T-test
Introduction
T-test comprises techniques such as a two-sample t-test, a one-sample t-test, and paired sample t-test. Two sample t-test is an independent sample t-test in which comparison of means for two groups is done. One Sample t-test compares the sample mean with the hypothesized population mean. The paired sample t-test measures a subject and assesses the impact of interaction on the subject. All the above-mentioned techniques fall under the inferential statistics (Berkman & Raise, 2011
The variables adopted in the exercise include democracy level, regions, mathematics utility, and grade level. Two sample t-test will compare means for democracy level across the regions while the one-sample test will compare the democracy level with the hypothesized value. The variables used for the analysis meet the assumptions of the aforementioned test. (Myers et al., 2010).
Scenario 1: One-Sample t-test
One sample t-test compares the sample mean of democracy level with the hypothesized value of the population (6). The hypothesis for the test will be as follows;
H0: µ = 6; the democracy level is 6
H1: µ≠ 6; the democracy level is not 6
Table 1: Note: The table provides the descriptive statistics for the level of democracy
| One-Sample Statistics | ||||
| N | Mean | Std. Deviation | Std. Error Mean | |
| Q46a. Level of democracy: today | 9369 | 5.55 | 2.877 | .030 |
Table 2: Note: The table provides the results of the one-sample t-test
| One-Sample Test | ||||||
| Test Value = 6 | ||||||
| t | df | Sig. (2-tailed) | Mean Difference | 95% Confidence Interval of the Difference | ||
| Lower | Upper | |||||
| Q46a. Level of democracy: today | -15.299 | 9368 | .000 | -.455 | -.51 | -.40 |
From the results of the one-sample t-test, the results are significant (M=5.55, SD=2.877); t(9368)= -15.299,p<0.05.Therefore the null hypothesis is rejected and democracy differs from the hypothesized value(6).
Scenario 2: Two-sample test
The two-sample t-test compares the mean for a continuous variable for two groups (Myers et al., 2010). The democracy level is the continuous variable while the region is the group variable. The hypothesis for the test would be as follows;
H0: µ1=µ2: Democracy level is the same for both North Africa and South Africa
H1: µ1≠µ2: Democracy level is not the same for both North Africa and South Africa
Table 3: Note: The table provides the descriptive statistics for the level of democracy across the two groups.
| Group Statistics | |||||
| Country by region | N | Mean | Std. Deviation | Std. Error Mean | |
| Q46a. Level of democracy: today | Southern Africa | 3263 | 5.81 | 2.785 | .049 |
| North Africa | 1022 | 4.99 | 3.069 | .096 | |
Table 2: Note: The table provides the results of the independent sample t-test
| 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 | |||||||||
| Q46a. Level of democracy: today | Equal variances assumed | 18.072 | .000 | 8.091 | 4283 | .000 | .828 | .102 | .627 | 1.029 |
| Equal variances not assumed | 7.690 | 1582.522 | .000 | .828 | .108 | .617 | 1.039 | |||
From the findings, there is a significant difference in the democracy for South Africa (M=5.81, SD=2.785) and North Africa (M=4.99, SD=3.069); t (4283) =8.091, p<0.05. The null hypothesis is rejected since the p-value is less than the significant level. Therefore, democracy levels vary between the two regions and the level of democracy is higher in South African compared to North Africa.
The findings show the mean value for the democracy level is 5.55 which varies significantly from the assumed value (6). Comparing for both North Africa and South Africa, there is a significant difference in the level of democracy. The level of democracy in North Africa is lower (4.99) compared to South Africa (5.81).
Reference
Berkman, E., & Reise, S. (2011). A conceptual guide to statistics using SPSS.
Myers, J., Wells, A., & Lorch, R. (2010). Research design and statistical analysis. Routledge.