. The line is calculated to make the sum of the squares of the deviation of the data points from the line a minimum value. Assumption: That the relationship between the two variables is linear.

Pearson’s Product Moment Correlation Coefficient Quantifies the linear relationship between two variables. Assumption: Data are measured on a ratio or interval scale. Comments: • The value of Pearson’s r is from o to 1 (perfect correlation) • A positive correlation means that both variables increase together, whereas a negative correlation means that as one variable increases the other decreases. • A statistically significant correlation does not prove