Problem Statement:
This statistical study involves the integration and analysis of two assessments to examine the relationship between selfidentified gender and final exam scores of a student population.
Solution:
Demographic Statistics
The archival database used for this study contained demographic variables describing the sample including identified gender, ethnicity, and year in school. The majority of the sample identified as female (n = 58, 55.24%) or male (n = 37, 35.24%) while a minority identified as transgender (n = 3, 2.86%), and nonbinary or nonconforming (n = 4, 3.81%). However, some respondents preferred not to disclose (n = 3, 2.86%). In terms of ethnicity, the majority of the sample identified as white (n = 45, 42.86%), while a minority identified as Black (n = 24, 22.86%), Asian (n = 20, 19.05%), Hispanic (n = 11, 10.48%), and Native (n = 5, 4.76%). Lastly, in terms of years, the majority of the sample identified as Junior year (n = 64, 60.95%), while a minority identified as Sophomore (n = 19, 18.10%), Senior (n = 19, 18.10%), and Freshman (n = 3, 2.86%).
Statistical Measures Used for this Study
This study selected students who identified as female or male to provide group comparisons of their final scores. The hypothesis of this study is ‘students who identify as female will have final scores than students who identify as male’. Ttests were utilized to examine the hypothesis.
Statistical Findings
The average final scores of students who identified as female (M = 62.93, SD = 0.97) were higher than those who identified as male (M = 60.03, SD = 1.34). To determine if this difference was significant, an independent sample ttest was performed. The findings of this analysis demonstrated that there was not a significant difference between the selfidentified genders (t (93) = 1.80; p = 0.076). Cohen’s d estimated the effect size between female and male student groups as 0.37, indicating that the selfidentified genders have a small effect on final scores.
INTERPRETATION OF FINDINGS
This study found that both female and male students achieved the same score on final exams. Hence, it can be inferred that female and male students can perform equally best and have shown the same competency in their final exams.
STATISTICS
Pivot Table
Row labels  Count of gender identity  Count of gender identity 
1  58  55.24% 
2  37  35.24% 
3  3  2.86% 
4  4  3.81% 
5  3  2.86% 
Grand Total  105  100.00% 
Row labels  Count of ethnicity  Count of ethnicity2 
1  5  4.76% 
2  20  19.05% 
3  24  22.86% 
4  45  42.86% 
5  11  10.48% 
Grand Total  105  100.00% 
Row labels  Count of year  Count of year2 
1  3  2.86% 
2  19  18.10% 
3  64  60.9S% 
4  19  18.10% 
Grand Total  105  100.00% 
Descriptive Statistics
Female  Male  
Mean  62.93  Mean  60.03 
Standard Error  0.97  Standard Error  1.34 
Median  63  Median  61 
Mode  68  Mode  60 
Standard Deviation  7.3553  Standard Deviation  8.1666 
Sample Variance  54.1004  Sample Variance  66.6937 
Kurtosis  0.3222  Kurtosis  0.1345 
Skewness  0.3935  Skewness  0.2243 
Range  33  Range  35 
Minimum  42  Minimum  40 
Maximum  75  Maximum  75 
Sum  3650  Sum  2221 
Count  58  Count 
37 
Homogeneity of Variances (Testing for Equality of Variances)

Female  Male 

Mean 62.93 60.03 

Variance  54.10  66.69 
Observations  58  37 
df  57  36 
F  0.8112  
P{F<=f) onetail  0.2361  
F Critica lonetail  0.6160  
Independent Samples Ttest
tTest: TwoSample Assuming Equal Variances

Female  Male 

Mean  62.93  60.03 
Variance  54.10  66.69 
Observations  58  37 
Pooled Variance  58.98  
Hypothesized Mean Difference  0  
df  93  
t Stat  1.7973  
P{T<=t) onetail  0.0378  
t Critica lonetail  1.6614  
P{T<=t) twotail  0.0755  
t Critica ltwotail  1.9858  
Calculation of Cohen’s d for Effect Size