U10A1-64 - One-Way ANOVA - Please follow instructions listed and see attachments for all details. SPSS Software Needed.. Do Not Bid if you do not have the software.

Section 1: Data File Description

The fictional data represents a teacher's recording of student demographics and performance on quizzes and a final exam across three sections of the course. Each section consists of 35 students which totals to 105 students (sample size, N = 105). The dataset has 21 variables but in this case only two variables will be analyzed. These are: gender and gpa variables. The gender variable is categorized as nominal since the numbers are arbitrarily assigned to represent group membership. The ‘gpa’ variable belongs to the interval data group since it has a true zero which is meaningful. Alternatively, gender could be categorized as a categorical variable while ‘gpa’ ‘as a continuous variable.

Section 2: Testing Assumptions

1. Articulate the assumptions of the statistical test.

Paste SPSS output that tests those assumptions and interpret them. Properly integrate SPSS output wher1e appropriate. Do not string all output together at the beginning of the section.

All statistical tests operate under a set of assumptions. For the t test, there are three assumptions:

· The first assumption is independence of observations.

· The outcome variable Y is normally distributed.

· The variance of Y scores is approximately equal across groups (homogeneity of variance assumption)

Figure 1: histogram of GPA

The histogram above shows that the variable is probably not normally distributed. The bell shape is absent and two peaks are evident.

Table 1: descriptives

Descriptives
	Statistic	Std. Error
GPA	Mean	2,78	,075
	95% Confidence Interval for Mean	Lower Bound	2,63
		Upper Bound	2,93
	5% Trimmed Mean	2,80
	Median	2,72
	Variance	,583
	Std. Deviation	,764
	Minimum	1
	Maximum	4
	Range	3
	Interquartile Range	1
	Skewness	-,052	,236
	Kurtosis	-,811	,467

With reference to the table 1 above, the ‘GPA’ variable is in the ideal range for skewness due to the fact that its absolute value for skewness are is less than .50 (approximately symmetric). The GPA variable is not ideal but acceptable since its kurtosis value is greater than .50 but less than 1. This new information gives mixed signals about the data being normal and only a normality test could iron out the differences.

Table 2: Normality test

Tests of Normality
	Kolmogorov-Smirnova	Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
GPA	,091	105	,033	,956	105	,001
a. Lilliefors Significance Correction

Looking at the table above, the p-value is less than 0.05. Therefore, the null hypothesis is rejected and thus it can be concluded that the variable is not normally distributed. However, since the sample size is sufficiently large, one does not need to worry about this violation. On the other hand, Levene’s test provides a p =0.566 (table 3) meaning that the null hypothesis should not be rejected. Thus the homogeneity of variances assumption is not violated. It’s also assumed that proper research procedures that maintain independence of observations were followed. Two of the three assumptions are met.

Section 3: Research Question, Hypotheses, and Alpha Level

The research question for this study is whether a relationship exists between the ‘Gender’ variable and the ‘GPA’ variable. Does one particular gender dominate the other in terms of academic performance (gpa)? The null hypothesis states that the means of the ‘GPA’ based on gender groups do not differ significantly whereas the alternative hypothesis states that there is a significant difference in the two ‘GPA’ groups based on the gender of the participants. The alternative hypothesis is non-directional meaning that the GPA for males could be higher than that for females or the GPA for females could be higher than that for males. The alpha level to be used is the standard .05 level of significance.

Section 4: Interpretation

1. Paste SPSS output for an inferential statistic. Properly integrate SPSS output where appropriate. Do not string all output together at the beginning of the section.

2.

Table 3: Independent samples t test results

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
								Lower	Upper
GPA	Equal variances assumed	,331	,566	2,004	103	,048	,302	,151	,003	,601
	Equal variances not assumed			1,994	83,974	,049	,302	,151	,001	,603

The test was carried out and indicated a p value 0f 0.048. This means that we shall have to reject the null hypothesis. This means that the two means are not equal.

The mean GPA for males and females differed significantly, t(103) =2.004, p = .048 (two-tailed). Mean GPA for the gender 1 group ( M = 2.90, SD = 0.748) was about 0.302 different from the mean GPA for the gender 2 ( M = 2.59, SD = 0.763). It could be said that the GPA for gender 2 is lower than that of GPA for gender 1. The effect size, as indexed by η^2 , was ; this is a small effect. The 95% CI for the difference between sample means, M 1 − M 2, had a lower bound of 0.003 and an upper bound of 0.601. This technically means that the difference between the two means cannot be zero since zero is not included in the confidence interval. This is in line with previous finding where the null hypothesis was rejected and it had been concluded that a significant statistical difference between the means was present.

Section 5: Conclusion

In conclusion, it is evident that a student’s previous performance between gender 1 and gender 2 is different. Gender 1 had higher GPA than Gender 2. A major limitation of this test is that one cannot compare more than two groups at a go. Another test has to be used in conjunction or instead of the independent samples t test.