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5 Steps of Model
1- Independent Random Sample / IR: level of measurment / Populations are Normally Distributed / Populations Variances are Equal
2- Ho:
Ha: At least one of the population means is different
3- Sampling distribution = F distribution
Alpha / DFW / DFB / F(critical)
4- Find "F" ratio
5- Interpret
F(obtained) > F(critical) - REJECT null hypothesis
Category A significantly varies
Example
H0: μ1 = μ2 = ... = μr, all the means are the same
Ha: two or more means are different from the others
α = 0.05 significance level
Whether the observed difference in means is too large to be the result of random selection. If the difference between treatments is a lot bigger than the difference within treatments, you conclude that it’s not due to random chance.
Example
The p-value is below your significance level of 0.05: it would be quite unlikely to have MSB/MSW this large if there were no real difference among the means. Therefore you reject H0 and accept Ha, concluding that the mean absorption of all the fats is not the same.
Example
STAT - TESTS - H: ANOVA (L1, L2, L3, L4)
Note that the mean square between treatments, 545.4, is much larger than the mean square within treatments, 100.9; p-value: 0.0069
Example
Hoping to produce a donut that could be marketed to health-conscious consumers, a company tried four different fats to see which one was least absorbed by the donuts during the deep frying process. Each fat was used for six batches of two dozen donuts each, and the table shows the grams of fat absorbed by each batch of donuts.
6 Steps of ANOVA
Σ
Analysis of Variance
What is ANOVA?
- Used to test differences between more than 2 means
- Extension of the T and Z tests
- Business, medicine and psychology
- One-way
- Two-way
- N-way Multivariate
1- Find the total sum of squares (SST)
ΣΣ
2- Find the sum of squares between each category (SSB)
3- Find the sum of square within each category (SSW)
SST-SSB
4- Find SSW + SSB degrees of freedom
SSW: n-k
SSB: k-1
5 - Find the mean square within + between
within: SSW/DFW
between: SSB/DFB
6- Find the "F" ratio
MSB/MSW
How to use ANOVA with a calculator
To perform an ANOVA
1. Enter the sample data into individual lists
2. Choose STAT, TESTS, ANOVA(
3. Enter the appropriate lists and press enter
For example, if you have 3 samples, it will look like: ANOVA(L1,L2,L3)
Example: Here are the raw sample data on the women's heights in inches as broken down by the four age groups. Perform ANOVA on the raw data to test the null hypothesis that the true average heights are the same for each age group.