ANOVA using SPSS
1) ANOVA:
ANOVA stands for analysis of variance. ANOVA is being used when we want to compare the two or more than two means i.e. μ1= μ2= μ3=…….= μn.
State the statistical assumptions of this test.
Assumptions for ANOVA:
1) Data should be normally distributed.
2) Samples (Groups) should be independent of each other.
3) The variance of the data in sample (Groups) should be same.
4) Error should follow normal distribution with mean zero and variance σ2 i.e. ξ ~ N(0, σ2).
Select any appropriate independent variable with three (3) or more levels and dependent.
2) The independent variable with three or more will be “BETTER FOR MAN TO WORK, WOMAN TEND HOME” because response to this question varies from person to person independently. The dependent variable will be “RESPONDENTS INCOME” because the income of a person depends on the work. Here we will see whether the response for “BETTER FOR MAN TO WORK, WOMAN TEND HOME” puts any significant impact on “RESPONDENTS INCOME”. If the outcome shows any significant impact then we will see who is more influential in employees’ job performance whether male or female. If the outcome doesn’t show any significant impact then the conclusion so drawn will be that “both male and the female are charismatic leaders (Both are influential in employees’ job performance)”.
Develop the null hypothesis and the alternative hypothesis for main effects.
3) Hypothesis:
Null Hypothesis:
H0: There is no significant difference in the population mean respondent income with respect different levels of BETTER FOR MAN TO WORK, WOMAN TEND HOME.
Vs
Alternative Hypothesis:
H1: There is no significant difference in the population mean respondent income with respect different levels of BETTER FOR MAN TO WORK, WOMAN TEND HOME.. It means at least two level have different mean population income.
Mathematically;
Null Hypothesis (Ho): µ1 = µ2 = µ3 = µ4
Alternative Hypothesis (Ha): µi ≠ µj (for some i ≠ j)
Where µi’s are given below:
µ1 = Population mean income with category as ‘STRONGLY AGREE”
µ2 = Population mean income with category as ‘AGREE”
µ3 = Population mean income with category as ‘DISAGREE”
µ4 = Population mean income with category as ‘STRONGLY DISAGREE”
Level of Significance = .05
Using SPSS, calculate an ANOVA. Include a post hoc test.
SPSS Output is given below:
ANOVA Analysis:
ANOVASS / df / MSS / F / p
Between Groups / 9.049 / 3 / 3.016 / .389 / 0.761
Within Groups / 2017.856 / 260 / 7.761
Total / 2026.905 / 263
Note - Post-Hoc analysis is not required because ANOVA table is not significant.
Report on the p value and the confidence interval. Interpret the confidence interval.
Since the p-value of the ANOVA table is bigger than the 5% level of significance so we will not be able to reject the null hypothesis. There is no post-hoc analysis since the ANOVA table is not significant and because of this there is no confidence interval.
Decide whether to reject or retain the null hypothesis based on main effects and/or post-hoc statistical tests.
There is no significant difference in the population mean respondent income with respect different levels of BETTER FOR MAN TO WORK, WOMAN TEND HOME as F(3,260) = 0.389, p=0.761.
It means the average income is same among all categories or responses for BETTER FOR MAN TO WORK, WOMAN TEND HOME.
Generate syntax and output files in SPSS. You will need to copy and paste these into your Application document.
Statistics Notations:
Name of Statistics / StatisticsSum of Squares / SS
Mean Sum of Square / MSS
Mean Difference / MD
Lower (95% Confidence Interval of the Difference) / L
Upper (95% Confidence Interval of the Difference) / U
Degrees of freedom / df
F-statistic value / F
Standard Error / SE
p-value (2-tailed) / P