1. Types of T-tests Independent T-tests Paired or correlated t-tests
Two independent groups that are mutually exclusive
Paired or correlated t-tests
One group with two measures over time

2. T-test Assumptions Both Dependent and Independent T-tests
Data are measured at the interval level
Normal distribution of the dependent variable.
Independent t-test
The independent variable is categorical and two levels (groups) – two mutually exclusive groups.
Variance of the two groups is similar – homogeneity of variance
Levene’s test
Null Hypothesis: There is no difference in the variance between the groups.
Scores are independent (come from different people)

3. Practice: Which T-test does one use?
Hypothesis: People who are exposed to a real spider will report a higher anxiety level than those who are exposed to a picture of a spider.
Hypothesis: Female nursing students will have a higher score on a scale assessing the perception of the image of nursing than male students.
Hypothesis: The number of cigarettes smoked per day will be lower following a cessation intervention.

4. Example: Independent t-test
Research Question: Do nonsmokers differ from smokers on their perception of overall health?
Two different groups of people are being compared:
smokers vs nonsmokers

5. Overall Health Scores – t-Test results  
Overall Health Scores – t-Test results n
Mean
Std Dev T df p
Nonsmokers 45
155.00
26.43
2.93 88
0.004
Smokers
141.00
36.57
OUTPUT—What to look for:
1.group statistics. We see that the mean health score for the nonsmoker group is (SD 26.43) and for the smokers the mean is (SD 36.57).
2. T statistic which is 2.93
3.The df (degrees of freedom) are 88. This is calculated by subtracting one degree of freedom from the n of each group (NS group 45-1 = 44, S 45-1 = 44) and then adding the result (88).
Finally, with alpha set at .05, we conclude that p=.004 is statistically significant (p<.05) and therefore that there is a statistically significant difference between the mean health scores of the smoking groups. On average, nonsmokers have a higher score.

6. Example: Paired t-test
Research Question: Is there a significant change in subjects’ anxiety levels when they are exposed to a picture of a spider versus a real live spider?
The same people are being compared at two different times.
Time 1 (spider picture) vs time 2 (live spider)

7. Anxiety Scores – t-Test results  
Anxiety Scores – t-Test results n
Mean
Std Dev T df p
Real Spider 12
47.00
11.02
2.47 11
0.031
Photo
40.00
9.29
The above table contains statistics for a paired sample. There are 12 patients in the sample and based on these results all 12 patients participated at both time periods.
The mean anx score for spider was 47 (SD 11) and the mean anx for viewing a photo of a spider was 40 (SD 9).
Next look at the value of the paired samples test, t=2.47, df=11, p=.031 and determine that the p-value is significant since the actual probability of this result is <.05.
Thus, the null hypothesis is rejected. We conclude that there is a statistically significant difference in anxiety scores and viewing a photo or being exposed to a real spider. The photo produced less anxiety.