Question

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Name: 2. a. Write all steps of a hypothesis test for two-way ANOV A to determine if there anre sagtheir gender and effects and an interaction effect difference in expected income at 30-years-old depending on their ge highest level of education expected. b. State the results in APA format. c. If the resul the post hoc results significant mairn Its are significant, interpret Between-Subjects Factors Value Label 215 Femate Highest level of education expected1 Less than College 141 Master's De Ph.D. MD, JD, etc 178 Descriptive Statistics Dependent Variable: Expected income at age 30 Highest level of education ex Less than College Degree Bachelor's Degree Masters Degree Ph D, MD, JD, etc Std. Deviation Male 37850 00 64342 86 57259.74 70520.85 60720.93 22485.726 117763 443 56446.622 50267.759 79258.866 16133.025 48 215 24 71 101 Total FemaleLess than College Degree 14268.720 22580.672 40482.326 26965.088 19582.645 84536,434 41283.876 45544.931 58265.758 35492.96 43287.13 63229.17 Bachelor's Degree Masters Degree Ph D., MD, JD, eto. Total Less than College Degree Bachelors Degree Master's Degree Ph. D., MD, JD, etc 43515.57 32904.55 141 178 96 49331.46 66875.01 51574.73 Total Tests of Between-Subjects Effects Expected income at age 30 Type IlI Sum of Dependent Variable: Mean Square Sig df 7 11311906670.9 923457 265.922 118973645587 5845.799 3.831 844 001 Model 79183346696.945 870101640601.605 18973645587.584 37605071294.410 8288387993.001 1475680176995,556 1 870101640601.605 ntercept 016 3 12535023764.803 2762795997.667 3272018130.811 010 ender edexpect 451 Name: Total 459 2775781840001,000 Corrected Total 458 1554863523692.501 Multiple Comparisons Dependent Variable: Expected income at age 30 LSD (1) Highest level of education 95% Confidence Interval (J) Highest level of education expected Mean Difference (U-JStd. Error Si. Lower Bound Upper Bound 2501.06 Less than College Degree Bachelors Degree -16911.06 9877.745 088 -36323.18 2499.27 54436.09 13504.84 36323.18 13157.7 2184.58 35353.10 16426.92 9630.481 089 33970.46 10413.816 001 16911.06 9877.745 .088 Ph.D.. MD, JD, etc Bachelor's Degree 2501.06 rec 484.14 : 6448 870 940 1-1 012189.42 Ph.D., MD, JD, etc -17059.41 7568.971 025 31934.24 Master's Degree rec 16426.92 9630.481 089 35353.10 Bachelor's Degree Ph.D.. MD. JD. etc. Less than College Degree Bachelor's Degree Master's Degree -484.14 | 644 8870丨 .940-13157.71 6-31778.39 13504.84 12189.42 3308.71 54436.09 31934.24 31778.39 7543.55 7243.317 016 33970.46. | 10413.816 .001 17059.41' 7568.971 025 17543.55 7243.317 016 .D,, MD, JD, etc. 2184.58 3308.71 he mean difference is significant at the.05 level. Answers:

Answer 1

(a)
The hypotheses are -
H0G: There is no main effect of Gender on expected income.
H1G: There is main effect of Gender on expected income.

H0L: There is no main effect of level of education on expected income.
H1L: There is main effect of level of education on expected income.

H0GL: There is no interaction between Gender and level of education on expected income.
H1GL: There is interaction between Gender and level of education on expected income.

From the anova output,
P-value for Gender is less than 0.05 significance level, we reject H0G.

P-value for Level of education is less than 0.05 significance level, we reject H0L.

P-value for Interaction (Gender * Edexpect) is greater than 0.05 significance level, we fail to reject H0GL.

(b)

A two-way between subjects ANOVA was conducted to compare the effect of gender on expected income in male and female conditions.

There was a significant effect of gender on expected income at the p <.05 level for the two conditions [F(1, 451) = 5.799, p = 0.016].

A two-way between subjects ANOVA was conducted to compare the effect of level of education on expected income in less than college degree, Bachelor degree, Master degree and Phd, MD, JD conditions.

There was a significant effect of level of education on expected income at the p <.05 level for the four conditions [F(3, 451) = 3.831, p = 0.010].

A two-way between subjects ANOVA was conducted to compare the interaction effect of gender and level of education on expected income in male and female conditions for gender and less than college degree, Bachelor degree, Master degree and Phd, MD, JD conditions for level of education.

There was no significant interaction effect of gender and level of education on expected income at the p <.05 level for the eight conditions [F(3, 451) = 0.844, p = 0.470].

(c)
From the post-hoc test, P-value (Sig.) is less than 0.05 for below combinatios.
- Less then College degree and Phd, MD, JD etc
- Bachelor degree and Phd, MD, JD etc
- Master degree and Phd, MD, JD etc

Based on these results, there is significant difference between expected income of Phd, MD, JD etc and Less then College degree, Bachelor degree or Master Degree.
There is no significant difference between expected income of Less then College degree, Bachelor degree and Master degree