Unit 4: Interval & Ratio Tests

Outline

4.1       Hypothesis

 • The null hypothesis is the hypothesis that sample observations results purely from chance. • The alternative hypothesis is the hypothesis that sample observations are influenced from some non-random cause, and that there is significance in the population.

4.2       Need for Statistical Tests

 When data support the alternative hypothesis, statistical tests indicate whether it is likely that the data contain sampling error (accept the null hypothesis) or represent the population (reject the null hypothesis).(p < .05) indicates that the probability of error is less than 5%, or that the results are significant at the .05 level.

4.3       The T-Test

 The t-test is used to compare the means of two groups. If t is greater than the critical value, reject the null hypothesis and assume the difference between the group means is significant. Use the formula below to calculate t. Find the critical value from the t-table.

4.4       One-way Analysis of Variance (ANOVA)

 Use the ANOVA worksheet to calculate the f-statistic. Look up the critical value for f in the f-table (on the back of the worksheet). If f is equal to or greater than the critical value, then reject the null hypothesis.

4.5       Post-hoc Tests

 Post-hoc tests indicate which group means are statistically significantly different. Tukey’s HSD (honestly significant difference) Test: • Find q in the q-table. • Use the formula below for HSD.

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