F-test
One more test that you will commonly find is the F-test.
In some ways the F-test is very similar to z-test and t-test.
However, there are some important differences as well.
A. Similarity to t-test.
1. Based upon a similar logic. Trying to determine if the differences between groups are due to chance or not.
2. Different distributions are used depending upon the size of the samples.
B. Difference
1. F-test must be used when comparing three or more groups from each other
Up to this point, we have been trying to determine if two groups are different from each other. However, some experimental designs involve more than two groups of people.
Remember, factorial designs often involve many different groups.
Well, F-tests are used when you are comparing several groups to find out if they are equal to each other or not.
C. Steps Involved
1. Calculate an F value for the groups being compared to each other.
You won't have to do this. But I do want you to know what an F-value is.
F scores are calculated by taking the variance between groups and dividing it by the variance within the groups.
Variance between groups looks at how far apart the groups are to each other.
The variance within groups looks at how close the scores within a group are to each other.
The more that groups are further apart from each other, while the scores within each group are close together the higher the F value.
F = distance between groups / distance within groups
Key Point: Basically, we want to know if there is more variance (distance) between groups than within groups.
If there is a lot more variance between groups than within groups then we want to know if these differences are due to chance or not.
2. Calculate the df.
df between is calculated by taking (K-1) (number of groups - 1)
df within is calculated by taking (N-K) (total number of people - number of groups)
When doing F-tests, must calculate two different types of degrees of freedom. Must know how many groups we are comparing. And must know the total number of people in all of the groups.
3. F-tests are nondirectional. Simply trying to determine if the groups are different from each other.
4. Look up the critical value for p < .05 and p < .01 in the appropriate column of the F-table.
If F-score is greater than the critical value at p < .05 or p < .01 then reject the null hypothesis and state that the groups are not equal to each other.
5. F-tests will only tell you if some of the groups are different from each other, but they won't identify which groups are actually different.
So, let's say that I conduct an F-test on ten different groups and I find that I can reject the null hypothesis.
What this means is that at least two of the ten groups, are different from each other, but I'm not sure which ones are.
Other tests can be used to determine which groups are different.
Example:
Say I'm trying to raise money for a charity and I want to know if it matters whether or not I use fear appeals, promises, or begging when I'm trying to solicit money?
So, I run an experiment to find out.
What is my Independent variable? (persuasive appeals)
How many levels does this variable have? (3 levels, fear appeals, promises, begging)
What is my dependent variable? (amount of money)
What is my research Hypothesis? M1 <> M2 <> M3
What is my Null Hypothesis? M1=M2=M3
So, lets say we do run an experiment, we randomly call a total of 9 people, with 3 people we use a fear appeal, with another 3 we use a promise, and with the other 3 we simply beg.
Here's the money we collect:
fear appeal X = $20
promise: X = $25
begging X = $30
1. Calculate an F-value
F = 6.25 (you don't have to do this)
2. Calculate the df
df between = (K-1)
df between = 3 - 1
df between = 2
df within = (N-K)
df within = (9-3)
df within = 6
3. Determine if F-observed is greater than the critical values at p < .05 and p < .01 for 2 and 6 df.
F-critical at 2 and 6 df is 5.14 at p < .05
F-critical at 2 and 6 df is 10.92 at p < .01
We can reject the null hypothesis at p < .05.
We are 95% certain that the groups are different from each other.
However, we don't know where the differences are at, but we know that they exist.
Summary:
1. z-test works well when comparing two groups composed of large samples
2. t-test should be used when comparing two groups composed of small samples
3. F-test should be used when comparing three or more groups with each other.
Overall, goal is the same: Determine whether differences are due to chance or manipulation of independent variable.