1. Difference between two groups Two-sample t test
April 3, 2000

2. Two-sample t test
Sometimes, we want to compare two different groups or samples to see if their means are different.
Did one class score higher on an exam than another?
Is the average GRE score of MPA students different than the average GRE score of MPH students?
Are the welfare to work rates higher for residents in Mon County (who has a day-care program) than those in Preston County (who does not).

3. Two-sample t test
The procedure for this statistic is very similar to a simple t test. The primary difference is that you must compute a standard error for each of the two groups.
There are different formulas for this test depending on whether or not the samples are independent of one another and whether or not they have equal variances. We will work with one type: independent samples, unequal variances.
Again, somewhat different process/formula than that shown in book.

4. Two-sample t test
For a sample of 30 female professors, the mean salary is $41,000 with a st dev of $3,000. (group 1)
For a sample of 50 male professors, the mean salary is $41,800 with a st dev of $3,400. (group 2)
Is the mean salary of men higher than the mean salary of women?

5. Two-sample t test
Two formulas needed

6. Two-sample t test
H1: The average salary of male professors is higher than the average salary of female professors.
H0:There is no difference in the average salary of male and female professors.
Select an alpha level.
 = .05

7. Two-sample t test
Group 1
Group 2

8. Two-sample t test

9. Two-sample t test So, t = 1.02 (ignore the minus sign)
Find tcr (one-tailed test)
 = .05
df = 78 (n1 + n2 - 2)
tcr = 1.66
Since t < tcr we fail to reject the null hypothesis. The mean salary of female professors is not statistically significantly different than the mean salary of male professors.

10. Two-sample t test
Practice problem

11. Correlation
Correlation examines the relationship between two variables.
The relationship can be expressed as a graph called a scattergram.

12. Correlation

13. Correlation
The relationship between the two variables can also be expressed as a number called the correlation coefficient.
one of many statistics referred to as measures of association.
The values of correlation coefficients range from -1 to +1.
The most commonly used measure of correlation is the Pearson product-moment correlation coefficient, designated as “r”.

14. Correlation The correlation coefficient signifies two things.
The direction of the relationship (positive or negative)
The strength or magnitude of the relationship (strong, moderate, weak, etc.)

15. Correlation
A positive correlation indicates that high values of one variable correspond with high values of the other variable and low values correspond with low values. When this occurs, the r value is a positive number (r=.66)
A negative correlation indicates that when the value for one variable is high the value for the other variable will be low. When this occurs, the r value is a negative number (r=-.66)

16. Correlation
A correlation coefficient of -1 or +1 represents a perfect correlation.
r = -1 is a perfect negative relationship
r = +1 is a perfect positive relationship
A correlation of 0 (r = 0) means that no linear relationship exists between the two variables.
The stronger the relationship between the two variables, the closer r is to 1.

17. Correlation
r = 0.82
There is a strong positive relationship. As female literacy increases in a country, female life expectancy also increases.

18. Correlation
R =
There is a strong negative relationship. As female literacy in a country increases, infant mortality decreases.

19. Correlation
r = 0.37
There is a moderate, positive relationship between birth rate and death rate for a country.

20. Correlation Coefficient
Suppose we are looking at the relationship between two variables: weight of a package of apples and price. If the scale is accurate, it looks like this.

21. Correlation Coefficient
There is a positive perfect relationship between the two variables. r= 1.0

22. Correlation Coefficient
Suppose the scale was a little off. Now the line might look like this. 12 10 8 6 4 2
WEIGHT 20 40 60 80
100
120
140
PRICE

23. Correlation Coefficient
Now there is not a perfect relationship. The r does not equal 1.0
Now, r - .96

24. Pearson’s r - formula

25. Pearson’s r
Practice problem

26. Correlation
Web site: Guessing correlations