Analyzing with ANOVA

PSY/210

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):

**What is/are the independent variable(s)? What is/are the dependent variable(s)?**

Independent variable is gender and the dependent variable is marital status.

**What would be an appropriate null hypothesis? Alternate hypothesis?**

: There is no significant difference in happiness score based on gender and marital status.

: There is significance difference in happiness score based on gender and marital status.

**What are the d****egrees of freedom for 1) gender**** 2) marital ****status**** 3) interaction be****tween gender and marital status**** and 4) error or within variance?**

Done below

Calculate the mean square for 1) gender 2) marital status 3) interaction between gender and marital status and 4) error or within variance. ** **

Done below

Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.** **

Done below

Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.** **

Done below

**If alpha is set at .05, what conclusions can you make?**

F-value is 2.277 and F-critical is 3.093266.Since F-value is less than F-critical, therefore null hypothesis is accepted and I conclude that the data provides sufficient evidence at 0.05 that there is no significant difference in happiness score based on gender and marital status.

Source | Sum of Squares(SS) | (degrees of freedom [df]) | Mean SquareSS / df | Fobt. | Fcrit. |
---|---|---|---|---|---|

Gender | 68.15 | 2-1=1 | 68.15 | MS(G) / MS(W) =7.407 | 3.942303 |

Marital Status | 127.37 | 3-1=2 | 63.685 | MS(Ms) / MS(W) =6.922 | 3.093266 |

Gender * Marital Status (A x B) | 41.90 | 2×1=2 | 20.95 | MS(G*M) / MS(W) =2.277 | 3.093266 |

Error (Within) | 864.82 | (N-ab)=94 | 9.2002 | NA | NA |

Total | 1102.24 | 99 | NA | NA | NA |

References

Steinberg, W. J., & Price, M. *Statistics alive**!* Los Angeles: Sage Publications.

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