ANOVA is an acronym for Analysis Of Variance. It is a method for comparing
3 or more means by using multiple F Tests. For ANOVA we must develop a
Null and Alternative Hypothesis, and once again the **" = "** goes with **H _{o}.**

The Hypothesis will be . (All means are equal)

Ha: at least one mean is different from the others.

The Test Statistic **F** = the variance between samples / the variance within samples.

** = MS treatment / MS error.**

(sample is also called treatment or factor)

To look up the F critical value we need: the numerator degrees of freedom **(k-1)**

the denominator degrees of freedom **k(n-1)**

Where "k" is the number of different samples (also called treatments, or factors)

"n" is the number of items within each sample.

In a **One Way ANOVA** we are comparing only one variable from each sample.

**One Way ANOVA**

Hot peppers are officially measured in laboratory units called scovill units. On a common scale they are "taste tested" and
ranked on a scale from 1 to 10 with 1 the mildest, 10 hottest. Four different peppers were considered for the
"Salsa in a jar" from section #7. The taste test rankings from 12 of each type of pepper were as follows:

Find: a) the variance between the different types of peppers, b) variance within each type of pepper, c) the F Test Statistic, d) the F critical value. Develop the Null and Alternative Hypothesis, and using a = 0.05 test your hypothesis. State your conclusion.

We will begin by entering the data into the appropriate LISTS. Press (you will see this screen).

Press [ always start from a clear list ]

Next enter each piece of data from sample1 into LIST1, sample2 into LIST2, etc.

(When you have finished all four LIST you should be looking at this screen)

3
Now press (you will again see this screen)

**Arrow right** to TESTS and **Arrow up** to **F : ANOVA (**

(you should see this screen.)

Press . (this screen appears)

Here we must enter all factors we want to test. For our problem it will be **L1, L2, L3, L4**.

so...press

This screen (the one on the right) can be seen by pressing the **Arrow down** key

As you can see from the screen the **MS Factor = 10.05** (this is the amount of variation between pepper types).

If we Arrow down we see that the **MS Error = 1.44** ( this is the amount of variance within each type of pepper).

The F Test Statistic is seen to be = 6.96. The **p-value = 0.00062**

The appropriate Hypothesis and Test :

**The Null Hypothesis is :**

**The Alternative Hypothesis is : Ha : at least one mean is different.**

Recall .

The **p-value = 0.00062 < 0.05 ** Therefore we should **reject Ho.**

From the tables in a Textbook we see that the **F c.v. = 2.83**
[k=3, n(k-1)=44]

Since our **F Statistic = 6.96 > 2.83. Again, we would reject Ho.**

In conclusion we say that at the 0.05 level of significance there is sufficient evidence to reject the claim that all four pepper types have the same mean "taste test" ranking.