Quantitative Research, Parametric Analysis

Paired Samples Statistics

Table 1 shows two variables' average ACT scores extracted from 1993 and 1994. We have a mean value of “15.98” in 1993 and “15.86” in 1994 for the same total number of 64 students for both years. The point is that the variance and standard error of the mean of 1993 are higher than the same variables in 1994; therefore, the normal distribution of the year 1993 is broader than 1994. On the other hand, the standard deviation value in 1993 is “1.84” is the same as in 1994. It happens for the standard error of mean value in 1993 is “2.30” compared with same variable in 1994 (2.2394), which are very close.

		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	average  ACT 1993	15.986	64	1.8401	0.2300
	average ACT 1994	15.861	64	1.8351	0.2294

Table 1, “Paired Samples Statistics” (CTU, 2022)

Paired Samples Correlations

Table 2 indicates the paired samples' correlations with a strong and positive correlation “0.972” between the average “ACT scores of 1993 and 1994 with the same number of students.” (CTU, 2022) The positive correlation indicated that those students with a higher score in 1993 had higher scores in 1994 than others. Thus, there is a high possibility that students with low ACT scores will have the same status in 1994. The significance P for the correlation “0.00” is lower than “0.05”, which indicates that the correlation is significant. Therefore, conducting paired T-Test samples t-test is fit for analyzing data.

		N	Correlation	Sig.
Pair 1	average  ACT score 1993 & average ACT score 1994	64	0.972	0.000

Table 2, “Paired Samples Correlations” (CTU, 2022)

Paired Samples Test (Paired Differences)

To find the hypothesis, we need the paired sample t-test (whether the hypothesis is impacted significantly in the mean or the second value.) In ACT scores of 1993 and 1994, we have the same number of students and the same students for analyzing the data, so the t-test is the best tool to analyze the differences between higher and lower ACT scores for the same groups. We also can use 2 tailed t-test to study the difference in both higher and lower scores in both years.

The mean difference in the ACT scores “0.1250” in 1993 is lower compared with 1994. The same happened for the standard deviation “0.4343”, which was lower in 1993 than in 1994. So, the t-test value for the paired samples is “2.303”, and the degree of freedom is 63 because the number of attendants is 64 students.

		Mean		Std. Deviation	Std. Error Mean	95% Confidence Interval of the Diff.		t	df	Sig. (2-tailed)
			Mean			Lower	Upper
Pair 1	average  ACT score 1993 - average ACT score 1994	1250	0.1250	0.4342	0543	0.0165	0.2335	2.303	63	0.025

Table 3, “Paired Samples Test” (CTU, 2022)

We have a 95% confidence interval or the average difference in ACT scores between those two years. (difference in scores of “0.0165” and “0.2335”).

Therefore, with all said, it failed to reject the alternate hypothesis because of the T-value (2.303), which is higher than the significant T-value.

Lastly, the new ACT program does not seem effective as the test scores were lower in 1994 compared with 1993.

Using SPSS

We could find a significant improvement in data on student performance in their ACT scores using “SPSS software tests in 1993 (act93) and ACT tests in 1994 (act94).” (CTU, 2022) The t-test pair sample found that the average ACT score in 1993 “acts93” was “15.986,” and the standard deviation was “(1.8401”. In comparison, we have (15.861) in 1994 (acts94) and a standard deviation of “1.8351” for the same group. Therefore, there are no significant improvements between these two years.

Based on Table 4., the mean value of alive people of 10 years is “264.87”, and the standard deviation of the same group is “52.981” and the standard deviation of “52.981”. The mean value of dead people of 10 years is “261.80”, and the standard deviation of the same group is (51.807). The is no significant difference between the cholesterol levels of alive people in 10 years compared with dead people in the same period of time.

Therefore, there is no significant difference in the “cholesterol levels vital10” of alive people in 10 years compared with the dead people of the same timeframe.

Table 4, “cholesterol levels analysis” (CTU, 2022)

 Based on Table 5, the “one-way ANOVA analysis” (CTU, 2022) shows that we have differences in the income levels in academic groups “[F(2, 914)=68.102, p=.000]”. The means plot shows that the group of least educational revel has lower income levels than the group of higher academic levels. Post-hoc comparison using the Tukey Honestly Significant Differences test shows that the mean score is less than the differences between the two groups of "high school juniors and colleges “M=-9006.727, SD=2397.441, & M=-24252.154, SD=2474.33.”

There is a significant difference in the "Junior college or more – High school & Junior college or more Less than high school" group with “M=15245.427, SD=1501.619, & M=24252.154, SD=2474.337”. However, there is no indication of significant differences in the High "School- Less than High school, & High school - Junior college or more" group “M=9006.727, SD=2397.441 & M=-15246.427, 1501.619” (CTU, 2022)

Table 5, “ANOVA analysis” (CTU, 2022)

Conclusion

The level of degrees indicated the level of income statistically. The "Less than high school – High school and junior, & Less than high school - Collage or more" group has a lower income than the "High School- Less than High school, & High school - Junior college or more" group.

 

References

CTU, (2022). Colorado Technical University. Student’s restricted panel. Retrieved 2022, from Colorado Technical University restricted area of assignments.