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# Statistical Examination of Gender Disparities in Academic Performance

In Data Analysis assignment, we delve into a thought-provoking question: Does gender impact a student's academic performance? To answer this, we integrate data from two assessments. The first part of the study is a deep dive into demographic statistics, examining the sample's gender, ethnicity, and year in school. The second part employs statistical methods to test the hypothesis that "students who identify as female will have final scores different from students who identify as male.

## Problem Statement:

This statistical study involves the integration and analysis of two assessments to examine the relationship between self-identified 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 non-binary or non-conforming (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’. T-tests 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 t-test was performed. The findings of this analysis demonstrated that there was not a significant difference between the self-identified 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 self-identified 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) one-tail 0.2361
F Critica lone-tail 0.6160

Independent Samples T-test

t-Test: Two-Sample 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) one-tail 0.0378
t Critica lone-tail 1.6614
P{T<=t) two-tail 0.0755
t Critica ltwo-tail 1.9858

Calculation of Cohen’s d for Effect Size