Data Analysis and Application (DAA) Assignment - Capella University

This assignment analyzes student GPA scores in relation to gender using a t-test within the Data Analysis and Application (DAA) template. The assignment begins with a description of the dataset, including variable types and sample size. It then details the assumptions of the t-test, presenting and interpreting SPSS output to assess normality and homogeneity of variance. A research question is formulated to determine if GPA scores differ between male and female students. Hypotheses are established, and an alpha level is set. The results of the t-test are then interpreted, leading to a conclusion about the relationship between GPA and gender, including limitations of the t-test.

Running head: Quant Design And Analysis
Quant Design And Analysis
Learner Name
Capella University

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Introduction
Information regarding the performance of students are given in the spss file. The objective of the
assignment is to conduct statistical tests to test a research question and also test the assumptions
underlying the test. The main variables to be tested are GPA and how it relates to gender, The
descriptives for the two variables are shown below.
Section 1: Data File Description
The dataset consists of 21 variables and the
test to be done here consists of analyzing
the properties of two variables. The
properties of all the variables in the dataset
are listed below:
Id - Qualitative, Nominal
Lastname - Qualitative, Nominal
Firstname - Qualitative, Nominal
Gender - Qualitative, Nominal
Ethnicity - Qualitative, Nominal
Year- Quantitative, Scale
Lowup – Quantitative, Ordinal
Section - Qualitative, Nominal
Gpa- Quantitative, Scale
Extcr - Qualitative, Nominal
Descriptives
Statistic
Std.
Error
gender Mean 1.39 0.048
95%
Confidence
Interval for
Mean
Lower
Bound 1.3
Upper
Bound 1.49
5% Trimmed Mean 1.38
Median 1
Variance 0.24
Std. Deviation 0.49
Minimum 1
Maximum 2
Range 1
Interquartile Range 1
Skewness 0.456 0.236
Kurtosis -1.828 0.467
gpa Mean 2.8622 0.06955
95%
Confidence
Interval for
Mean
Lower
Bound 2.7243
Upper
Bound 3.0001
5% Trimmed Mean 2.8873
Median 2.84
Variance 0.508
Std. Deviation 0.71266
Minimum 1.08
Maximum 4
Range 2.92
Interquartile Range 1.19
Skewness -0.22 0.236
Kurtosis -0.688 0.467

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Review- Qualitative, Nominal
quiz1- Quantitative, Scale
quiz2 - Quantitative, Scale
quiz3 - Quantitative, Scale
quiz4 - Quantitative, Scale
quiz5 - Quantitative, Scale
final - Quantitative, Scale
total - Quantitative, Scale
percent - Quantitative, Scale
grade - Nominal
passfail – Nominal
The sample size for the data is 105.
Section 2: Testing Assumptions
The t test done here works as it should under a few assumptions. They are:
1. The scale of measurement for the variables that are to be tested should be continuous or
ordinal
2. The data that is collected should be from a random sample.
3. The variables should have a normal distribution.
4. The last assumption is that of homogeneity of variance. Equal variance happens when
both the samples have equal variance.
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
gender .397 105 .000 .619 105 .000

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gpa .100 105 .012 .961 105 .004
a. Lilliefors Significance Correction
From the Shapiro- Wilk test the p value can be seen to be less than 0.05 which violates the
conditions for normality.

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As the significance value for the Levene’s test for homogeneity of variance is greater than 0.05
the null hypothesis cannot be rejected and it can be said that the variances are homogenous
across the group.
Though the test for normality showed that the variables are not normally distributed the test can
be proceeded with because gender is a binary variable with values coded as 1 or 2 and the
histogram and Q-Q plot of GPA shows that gpa is almost approximately normally distributed.
Section 3: Research Question, Hypotheses, and Alpha Level
The gpa scores for the individual students listed can be further subdivided into two categories i.e
male and female. An interesting research question that can answered with a t test is whether the
gpa scores vary for male and female students. As the assumptions for a t test are already met the
research question can be answered by conducting a two sample t test in spss.
The null hypothesis can be set that there is no difference in gpa scores across gender. And
therefore the alternative hypothesis is that there exists a difference in mean gpa across male and
female groups.
The alpha level can be set as the standard 0.05 as in such social sciences question.
Section 4: Interpretation

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The levene’s test shows the homogeneity of variance across the genders.
The p value for the two sided test is 0.048 (t= 1.99, df = 103 and p = 0.048) which is less than the
standard value of 0.05.
Thus the null hypothesis can be rejected and it can be concluded that there is a significant
difference between the gpa scores between males and females.
Section 5: Conclusion
There are naturally some limitations of the t test that have been found while conducting
statistical tests. In real life it is hard to come upon a perfectly normalized dataset. So some error
naturally comes into the test. It is hard to find raw data that is really randomly sampled
However from the overall calculations done for the task it can be seen that even though t test is
an often used statistical test, some errors in its assumptions can be ignored to give us a
reasonably good prediction for the results.

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References
Burns, R. P., & Burns, R. (2008). Business research methods and statistics using SPSS. Sage.
Green, S. B., & Salkind, N. J. (2016). Using SPSS for Windows and Macintosh, books a la carte.
Pearson.