The performance of the class is quantified by the GPA measurements. Although success is shown in the GPA, the issue is that it fails to show the various factors in the outcome of the GPA. The sex of students is among these factors. The paper explores the connection between examination performance and sex.
The dataset in this article is the.sav degree; it was used to evaluate students’ gender performance (George & Mallery, 2016). The data collection is the data of 105 students analyzed. It includes information on different variables, including population variables and output variables. The variable GPA measures the student performance and the explanatory variable Gender that defines the student’s gender. In the dataset, the Gender is the dichotomous ratio variable, and GPA represents the continuous ratio variable.
Section 2: Testing Assumption
A two-sample t-test shows whether there is a difference between the male and female student. These are the results and the discussion of the tests of the two-sample and t-test assumptions.
Histogram: Female Student GPA
Histogram: Male students’ GPA
gender Statistic Std. Error
gpa Female Mean 2.8866 .09423
95% Confidence Interval for Mean Lower Bound 2.6984
Upper Bound 3.0751
5% Trimmed Mean 2.9109
Std. Deviation .74785
Interquartile Range 1.25
Skewness -.131 .303
Kurtosis -.927 .597
Male Mean 2.5807 .11722
95% Confidence Interval for Mean Lower Bound 2.3440
Upper Bound 2.8175
5% Trimmed Mean 2.5848
Std. Deviation .75966
Interquartile Range .73
Skewness .182 .365
Kurtosis -.451 .718
Table 2 T
The Shapiro-Wilk Normality
Tests of Normality table
gender Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
gpa Female .103 63 .097 .949 63 .011
Male .109 42 .199* .954 43 .091
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
The histogram and the tables of the output above are the results of the assumption. The histogram shows that the bio-modal GPA of the females will affect the normality of the distribution while the figure 2 is the males students’ GPA. There is no indications of violation of normality by the look of the skewness value for table one. The Shapiro-Wilk p-value is less than 0.05 for females; violating the normality assumption while the p-values for males is greater than 0.05 showing a normal distribution.
Section 3: Research Question, Hypotheses, and Alpha level
Research Question: Does the GPA score vary with a student’s sex?
Statement of Hypothesis:
Null Hypothesis: There is no difference between the males’ and the females’ GPA score.
Alternative Hypothesis: The males’ and females’ GPA score are not the same.
The Alpha Level Test: The statements above =0.05
Section 4: Interpretation
The T-test Output
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
gpa Equal variances assumed .373 .545 2.041 103 .045 .30595 .14991 .00863 .60327
Equal variances not assumed 2.034 87.061 .046 .30595 .15039 .00703 .60486
The test statistic t (df=103) = 2.041, and P-value = 0.044.
The effect size for test is as shown in the formula.
Cohen^’ s d =(female mean GPA-Male mean GPA)/(pooled standard deviation)=(2.5808 – 2.8868) ⁄ 0.753769 = 0.40596.
The Cohen’s d shows that the difference between the males and females is not consistence and it is small. For the females’ GPA, the M is 2.8868, and SD is .74785 while for the males, M is 2.5807 and SD is .75965. The mean difference between the two groups is .30595 and the 95% confidence interval mean diff of 0.00864, 0.60328. The test statistics p-value < 0.05 refutes the null hypothesis that the male and females GPA scores are the same. Section 6: Conclusion In conclusion, the t-test shows inconsistency with the null hypothesis thus showing that there is indeed a significant difference between the male and the female GPA scores. One of the strengths of the t-test is the variance homogeneity in both the males and the females (Reid, 2013). Besides, the significant weakness is the fact that the female group seems to violate the normality assumption (Hinton, McMurray & Brownlow, 2014). Thus, the test shows that GPA scores is not affected by gender. References Hinton, P. R., McMurray, I., & Brownlow, C. (2014). SPSS explained. Routledge, 119-123. George, D., & Mallery, P. (2016). IBM SPSS statistics 23 step by step: A simple guide and reference. Routledge, 4. Reid, H. M. (2013). Introduction to statistics: Fundamental concepts and procedures of data analysis. Sage Publications, 278-281.