Independent sample t test spss

DATA ANALYSIS AND APPLICATION: T-tests 4

Data Analysis and Application: T-tests
Heather A. Lacharite
Capella University
Introduction to T-tests
A rudimentary inferential statistic that is frequently used in psychological study is called the t-test. There are always two variables when involving t-tests. There is the predictor variable (X) and the outcome variable (Y). Along with the logic of t-tests, all inferential statistics include independent variables of t-tests and all function under assumptions. In this paper, we will also explore the null and alternative hypothesis for t-tests. The null hypothesis predicts no significant difference in population means. When speaking of a directional alternative hypothesis for a t test, the researcher will conclude that the population means vary in a precise track. In terms of a non-directional alternative hypothesis, the research will propose that the population means vary, however, it will not specify which mean is preeminent.

Data Description

Lacharite (2017), previously reported the description of the data as:

“Gender: Categorical variable, having two values 1 for female and 2 for male. The scale of measurement here is nominal

GPA: It is the cumulative grade point average of students at the start of the course. The scale of measurement here is ratio. GPA has a value of 1-4.

Total: It is the combined scores of quizzes one, two, three, four, five, and the final exam. It is a value between 1-100, and it is an interval measurement.

Final: This is only the final score, also an interval measurement

The sample size is 105” (p. 3).

Per Howell (2011), an independent samples t-test compares the mean scores of two groups on a given variable. For this assignment, descriptive statistics, visual representation of the distribution, test of normality, as well as an independent samples t-test and test of homogeneity will be created and computed. GPA and Gender are the variables used for this assignment. Gender, which is measured on nominal scale of measurement is the first variable. This variable is considered a dichotomous variable that has values of 1 and 2. GPA is the second variable yet this variable is measured on an interval scale rather than a nominal scale.

Section 2: Testing Assumption
Some assumptions that can be made are, that the dependent variable can be considered as normally distributed, this can be checked with the Q-Q plot. The next assumption is that the two groups are considered independent of each other. In addition, the two groups have no effect on the dependent variable. This can be checked by using the Levene’s Test.

Case Processing Summary

gender

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

gpa

dimension1

1

64

100.0%

0

.0%

64

100.0%

2

41

100.0%

0

.0%

41

100.0%

Descriptive

Gender

Statistic

Std. Error

gpa

1

Mean

99.33

1.779

95% Confidence Interval for Mean

Lower Bound

95.76

Upper Bound

102.89

5% Trimmed Mean

98.79

Median

99.00

Variance

174.039

Std. Deviation

13.192

Minimum

75

Maximum

137

Range

62

Interquartile Range

20

Skewness

.451

.322

Kurtosis

.224

.634

2

Mean

101.82

2.207

95% Confidence Interval for Mean

Lower Bound

97.32

Upper Bound

106.31

5% Trimmed Mean

101.41

Median

100.00

Variance

160.716

Std. Deviation

12.677

Minimum

83

Maximum

128

Range

45

Interquartile Range

20

Skewness

.354

.409

Kurtosis

-.731

.798

Tests of Normality

gender

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

gpa

dimension1

1

.079

55

.200*

.972

55

.235

2

.101

33

.200*

.960

33

.261

a. Lilliefors Significance Correction

*. This is a lower bound of the true significance.

After reviewing the descriptive table output by the SPSS software, it can be determined that both samples are drawn from normal population. Since the p-value is > than 0.05, the samples are considered drawn from normal population. An unpaired t-test can be conducted since both samples are independent of each other. The t-test will assess for a significant difference of the two-sample’s means. As listed, there is a sum of 55 observations for gender 1. Within those 55 observations there is a mean GPA of 99.33 and a standard deviation of 13.192. In looking at Gender 2, there is a sum of 33 observations. Within the 33 observations there is a mean GPA of 101.82 and a standard deviation of 12.677. With these calculations, one can conclude there is a difference of -2.491 between the two samples.

The Shapiro-Wilk Test is considered a formal statistical test of normality. For this test, to have a normal distribution results would have to indicate a value of 1.0. Anything less than 1.0 would represent a departure from a perfect normal shape. Thus, we can conclude for this assignment the normal distribution is slightly departing from a perfect normal shape as the value is indicating a 0.972 for gender 1 and 0.960 for gender 2.

In terms of the Levene’s Test for Equality of Variances, it shows if the second assumption is satisfied. There is approximate equal variance between the two groups on the dependent variable. The significant value will need to be 0.05 or less for either variance to be measured as considerably diverse. A value 0.05 or greater would tell that the variances are not considerably diverse. The Levene’s Test for Equality determined the variances show there is no treatment effect due to the fact they are almost equal. Given the value is 0.959, it is greater than 0.05 therefore the variances are almost equal or has no treatment effect

Section 3: Research Question, Hypotheses, and Alpha Level

Per Howell (2011), an inferential procedure is utilized in statistics to make inferences about unknown populations or scores that vary depending on the data that is utilized and the purpose of making the inference. Regression analysis is a procedure utilized to analyze several variables. It focuses on the relationship between a dependent variable and on or more independent variables. Therefore, regression analysis was the inferential procedure used in this assignment. Per Howell (2011), assuming there is not a significant difference between the population mean and the sample mean is a null hypothesis. Furthermore, he explains that an alternative hypothesis assumes there is in fact a significant difference. The alpha level is another term for the level of significance. The alpha level for this assignment is .05. Below is the null and alternative hypothesis’s in statistical form that can be tested, along with the research question the t-test will answer:

Null Hypotheses (H o): There is no real difference between gpa of males and females.

Alternative Hypothesis (Ha): There is a significant difference between gpa of males and females

Research Question: Are female GPA’s higher than males?

When an independent sample t test was completed to test the hypothesis’s, the null hypothesis can be accepted. This is concluded due to the t-statistics value is 0.87 with 86 degrees of freedom. Furthermore, 0.387 is the p-value for the t statistic, which is less than 0.05. With a 5% level of significance the null hypothesis is acceptable. The result being, GPA between males and females has no real difference.

Interpretation
In using the Shapiro-Wilks and Kolmogorov-Smirnov tests, the outcomes precisely demonstrate adequate indication that the test of normality of, GENDER and IQ, were drawn from a normal population. Q-Q plots, box plots and the descriptive statistics, supported this conclusion. It was detected that the two samples were autonomous of one another, which allowed for an unpaired t-test which will test the mean of the two samples for a significant difference. In addition, it was observed that Gender 1 has 55 subjects with a mean IQ of 99.33 and a standard deviation of 13.192, while Gender 2 has 33 subjects with a mean IQ of 101.82 and a standard deviation of 12.677. As previously stated, the difference between the two samples IQ were observed at -2.491.

In examining the top line of the results from the independent sample t-tests, it displays the variances are approximately equal (-.870 and -.879), but the essential point will display variances that are not equal. However, based on the Levene’s test, results demonstrate an approximate equal variance due to the p-value being .959. Looking at the value of t-statistics, we see the value calculated at 0.870 with degrees of freedom calculated at 86. Given 0.870 is greater than 0.05 and represents a 5% level of significance, we can accept the null hypothesis. By accepting the null hypothesis, it is being determined there is no real difference between the IQ’s of males and females.

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

.003

.959

-.870

86

.387

-2.491

2.863

-8.183

3.201

Equal variances not assumed

-.879

69.665

.383

-2.491

2.835

-8.145

3.163

Conclusion
Overall, t-tests have been designed for independent means that are established on certain presumptions. If the said presumptions end up being inaccurate then the results of the analysis can be labeled flawed. When using t-tests it is important to remember it only examines the means and does not provide information on individual scores. This could be considered a strength or weakness depending on the context of one’s research. A limitation of the t-test is that it usually requires a larger sample size. A sample size too small can be considered as having deficient power (Connelly, 2011). The t-test can however be universally utilized if you have two different groups means to be analyze. This can be with GPA and gender like in this assignment, or in a brewery as this is where the t-test was developed. The t-test monitored the quality of stout at the Guinness brewery in Dublin, Ireland (Connelly, 2011). Some other highlights of t-tests include, it’s calculation is done with ease, it tells you how different the mean of one sample is from the rest of the group, and requires little data. In my opinion, the t-test is a great statistical test die to the fact that it is important to keep track of the conclusions of the mean rather than single scores of the individuals, which can give researchers a more majority oriented position.

References
Connelly, L. M. (2011). t-tests. Medsurg Nursing, 20(6), 341. Retrieved from http://search.proquest.com.library.capella.edu/docview/908549522?accountid=27965

Howell, D.C. (2011). Fundamental statistics for the behavioral sciences (7th ed).

Belmont, CA: Wadsworth Cengage Learning.

Lacharite, (2017). Correlations. Unpublished Manuscript. Capella University.