Problem Description:
In this SPSS Analysis homework, we conducted a statistical analysis to determine whether there is a statistically significant difference between the mean GPAs of male and female students. The dataset includes various categorical and numerical variables, with "gender" being the primary focus. The homework involves several key steps, including data analysis planning, testing assumptions, obtaining results, and concluding.
Solution:
STEP 1: THE DATA ANALYSIS PLAN
Id: Categorical, nominal
Lastname: Categorical, nominal
Firstname: Categorical, nominal
Gender: Categorical, nominal
Ethnicity: Categorical, nominal
Year: Categorical, Ordinal
Lowup: Categorical, ordinal
Section: Categorical, nominal
Gpa: scale
Extcr: Categorical, nominal
Review: Categorical, nominal
quiz1: Scale
quiz2: Scale
quiz3: Scale
quiz4: Scale
quiz5: Scale
final: Scale
total: Scale
percent: Scale
grade: Categorical, nominal
passfail: Categorical, nominal
Null hypothesis (H0): There is no statistically significant difference between the mean GPA of the two gender
Alternate hypothesis (H0): There is a statistically significant difference between the mean GPA of the two gender
STEP 2: TESTING ASSUMPTION
Test of Homogeneity of Variances

Levene Statistic 
df1 
df2 
Sig. 


gpa 
Based on Mean 
.095 
1 
103 
.758 
Based on Median 
.090 
1 
103 
.764 

Based on Median and with adjusted df 
.090 
1 
99.430 
.764 

Based on trimmed mean 
.104 
1 
103 
.747 
Here, the F is the test statistic of Levene’s test while the sig. is the pvalue corresponding to this test statistic.
Using the pvalue based on the Mean, the pvalue of the levene’s test is .758 hence we conclude that the variance observed in GPA is not significantly different concerning gender. We therefore will be using the equal variance assumed row for the interpretation of our ttest.
STEP 3: RESULTS AND INTERPRETATION
Group Statistics

gender 
N 
Mean 
Std. Deviation 
Std. Error Mean 

gpa 
1 
64 
2.9719 
.67822 
.08478 
2 
41 
2.6910 
.73942 
.11548 
Independent Samples Test

Levene's Test for Equality of Variances 
ttest for Equality of Means 


F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

gpa 
Equal variances assumed 
.095 
.758 
1.999 
103 
.048 
.28090 
.14055 
.00215 
.55965 
Equal variances not assumed 


1.961 
79.985 
.053 
.28090 
.14326 
.00419 
.56599 
Gender 1 is female and gender 2 is male. The mean GPA for the female gender is 2.9719 with a standard deviation of .67822 while the mean GPA for the male gender is 2.6910 with a standard deviation of .73942.
The second table shows whether there is a statistically significant difference between these values. The equal variance assumed row will be used because Levene’s test for equality of variances is not statistically significant.
The column Sig. (2tailed) contains the pvalue of the ttest which is 0.048, being less than 0.05, we will report that the mean GPA of females is significantly higher than the mean GPA of males.
The pvalue < 0.05, therefore we reject the null hypothesis and accept the alternate hypothesis that: There is a statistically significant difference between the mean GPA of the two genders.
STEP 4: STATISTICAL CONCLUSION
I have stated a null hypothesis and its alternate for an independent sample ttest that entails comparing the mean GPA between males and females for statistically significant differences. A Levene test was conducted to see if the variance observed between the two groups was statistically significant or not and it was found that the difference in variance was not statistically significant hence equal variance can be assumed.
Finally, a ttest was conducted and it showed that there is a statistically significant difference between the average GPA of females and that of males. Females have a higher mean, 2.9719, compared to males’ 2.6910. This implies that females, on average are more likely to have higher GPAs than males.
Possible alternative explanations for the result include that maybe a small sample size means the population is not well represented. Another observation is that only gender is considered here. Maybe if some other variables such as ethnicity and year were factored in, a difference would be observed in the outcome of this analysis.
A known limitation of the independent sample ttest is its sensitivity to sample sizes, independent sample ttest is known to be less robust to violations of the equal variance and normality assumptions when sample sizes are unequal as in this sample.