powerpoint
Using t Test and ANOVA With Sun Coast Remediation Data Set 1
Using t Test and ANOVA With Sun Coast Remediation Data Set 5
Data Set
Tammie Witcher
Data Analysis: Hypothesis Testing
Independent Samples t Test: Hypothesis Testing
Ho4: There is no statistically significant difference in mean values for Group A and Group B.
Ha4: There is a statistically significant difference in mean values for Group A and Group B.
Table 1: Two-sample independent t-test assuming equal variances
|
|
Group A Prior Training Scores |
Group B Revised Training Scores |
|
Mean |
69.79 |
84.77 |
|
Variance |
122.00 |
26.96 |
|
Observations |
62.00 |
62.00 |
|
Pooled Variance |
74.48 |
|
|
Hypothesized Mean Difference |
0.00 |
|
|
df |
122.00 |
|
|
t Stat |
-9.67 |
|
|
P(T<=t) one-tail |
0.000 |
|
|
t Critical one-tail |
1.66 |
|
|
P(T<=t) two-tail |
0.000 |
|
|
t Critical two-tail |
1.98 |
|
The two tailed p-value leads to the rejection of the null hypothesis, t(122) = -9.67, p = 0.000. It is therefore concluded that there is a statistically significant difference in the means for group A (M = 69.79, SD = 122) and group B (M =84.77, SD = 26.96) at the 1% level of significance.
Dependent Samples (Paired Samples) t Test: Hypothesis Testing
Ho5: There is no statistically significant difference in mean values for Pre-Exposure μg/dL and Post-Exposure μg/dL.
Ha5: There is a statistically significant difference in mean values for Pre-Exposure μg/dL and Post-Exposure μg/dL.
Table 2: Two-sample pared t-test
|
|
Pre-Exposure μg/dL |
Post-Exposure μg/dL |
|
Mean |
32.86 |
33.29 |
|
Variance |
150.46 |
155.50 |
|
Observations |
49.00 |
49.00 |
|
Pearson Correlation |
0.99 |
|
|
Hypothesized Mean Difference |
0.00 |
|
|
df |
48.00 |
|
|
t Stat |
-1.93 |
|
|
P(T<=t) one-tail |
0.030 |
|
|
t Critical one-tail |
1.68 |
|
|
P(T<=t) two-tail |
0.060 |
|
|
t Critical two-tail |
2.01 |
|
The two tailed p-value of the paired t test leads to the rejection of the null hypothesis, t(96) = -1.93, p = 0.030. It is therefore concluded that there is a statistically significant difference in the means for Pre-Exposure μg/dL (M = 32.86, SD = 150.46) and Post-Exposure μg/dL (M = 33.29, SD = 155.50) at the 5% level of significance.
ANOVA: Hypothesis Testing
Ho5: All the groups means are the equal.
Ha5: There exists at least one group mean that is statistically significantly different from the other group means.
Table 3: Single factor analysis of variance
|
SUMMARY |
|
|
|
|
|
|
|
Groups |
Count |
Sum |
Average |
Variance |
|
|
|
A = Air |
20.00 |
178.00 |
8.90 |
9.36 |
|
|
|
B = Soil |
20.00 |
182.00 |
9.10 |
3.04 |
|
|
|
C = Water |
20.00 |
140.00 |
7.00 |
6.63 |
|
|
|
D = Training |
20.00 |
108.00 |
5.40 |
1.41 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
|
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
|
Between Groups |
182.80 |
3.00 |
60.93 |
11.92 |
0.000 |
2.72 |
|
Within Groups |
388.40 |
76.00 |
5.11 |
|
|
|
|
|
|
|
|
|
|
|
|
Total |
571.20 |
79.00 |
|
|
|
|
The p-value of the results of the ANOVA procedure leads to the rejection of the null hypothesis that all the group means are equal, F(3, 76) = 11.92, p = 0.000. It is therefore concluded that there is at least one group mean that is statistically significantly from the other means at the 1% level of significance.