In this paper, we will discuss and describe the application of t-test in testing the difference between the two groups of independent samples. The goal of this task is to interpret the three outputs of t-test provided.
Problem #1
The first output is given in wk6STAT1.pdf. In this test, the mean values of education in years of Never Married and Married groups are compared. There are 217 cases in Never Married group and 335 cases in Married group. The mean value of education in the Never Married group is 16.306 years with a standard deviation of 3.58 years. The mean value of education in the Married group is 17.109 years with a standard deviation of 3.223 years. Student’s t-test for independent samples was conducted to examine the difference in mean values. According to the results, the difference in means appeared to be significant (t=-2.674, p=0.008 for separate variance, t=-2.734, p=0.006 for pooled variance). Since p-value of the test is less than 0.05, we can conclude at the 5% level of significance that there is a significant difference in the mean values of education in years between Never Married and Married group (Stattrek.com, 2016).
There are no results of Levene’s test given to conclude about the variance, whether they are approximately equal or not (Statistics-help-for-students.com, 2016). In case of separate variance, we are 95% confident that the difference between population mean values is between -1.392 and -0.213 years. In case of pooled variance, we are 95% confident that the difference between population mean values is between -1.379 and -0.226 years (Onlinestatbook.com, 2016).
Problem #2
The second output is given in wk6STAT2.pdf. In this test, the mean values of education in years of Unemployed and Part-Time groups are compared. There are 100 cases in the Unemployed group and 155 cases in the Part-Time group. The mean value of education in the Unemployed group is 15.095 years with a standard deviation of 3.229 years. The mean value of education in the Part-Time group is 16.432 years with a standard deviation of 3.017 years. Student’s t-test for independent samples was conducted to examine the difference in mean values. According to the results, the difference in means appeared to be significant (t=-1.337, p=0.001 for separate variance, t=-1.337, p=0.001 for pooled variance). Since p-value of the test is less than 0.05, we can conclude at the 5% level of significance that there is a significant difference in the mean values of education in years between the Unemployed and the Part-Time group.
There are no results of Levene’s test given to conclude about the variance (whether they are approximately equal or not). In case of separate variance, we are 95% confident that the difference between population mean values is between -2.133 and -0.541 years. In case of pooled variance, we are 95% confident that the difference between population mean values is between -2.121 and -0.554 years.
Problem #3
The second output is given in wk6STAT3.pdf. In this test, the mean values of education in years of Male and Female groups are compared. There are 250 cases in the Male group and 418 cases in the Female group. The mean value of education in the Male group is 16.566 years with a standard deviation of 3.858 years. The mean value of education in the Female group is 16.647 years with a standard deviation of 3.195 years. Student’s t-test for independent samples was conducted to examine the difference in mean values. According to the results, the difference in means appeared to be not significant (t=-0.280, p=0.780 for separate variance, t=-0.081, p=0.769 for pooled variance). Since p-value of the test is greater than 0.05, we failed to reject the null hypothesis. At the 5% level of significance that there is no enough evidence to conclude about the significant difference in the mean values of education in years between the Male and the Female group.
There are no results of Levene’s test given to conclude about the variance (whether they are approximately equal or not). In case of separate variance, we are 95% confident that the difference between population mean values is between -0.651 and 0.488 years. In case of pooled variance, we are 95% confident that the difference between population mean values is between -0.624 and 0.462 years.
References
Onlinestatbook.com,. (2016). Confidence Interval on the Difference Between Means. Retrieved 27 February 2016, from http://onlinestatbook.com/2/estimation/difference_means.html
Statistics-help-for-students.com,. (2016). How do I interpret data in SPSS for an independent samples T-test?. Retrieved 27 February 2016, from http://statistics-help-for-students.com/How_do_I_interpret_data_in_SPSS_for_an_independent_samples_T_test.htm#.VtF5xvmLSUk
Stattrek.com,. (2016). Difference in Means. Retrieved 27 February 2016, from http://stattrek.com/estimation/difference-in-means.aspx?Tutorial=AP
