The following figures are from your lab handout. The means in all 3 graphs in Fi

Question

The following figures are from your lab handout. The means in all 3 graphs in Figure 6 are the same. Group 1 values 11 Group 2 values Low variability Medium variability High variability Group 1 mean Group 2 mean Figure 5. The t-test Figure 6. t-test comparison of distributions If t-tests were run to determine whether the two groups were significantly different than one another, which data set would be more likely to be significantly different (Low, Medium, or High variability)? Explain why. In which data set would the difference between the means most likely be due to chance (Low, Medium, or High variability)? Explain why. ·

Explanation / Answer

The t test is a statistical test that measures whether two means of the two groups (1 and 2) are significantly different. Figure 5 indicates the distributions in group 1 and 2 of the study. It indicates where the two group means are located in this idealized distribution. There is very little overlap between the curves in the low variability graph. The difference in the groups in high variability graph is least striking because of maximum overlap between the two bell shaped curves.

T value: The t value will indicate whether there is statistical difference between the two groups.

The t value= difference between the two means/ variability between the groups.

The difference between the means is the distance between the two group means, while the variability/ dispersion of score is the distance between edges of the two curves (left to left and right to right). The t values essentially give the signal: noise ratio.

The t values are analyzed in a t distribution table. For this analysis, an alpha value and degree of freedom is required. An alpha value is set which is usually 0.05. This value indicates that 5 times out of 100, there is statistical difference between the two group means. The degree of freedom is the sum of the values in both groups -2. If the t value is high, then there is more probability that the differences are significant. If t is closer to 0, there is no difference between the groups.

The differences in the means in all three graphs of figure 6 are nearly the same (differences between the dashed lines of both groups). A slight difference exists for the differences in group means. On the other hand, the variability values differ quite a lot. There is a very high value for variability for the high variability dataset while the low variability dataset has a much smaller value of variability (they two curves are distinct). The medium dataset has a variability value between the high and low variability datasets.

The t value for the low variability dataset will be high as the variability between the two groups is the lowest. The t value for the high variability dataset will be low, as the variability between the two groups is the highest. The medium variability graph will have a t value between the low and high variability graphs.

The t values if high, indicates that the null hypothesis is rejected. This indicates that there is a statistical difference between the two groups. Thus, there is statistically significant difference between the groups in the low variability dataset. There is no difference between the two group means for high variability data set, indicating to accept the null hypothesis due to low t value. In this dataset, there is no statistical significant difference between the two groups.

The difference in the group means for the high distribution data set is mostly due to chance, as the variability is high. A high t value would indicate that the likelihood of obtaining significant differences in the two group means in high. The high variability data set will have a low t value, indicating that differences between the means are mostly likely be due to chance.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.