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Analyzing Gender-Based Differences in Student GPAs in SPSS

In this statistical analysis, we use SPSS to answer the question of whether gender plays a role in shaping the academic performance of students. Our hypothesis (H1) postulated that there is a substantial difference in the mean GPAs between male and female students. Through rigorous examination of the data and the application of statistical tests, we aimed to shed light on this important question and to provide valuable insights into the educational landscape. Let's explore the evidence and findings that support this hypothesis.

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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 p-value corresponding to this test statistic.

Using the p-value based on the Mean, the p-value 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 t-test.

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   		    
t-test for Equality of Means   
   
F   		    
Sig.   		    
t   		    
df   		    
Sig. (2-tailed)   		    
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. (2-tailed) contains the p-value of the t-test 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 p-value < 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 t-test 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 t-test 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 t-test is its sensitivity to sample sizes, independent sample t-test is known to be less robust to violations of the equal variance and normality assumptions when sample sizes are unequal as in this sample.