# Assignment: Psychological Statistics/Analyzing With ANOVA

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# Assignment: Psychological Statistics/Analyzing With ANOVA

Assignment: Psychological Statistics/Analyzing With ANOVA

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Analyzing with ANOVA

Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):

1. What are the independent variables and their levels? What is the dependent variable?
2. State all null hypotheses associated with independent variables and their interaction? Also suggest alternate hypotheses?
3. What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
4. Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
5. Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
6. Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
7. If alpha is set at .05, what conclusions can you make?
 Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit. Gender 68.15 ? ? ? ? Marital Status 127.37 ? ? ? ? Gender * Marital Status (A x B) 41.90 ? ? ? ? Error (Within) 864.82 ? ? NA NA Total 1102.24 99 NA NA NA

Please Note: The table that you see in the assignment has been slightly modified from the one presented in the module notes since it is beyond the scope of this unit to have students calculate p values. Instead you are asked to calculate the F value and compare it to the critical F value to determine whether the test is significant or not.

### What is Analysis of Variance (ANOVA)?

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.

The t- and  developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method. ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher’s book, “Statistical Methods for Research Workers.” It was employed in experimental psychology and later expanded to subjects that were more complex.

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