Anova
Analysis of Variance
(ANOVA)
Dr. H. Johnson
ANOVA
• Analysis of variance (ANOVA) is a powerful hypothesis testing procedure that extends the capability of t-tests beyond just two samples.
• Many types of ANOVAs, today we will learn about a oneway independent-measures ANOVA
• Later we’ll learn one-way repeated-measures ANOVA .
• We’ll also learn two-factor ANOVA after that.
• These ANOVAs are by no means all of them! There are a
LOT more types!
One-Way ANOVA
• The independent measures ANOVA is used in the same types of situations that the independent measures t-test had been used, except that the ANOVA allows for the comparison of more than just two groups.
• Before the advent of the computer, if someone had three groups in an experiment, they would often use a series of t-tests to compare all possible combinations of means.
• If you had three samples to compare then, using t-tests, we would have to do M1 vs. M2, M1 vs. M3, and M2 vs. M3
• Each time we do a t-test, the type I error rate is equal to a.
• The experiment-wise error rate (a) is held at .05 in an ANOVA.
One-Way ANOVA
Preliminary Example
Pretend you wanted to know the effects of different temperatures on the ability to learn. You assigned n = 5 subjects to each of three treatment conditions. Each of the five subjects in each group were placed into a room of the appropriate temperature and were asked to solve problems. The DV is the number of problems correctly solved.
Temperature of room
50o
70o
90o
0
4
1
1
3
2
3
6
2
1
3
0
0
4
0
One-Way ANOVA
Preliminary Example
New Statistical Notation
Temperature of room
50o
70o
90o
0
4
1
1
3
2
3
6
2
1
3
0
0
4
0
Some slightly new statistical symbols and notation will be introduced in
ANOVA.
A factor is something that is manipulated by an experimenter. In this experiment we have a single factor, temperature of room.
Since a factor is manipulated, it must have at least two levels. In
(ANOVA)
Dr. H. Johnson
ANOVA
• Analysis of variance (ANOVA) is a powerful hypothesis testing procedure that extends the capability of t-tests beyond just two samples.
• Many types of ANOVAs, today we will learn about a oneway independent-measures ANOVA
• Later we’ll learn one-way repeated-measures ANOVA .
• We’ll also learn two-factor ANOVA after that.
• These ANOVAs are by no means all of them! There are a
LOT more types!
One-Way ANOVA
• The independent measures ANOVA is used in the same types of situations that the independent measures t-test had been used, except that the ANOVA allows for the comparison of more than just two groups.
• Before the advent of the computer, if someone had three groups in an experiment, they would often use a series of t-tests to compare all possible combinations of means.
• If you had three samples to compare then, using t-tests, we would have to do M1 vs. M2, M1 vs. M3, and M2 vs. M3
• Each time we do a t-test, the type I error rate is equal to a.
• The experiment-wise error rate (a) is held at .05 in an ANOVA.
One-Way ANOVA
Preliminary Example
Pretend you wanted to know the effects of different temperatures on the ability to learn. You assigned n = 5 subjects to each of three treatment conditions. Each of the five subjects in each group were placed into a room of the appropriate temperature and were asked to solve problems. The DV is the number of problems correctly solved.
Temperature of room
50o
70o
90o
0
4
1
1
3
2
3
6
2
1
3
0
0
4
0
One-Way ANOVA
Preliminary Example
New Statistical Notation
Temperature of room
50o
70o
90o
0
4
1
1
3
2
3
6
2
1
3
0
0
4
0
Some slightly new statistical symbols and notation will be introduced in
ANOVA.
A factor is something that is manipulated by an experimenter. In this experiment we have a single factor, temperature of room.
Since a factor is manipulated, it must have at least two levels. In