This paper shows the results of the analysis of the data on the GPA of 105 students. The hypothesis that the gender of a student has an impact on his or her GPA is checked via the t-test.
Data File Description
Briefly describe the goal of your analysis.
This analysis aims to identify whether gender affects the GPA of students.
State at your research question, null, and alternate hypothesis.
Research question: can the gender of a student significantly influence his or her GPA? Null hypothesis: There is no significant difference in GPA between female and male students. Alternative hypothesis: The GPA of male and female students differs significantly.
Specify the variables used in this analysis (predictor, outcome) and the scale of measurement of each variable.
The outcome variable: GPA of a student. Continuous variable. The main predictor variable: gender of a student. Nominal variable.
State the sample size (N) and the alpha level you will use (.05 unless otherwise specified).
N = 105
Explain why the analysis is a good choice based on the nature of your variables
The gender variable is nominal, while the GPA of a student is measured in absolute values. It is possible to use the t-test to compare the average GPA values of the two specified groups of students.
Articulate and test the assumptions of the t-test.
Firstly, the dependent variable should be normally distributed. Secondly, the compared samples should be independent. Finally, the variances of the compared samples should be equal (Kim, 2015). To test the normality, one can use the Shapiro-Wilk test. To test whether the variances of the two groups are equal, one can use the Levene test. The results of both tests can be found below.
Paste the SPSS histogram output for each variable and discuss your visual interpretations.
There are more females than males in the sample.
The bars do not form the shape of a bell. The distribution of the GPA is probably not normal.
There are more students with white skin than students of any other race.
There are more junior students than students of any other year of study.
Most of the students in the sample belong to the upper division.
Students in the sample are almost uniformly distributed among the three sections.
The majority of students in the sample have not done an extra credit project.
The majority of students in the sample attended review sessions.
It seems that the majority of students in the sample had rather high grades for the quizzes.
The distribution of the grades for the final test is closer to normal than the distributions of the grades for quizzes.
This histogram is similar to the previous one, which might be due to the fact that the final test accounted for a very considerable part of the total points.
The majority of students in the sample accumulated between 75 and 85 percent of the possible points, which means that they got good grades.
Paste SPSS descriptive output showing skewness and kurtosis values and interpret them.
It can be seen that all variables in the table above have a negative skewness, which means that their distributions are skewed to the left. This means that the values in the right tail of the distribution are more frequent than those in the left tail. It can also be seen that only the kurtosis of the variable «quiz4» is close to zero.
Paste the SPSS descriptive output showing skewness and kurtosis values for gpa and interpret them.
The skewness of the GPA is close to 0, which means that the distribution is almost symmetric around the mean value. The negative kurtosis means that the tails of the distribution are lighter compared to that of the normal distribution.
Paste the SPSS output for the Shapiro-Wilk test of gpa and interpret it.
The p-value (.001) is smaller than the significance level. The null hypothesis that the distribution of GPA is normal should be rejected.
Report the results of the Levene test and interpret it.
The p-value (.566) is greater than the significance level. The null hypothesis that there is no significant difference in variance among the two groups should be accepted.
Analyze whether or not the assumptions of the t-test are met. If assumptions are not met, discuss how to ameliorate violations of the assumptions
Except for the normality, the assumptions of the t-test are met. In order to overcome the problem of non-normal distribution, one can, for instance, increase the size of the sample.
Research Question, Hypotheses, and Alpha Level
Paste the SPSS output of the t-test. Include the following:
- Degrees of freedom.
- p value.
- Effect size.
- Interpretation of effect size.
- Means and standard deviations for each group.
- Mean difference.
- 95% confidence interval of the difference of sample means.
Interpret statistical results against the null hypothesis and state whether it is accepted or rejected
The null hypothesis argues that the population mean GPA of females equals the population mean GPA of males. P-value (.048) is smaller than the significance level, and thus the null hypothesis should be rejected.
Report the test statistics. t = 2.004
Interpret statistical results against the null hypothesis.
The alternative hypothesis that the population mean GPA of females is greater than the population mean GPA of males should be accepted.
Provide a brief summary of your analysis and the conclusions drawn.
The null hypothesis argued that the population mean GPA of female students is the same as the population mean GPA of male students. The null hypothesis was rejected, and the alternative hypothesis that the population mean GPA of female students is greater than the population mean GPA of male students was accepted.
Analyze the limitations of the statistical test.
As it was already mentioned, the t-test assumes the normality of the dependent variable, while the distribution of the GPA is not normal.
Provide any possible alternate explanations for the findings and potential areas for future exploration.
The sample size is relatively small to state that, on average, females have a higher GPA than males. It is reasonable to conduct the same research using a bigger sample.
State your conclusions as well as two strengths and two limitations of the statistical test.
The t-test for the independent samples showed that the population mean GPA of female students is greater than that of male students. However, this does not imply that females are cleverer than males or more successful in studying.
The first strength of the t-test is the simplicity of the interpretation of the results. The second is the ease of the calculations. The main weakness of the t-test is the assumption of normality. Moreover, the t-test is not appropriate if the dependent variable is nominal or ordinal.
Kim, T. K. (2015). T test as a parametric statistic. Korean Journal of Anesthesiology, 68(6), 540–546.