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Statistical Examination of Gender Disparities in Academic Performance

August 28, 2023
Charles Pearce
Charles Pearce
🇬🇧 United Kingdom
Statistical Analysis
Charles Pearce is a seasoned Statistics Analysis Assignment expert who holds a Master's degree in Statistics from the University of Bath. With over 8 years of experience in the field, John has honed his expertise in various statistical methodologies.
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Key Topics
  • Problem Statement:
  • Solution:
    • Demographic Statistics
    • Statistical Measures Used for this Study
  • Statistical Findings
    • INTERPRETATION OF FINDINGS
    • STATISTICS

In the 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 labelsCount of gender identityCount of gender identity
15855.24%
23735.24%
332.86%
443.81%
532.86%
Grand Total105100.00%
Row labelsCount of ethnicityCount of ethnicity2
154.76%
22019.05%
32422.86%
44542.86%
51110.48%
Grand Total105100.00%
Row labelsCount of yearCount of year2
132.86%
21918.10%
36460.9S%
41918.10%
Grand Total105100.00%

Descriptive Statistics

FemaleMale
Mean62.93Mean60.03
Standard Error0.97Standard Error1.34
Median63Median61
Mode68Mode60
Standard Deviation7.3553Standard Deviation8.1666
Sample Variance54.1004Sample Variance66.6937
Kurtosis-0.3222Kurtosis-0.1345
Skewness-0.3935Skewness-0.2243
Range33Range35
Minimum42Minimum40
Maximum75Maximum75
Sum3650Sum2221
Count58Count

37

Homogeneity of Variances (Testing for Equality of Variances)

FemaleMale

Mean 62.93 60.03

Variance54.1066.69
Observations5837
df5736
F0.8112
P{F<=f) one-tail0.2361
F Critica lone-tail0.6160

Independent Samples T-test

t-Test: Two-Sample Assuming Equal Variances

FemaleMale
Mean62.9360.03
Variance54.1066.69
Observations5837
Pooled Variance58.98
Hypothesized Mean Difference0
df93
t Stat1.7973
P{T<=t) one-tail0.0378
t Critica lone-tail1.6614
P{T<=t) two-tail0.0755
t Critica ltwo-tail1.9858

Calculation of Cohen’s d for Effect Size

calculation of cohens d for effect size

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