# DATA ANALYSIS AND APPLICATION TEMPLATE

Running head: DATA ANALYSIS AND APPLICATION TEMPLATE 1

DATA ANALYSIS AND APPLICATION TEMPLATE 7

Data Analysis and Application (DAA) Template

Capella University

Calvin Handy

[8a1] Unit 8 assignment 1

Course: PSY7864

Instructor: Gennaro Ottomanelli

Date: 3/04/2019

Data Analysis and Application (DAA) Template

Section 1: Data File Description

Data set collected by a teacher across three class sections with each section consisting of about 35 students (N = 105). The student data is comprised of student demographics and performance which is based on a selection of quizzes, final and a total score within the class. Twenty-one variables were assigned overall, with student gender (1= female; 2= male) using the nominal, or categorical, scale of measurement consisting of 41 males and 64 females while GPA (previous grade point) is employ a ratio measurement. The variable gender is a dichotomous (categorical) variable with two categories (male and female) whereas GPA is continuous and has a quantitative value. The measurement scale for gender is nominal scale whereas GPA is ratio scale (Warner, 2013).

Section 2: Testing Assumptions

The assumption that are required to be made before running a statistical t test analysis is that the response variable Y must be quantitative and approximately normally distributed, i.e. it must be normally distributed when the sample size is less than 25 observations. Another assumption is the homogeneity of variance, which states that the variance of the response variable Y is approximately equal across the observations (groups), i.e., the observation that are being compared must show equal variance. There must be independence both between and within groups for the t test to be appropriate. In this case, Gender and GPA must be independent from each other. The last assumption is the robustness of the violation of the assumptions especially when the sample size is too small. In our case, the sample size is the equal and large enough, hence, this assumption is met (Warner, 2013).

From the histogram above, it clearly indicates that the GPA score is approximately normal although it is slightly left-skewed hence the normality assumption is met. Much of the data lie within the superimposed normal curve.

Descriptives

Statistic

Std. Error

gpa

Mean

2.8622

.06955

95% Confidence Interval for Mean

Lower Bound

2.7243

Upper Bound

3.0001

5% Trimmed Mean

2.8873

Median

2.8400

Variance

.508

Std. Deviation

.71266

Minimum

1.08

Maximum

4.00

Range

2.92

Interquartile Range

1.19

Skewness

-.220

.236

Kurtosis

-.688

.467

The skewness of the data indicates that the data is slightly left-skewed. Since 0.236*3 = 0.708 > |-.236|, then the data is approximately normally distributed. Kurtosis describes the flatness of the data. With kurtosis -1.0 < -0.688 |-.688|.

Tests of Normality

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

gpa

.100

105

.012

.961

105

.004

a. Lilliefors Significance Correction

The Shapiro-Wilk test is .961 with a p value .004 .05, the we can conclude that the variability between the gender and grade is not statistically significant. Therefore, equal variance is assumed (George, D., & Mallery, P., 2016).

From the analysis above, it is evident that the GPA data is normally distributed because the normality assumption are met by the graphical representation using histogram and the skewness and kurtosis. The assumption of homogeneity of variance is also met supporting the normality of the data.

Section 3: Research Question, Hypotheses, and Alpha Level

Research question: Is there a significant difference between GPA score for Male and Female?

Null Hypothesis (H0): There is no significant difference between the GPA score of Male and Female

Alternative Hypothesis (H1): There is a significant difference between the GPA score for Male and Female

Alpha level is 0.05

Section 4: Interpretation

Group Statistics

gender

N

Mean

Std. Deviation

Std. Error Mean

gpa

1

64

2.9719

.67822

.08478

2

41

2.6910

.73942

.11548

The result above was done to test the homogeneity of variance between both genders relative to the GPA score together with the descriptive statistics for both groups. The difference between the means of groups (M1 – M2) = (2.9719 – 2.6910) = 0.2809 GPA. Therefore, the difference between the least score and highest GPA score between the two groups differed by 0.2809 which is not a large difference in score. The standard deviation for each group is .67822 and .73942 for Female (Group 1) and Male (Group 2) respectively (Bonett, 2015).

The Levene F value is small (F = .095) and is not statistically difference (p = .758). The Levene F test is not statistically different since (p > .05) Therefore, there is not enough evidence to reject the null hypothesis and thus homogeneity of variances t is reported. Similarly, the equal variances t test result was statistically significant, t (103) = 1.999, p = .048, two-tailed. Hence, at α = 0.05 and using two-tailed as the criterion, the .2809 difference in GPA score between the Male and Female was not statistically significant.

The effect size (η2) is determined as below;

η2 = t2 ÷ (t2 + df)

= 1.9992 ÷ (1.9992 + 103)

= 0.0373 ≈ 0.04. This implies that 4% of the variance of the GPA score is predicted from the gender of the students. This is not a large predictor to the variability of the GPA between the two groups (Warner, 2013).

The upper 95% confidence interval for the difference between the groups is .55965 while the lower CI is .00215.

Section 5: Conclusion

The analysis above clearly shows that there is no enough evidence to reject the null hypothesis hence we can conclude that there is no difference between the GPA score between Male and Female with 5% alpha level. We are 95% confident that the mean difference between the gender lies within the CI. The Levene F test asserts that the variability between the group in not significant at alpha = 0.05. In relation to the test-statistic approach, the variability between the male and female is insignificant since p > 0.05.

References Bonett, D. G. (2015). Interval estimation of standardized mean differences in paired-samples designs. Journal of Educational and Behavioral Statistics, 40(4), 366–376. George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 step by step: A simple guide and refrence (Vol. 14th). New York and London: Routledge. Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques. Thousand Oaks, California: SAGE Publications, Inc.

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