Some Examples  of Statistical Analysis Using a t-Test

Example #1

A researcher wishes to learn if a certain drug slows the growth of tumors. She obtained mice with tumors and randomly divided them into two groups. She then injected one group of mice with the drug and used the second group as a control. After 2 weeks, she sacrificed the mice and weighed the tumors. The weight of tumors for each group of mice is below.

The researcher is interested in learning if the drug reduces the growth of tumors. Her hypothesis is: The mean weight of tumors from mice in group A will be less than the mean weight of mice in group 2.

	Group A     Treated with Drug	Group B Control- Not Treated
	0.72	0.71
	0.68	0.83
	0.69	0.89
	0.66	0.57
	0.57	0.68
	0.66	0.74
	0.70	0.75
	0.63	0.67
	0.71	0.80
	0.73	0.78
Mean =	`    0.675	0.742

A t-test can be used to test the probability that the two means do not differ. The alternative is that tumors from the group treated with the drug will not weigh less than tumors from the control group.

This is a one-tailed test because the researcher is interested in if the drug decreased tumor size. She is not interested in if the drug changed tumor size.

The values from the table above are entered into the spreadsheet as shown below.

The t-test shows that tumors from the drug group were significantly smaller than the tumors from the control group because p < 0.05. The researcher therefore accepts her hypothesis that the drug reduces the growth of tumors.

Example #2

A researcher wishes to learn whether the pH of soil affects seed germination of a particular herb found in forests near her home. She filled 10 flower pots with acid soil (pH 5.5) and ten flower pots with neutral soil (pH 7.0) and planted 100 seeds in each pot. The mean number of seeds that germinated in each type of soil is below.

	Acid Soil       pH 5.5	Neutral Soil pH 7.0
	42	43
	45	51
	40	56
	37	40
	41	32
	41	54
	48	51
	50	55
	45	50
	46	48
Mean =	43.5	48

The researcher is testing whether soil pH affects germination of the herb.

Her hypothesis is: The mean germination at pH 5.5 is different than the mean germination at pH 7.0.

A t-test can be used to test the probability that the two means do not differ. The alternative is that the means differ; one of them is greater than the other. 

This is a two-tailed test because the researcher is interested in if soil acidity changes germination percentage. She does not specify if it increases or decreases germination. Notice that a 2 is entered for the number of tails below.

The t-test shows that the mean germination of the two groups does not differ significantly because p > 0.05. The researcher concludes that pH does not affect germination of the herb.

Example #3

Suppose that a researcher wished to learn if a particular chemical is toxic to a certain species of beetle. She believes that the chemical might interfere with the beetle’s reproduction. She obtained beetles and divided them into two groups. She then fed one group of beetles with the chemical and used the second group as a control. After 2 weeks, she counted the number of eggs produced by each beetle in each group. The mean egg count for each group of beetles is below.

	Group 1    fed chemical	Group 2    not fed chemical (control)
	33	35
	31	42
	34	43
	38	41
	32
	28
Mean =	32.7	40.3

The researcher believes that the chemical interferes with beetle reproduction. She suspects that the chemical reduces egg production. Her hypothesis is: The mean number of eggs in group 1 is less than the mean number of group 2.

A t-test can be used to test the probability that the two means do not differ. The alternative is that the mean of group 1 is greater than the mean of group 2. 

This is a 1-tailed test because her hypothesis proposes that group B will have greater reproduction than group 1. If she had proposed that the two groups would have different reproduction but was not sure which group would be greater, then it would be a 2-tailed test. Notice that a 1 is entered for the number of tails below.

The results of her t-test are copied below.

The researcher concludes that the mean of group 1 is significantly less than the mean for group 2 because the value of P < 0.05. She accepts her hypothesis that the chemical reduces egg production because group 1 had significantly less eggs than the control.