## Doing Oneway Repeated Measures ANOVAs

Qn1. Download the file websearch2.csv from the course materials. This file describes a study in which subjects were asked to find 100 distinct facts on the web using different search engines. The number of searches required and a subjective effort rating for each search engine were recorded. How many subjects took part in this experiment?

Qn2. To the nearest hundredth (two digits), what was the average number of searches required for the search engine that had the greatest average overall?

Qn3. Conduct an **order effect test** on Searches using a **paired-samples t-test assuming equal variances**. To the nearest ten-thousandths (four digits), what is the p-value from such a test? Hint: Use the reshapape2 library and the dcast function to create a wide-format table with columns for each level of Order.

Qn4. Conduct a paire-samples t-test, assuming equal variances, on searches by Engine.To the nearest hundredths (two digits), what is the absolute value of the t statistic for sich a test? Hint: use the reshape2 library and the dcast function to create a wide-format table with columns for each elvel of engine.

Qn5. Conduct a **nonparametric Wilcoxon signed-rank test** on the Effort Likert-type ratings. Calculate an exact p-value. To the nearest ten-thousandth (four digits), what is the p-value from such a test? Hint: Use the coin library and its wilcoxsign_test function with distribution = “exact”

Qn6. Download the file websearch3.csv from the course materials. This file describes a study just like the one from websearch2.csv, except that now the three search engines were used instead of two. Once again, the number of searches required and a subjective effort rating for each search engine were recorded. How many subjects took part in this new experiment?

Qn7. To the nearest hundredth (two digits), what was the average number of searches required for the search engine that had the greatest average overall?

Qn8. **Conduct a repeated measures ANOVA** to determine if there was an order effect on searches. First determine whether there is a **violation of sphericity**. To the nearest ten-thousandths (four digits), what is the value of Mauchly’s W criterion? Hint: use the ez library and its ezANOVA function passing within-Order, among other things, to test for order effects.

Qn9. Interpret the result of Mauchly’s test of sphericity, and then interpret the appropriate repeated measures ANOVA result. To the nearest ten-thousandth (four digits), what is thep-value from the appropriate F-test?

Qn10, Conduct a repeated measures ANOVA on searches by Engine. First determine whether there is a violation of sphericity. To the nearest ten-thousandth (four digits), what is the value of Mauchly’s W Criterion? Hint: use the ez library and its ez ANOVA function passing within-Engine, among other things, to test a significant main effect.

Qn11. Interpret the result of Mauchly’s test of sphericity, and then interpret the appropriate repeated measures ANOVA result. To the nearest ten-thousandth (four digits), what is the p-value from the appropriate F-test?

Qn12. Strictly speaking, given the result of the repeated measures ANOVA examining searches by Engine, are post hoc pairwise comparisons among levels of Engine Warranted?

```
-yes
-No
```

Qn13. Whatever your previous answer, proceed to do post hoc pairwise comparisons. Conduct manual pairwise comparisons of searches among levels of engine using paired-samples t-tests, assuming equal variances and using Holm’s sequential Bonferroni procedure to correct for multiple comparisons. To the nearest ten-thousandths (four digits), what is the smallest corrected p-value resulting from this set of tests? Hint: use the reshape2 library and dcast function to create wide-format table.

Qn14. **Conduct a nonparametric Friedman test** in the Effort Likert-type ratings. Calculate an asymptomatic p-value. To the nearest ten-thousandth (four digits), what is the c**hi-square statistic** from such a test? Hint: Use the coin library and the friedman_test function.

Qn15. Strictly speaking, given the result of the Friedman test examining Effort by Engine, are post hoc pairwise comparisons among levels of engine warranted?

-Yes

Qn16. Whenever your previous answer, proceed to do p**ost hoc pairwise comparisons**. Conduct manual **pairwise comparisons of Effort** among levels of Engine using Wilcoxon signed-rank tests, Using Holm’s sequential Bonferroni procedure to correct for multiple comparisons. To the nearest ten-thousandth (four digits), what is the smallest corrected p-value resulting from this set of tests? Hint: Use the reshape2 library and dcast function to create wide-format table. Then use the wilcox.test function with paired=TRUE (and to avoid warnings, exact = FALSE).

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