# t – Test and ANOVA

Part A. Dependent t-test
An exploratory data analysis for CreativityPre and CreativityPost indicates that there were 40 subjects and the mean score for creativity pre-test was 40.15, SD = 8.304 while that of creativity post test was 43.35, SD = 9.598 (Table 1).
Null hypothesis (H0): Participation in a creative writing course does not result in increased scores of a creativity assessment.
Alternative hypothesis (H1): Participation in a creative writing course results in increased scores of a creativity assessment.
Comparison of means
There was a significant difference between the means for creativity pre-test scores (M=40.15, t(39) = 2.671, p<.05) and creativity post-test scores (M= 43.35, t(39) = 2.671, p<.05, 2-tailed) (Table 2 and 3). This implies that scores of a creativity assessment were significantly higher after participating in a creativity writing course. As such, the alternate hypothesis is accepted: Participation in a creative writing course results in increased scores of a creativity assessment. Part B. Independent t-test The mean creativity scores for the pre-test and post-test groups was 41.75, and a standard deviation for the same data is 9.062 (Table 4). The bar graphs (Figure 3) display the mean creativity scores for post-test to be higher than for pre-test scores. H0: Participation in a creative writing course does not result in increased scores of a creativity assessment. H1: Participation in a creative writing course results in increased scores of a creativity assessment. Comparison of means The t-statistic from Table 6 is used to interpret whether the variances in the pre-test and post-test creativity scores are significantly different, t(78) = -1.595, p>.05. Since the independent t-test is greater than .05, the variances can be assumed to be equal. The independent t-test is non-significant (p = .115 for 2-tailed test) since this is greater than .05 and the null hypothesis is promote. Therefore, participation in a creative writing course does not result in increased scores of a creativity assessment.
Comparison of designs
From the within subjects design, there was a significant difference between the pre-test and post-test creativity scores. As such, the within subjects design accepted the alternate hypothesis that participation in a creative writing course results in increased scores of a creativity assessment. On the other hand, the between subjects design portrayed that the difference between the pre-test and post-test scores was non-significant. In other words, the null hypothesis that participation in a creative writing course does not result in increased scores of a creativity assessment was promoted. The two tests therefore resulted into different findings.
For the within-subjects design, the mean for pre-test scores was expected to be roughly equal to the mean for post-test scores since the subjects of the study were from the same population (Goodwin, 2009) but this was not the case. It is therefore a surprise that the null hypothesis was not accepted yet it should have been true for two samples of data obtained from the same population. In the between subjects design, it was expected that there would be a difference between the means for the two groups since the two samples were merged and the assumption was that the samples came form the same population (Goodwin, 2009). It was therefore expected that the null hypothesis would be accepted.
From this activity, I have appreciated that comparing means for within subjects is a good way of testing hypotheses as it is possible to identify differences in the means. This therefore provides a basis for accepting or not accepting the null hypothesis. In addition, the between subjects design has portrayed that it can be utilized in cases where the sample comes from the same population despite lack of knowledge on the distribution of the data.
Part C. ANOVA
Exploratory data analysis/hypotheses
“White Coat Syndrome” presents as a rise in blood pressure while in medical settings while the blood pressure is normal in other conditions (Sine, n.d.). This section tests for support for existence of ‘White Coat Syndrome’. For the 10 participants who were tested for blood pressure at home, the mean systolic pressure was 122.90, with a standard deviation of 7.094. The mean diastolic pressure was 82.90, with a standard deviation of 2.685 (Table 7). According to Table 8, the mean systolic and diastolic blood pressures for participants tested in a doctor’s office setting were 132.60, SD = 8.369 and 83.20, SD = 3.360 respectively. According to Table 9, the mean systolic and diastolic blood pressure for participants tested in a classroom setting were 118.80, SD = 5.554 and 82.60, SD = 2.675 respectively. The standard deviation for the sample was 5.554 and 2.675 for systolic and diastolic blood pressure respectively.
Figure 4 indicates that systolic blood pressure is highest when blood pressure is measured in a doctor’s office, lower in a home setting and lowest in a classroom setting. The diastolic blood pressures were almost the same in all settings although it was slightly higher in a doctor’s office.
H0: Systolic blood pressures are not equivalent in a home setting, doctor’s office and in a classroom setting but diastolic blood pressures are equivalent in the same settings.
H1: Systolic blood pressures are equivalent in a home setting, doctor’s office and in a classroom setting but diastolic blood pressures are not equivalent in the same settings.
ANOVA
The mean systolic blood pressures for participants tested at home, in the doctor’s office and in classroom were 122.90, 132.60, and 118.80 respectively. The standard deviations for systolic blood pressures at home, in the doctor’s office and in a classroom setting were 7.094, 8.369, and 5.554 respectively (Table 10). From Table 11, it is evident that the analysis of variance shows a significant difference between the means for the three groups of settings, F(2, 27) =9.964, p<.05 (Table 11). After performing post-hoc analyses to determine differences between the groups, it is evident that there is variability in the means of systolic blood pressures depending on the setting. Using the Tukey HSD test, it is clear that there is a significant difference between systolic blood pressure taken in a home setting compared to taking the blood pressure in a doctor’s office (p = .013) which is less than .05. However, there is no significant difference when systolic blood pressure at home and in a classroom setting (p =.412) which is greater than .05 (Table 12). Table 12 also indicates a significant difference between systolic blood pressure taken in a doctor’s office compared to tests done in a classroom setting (p =.001) which is less than .05. The effect size r for the systolic blood pressures is calculated as: R2 = SSM/SST (Field, 2009) Where SSM is between-groups effect size and SST is total amount of variance in data R2 =1004.467/2365.367 r= 0.652 Converting the r into percentage, it implies that taking systolic blood pressure at a doctor’s office causes a 65% change in systolic blood pressure compared to taking the same measure in a home setting while all other variables are held constant. The mean diastolic blood pressures for participants tested at home, in the doctor’s office and in classroom are 82.90, SD = 2.685; 83.20, SD = 3.360 and 82.60, SD= 2.675 respectively (Table 13). The analysis of variance shows that there is no significant different between the means for the three groups of settings, F(2, 27) = .105, p>.05 (Table 14). After performing post-hoc analyses to determine differences between the groups, it is evident that there is no significant variability in the means of diastolic blood pressures depending on the setting.
Using the Tukey HSD test, it is clear that there is no significant difference between diastolic blood pressure taken in a home setting compared to taking the blood pressure in a doctor’s office (p = .971) which is greater than .05. This is the same for diastolic blood pressures taken at home compared to those taken in a classroom setting (Table 15). Table 15 also indicates a non-significant difference between diastolic blood pressure taken in a doctor’s office compared to tests done in a classroom setting (p =.891) which is greater than .05.
The effect size r for the diastolic blood pressures is calculated as:
r2 = SSM/SST (Field, 2009)
Where SSM is between-groups effect size an SST is total amount of variance in data
r2 =1.8/232.7
r= .088
Converting the r into a percentage, it implies that taking diastolic blood pressure at a doctor’s office causes 8.8% change in diastolic blood pressure compared to taking the same measure in a home setting while all other variables are held constant. In summary, the null hypothesis “systolic blood pressures are not equivalent in a home setting, doctor’s office and in a classroom setting but diastolic blood pressures are equivalent in the same settings” is accepted.

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