F-Tables & Basic Ratios. Outline of Today’s Discussion 1.Some F-Table Exercises 2.Introduction...

F-Tables&

Basic Ratios

Outline of Today’s Discussion

1. Some F-Table Exercises

2. Introduction to Basic Ratios [Between-Subject ANOVA]

3. Independent Samples ANOVA in SPSS

Part 1

Some F-Table Exercises

Some F-Table Exercises

1. For the rest of your careers, you will likely be looking at ANOVAs, that is F-ratios, and so-called F-tables.

2. Let’s get some practice in really understanding it…

Some F-Table Exercises

Here’s a sample F-table.What are other names for these terms?

Some F-Table Exercises

According to the F-Table, should wereject or retain the null-hypothesis?

Some F-Table Exercises

According to the F-Table,does this study have validity?

Some F-Table Exercises

According to the F-Table, how many groups were there?

Some F-Table Exercises

According to the F-Table,how many participants were there

in each group?

Some F-Table Exercises

According to the F-Table,which groups, if any,

differed significantly from each other?

Some F-Table Exercises

According to the F-Table which was greater, the variance between groups,

or the variance within the groups?

Some F-Table Exercises

According to the F-Table, was the homogeneity of variance

assumption satisfied?

Some F-Table Exercises

1. Now, let’s further develop our understanding about the computations represented in the F-Table.

2. In each of the following F-Tables, some information is missing. Your job is to fill in the missing elements.

Some F-Table Exercises

Source SS df Mean Square F-Ratio pBetween Groups 40 3 13.33333333 14 ?Within Groups 20 21 0.952380952

Total 60 24 -

Is this F-ratio significant?(Hint: You can use your new excel tricks.)

Some F-Table Exercises

Fill in the blanks.

Source SS df Mean Square F-Ratio pBetween Groups 35 2 17.5 17.5 0.00189Within Groups ? ? ?

Total 42 9 -

Some F-Table Exercises

Fill in the blank.

Source SS df Mean Square F-Ratio pBetween Groups 10 2 5 ? 0.10628Within Groups 9 6 1.5

Total 19 8 -

Some F-Table Exercises

Source SS df Mean Square F-Ratio pBetween Groups ? 5 40 2 0.09688Within Groups ? 45 20

Total ? 50 -

Fill in the blanks.

Part 2

Introduction to “Basic Ratios”[Between-Subject ANOVA]

Introduction To Basic Ratios

1. One can calculate the F-ratio after finding the variances for each group, and the variances for the sample means.

2. There is an alternate method for making those calculations!

3. This method relies on so called “basic ratios”, which are special quantities that allow for simpler (?) manual computations of ANOVA.

Introduction To Basic Ratios

1. Each basic ratio is symbolized by a somewhat arbitrary capital letter (or perhaps a pair of capital letters).

2. By convention, basic ratios are written in side of brackets: Example [Y], or [A] or [T].

3. Let’s look at the most basic of the basic ratios…

Introduction To Basic Ratios

X 2[Y]

[Y] = The sum of the individual squared scores. (Square them first, then sum them.)

The basic ratio for individual participants is called [Y]

Introduction To Basic Ratios[Y] = The Sum of the Squared Scores

Raw Scores

SquaredScores

Introduction To Basic Ratios

[A] = The sum of the squared column totals, divided by # of subjects per condition.

(Square them first, then sum them.) Each column total corresponds to a

different level (a) of the I.V..

[A]

Ta

2

na

The basic ratio for groups (or conditions) is called [A]

Introduction To Basic Ratios

[A] = The Sum of the Squared Column Totals divided by n.

[A] = (1024 + 196 + 2116) / 6

Introduction To Basic Ratios

The basic ratio for grand total is called [T]

[T] = The grand total squared, divided by the total number of scores.

(Sum them first, then square them.) The total number of scores (N) equals a * n.

[T]

G2

N

Introduction To Basic Ratios

[T] = The Grand Total Squared divided by (capital) N.

[T] = 8464 / 18

Introduction To Basic Ratios

1. We can use these (and other) basic ratios to ‘build up’ the quantities in our F-Summary table.

2. Basic ratios are FLEXIBLE in the sense that we can use them for between-subjects or within-subjects ANOVAs, or one-way or factorial ANOVAs.

3. Let’s see how they work for the one-way between subjects case…

Between Subjects ANOVAs [Basic Ratios]

1. The basic ratios can be combined in various ways to give us the SS values in our F-Summary table.

2. The formulas for combining basic ratios are on your hand out…

Between-Subjects One-Way ANOVAUsing Basic Ratios

The F Table using basic ratios

Source SS DF Mean Square FBetween Conditions [A] - [T] a-1 SSb / DFb MSb / MSw

Within Conditions ("error") [Y] - [A] N - a SSw / DFw

Basic Ratios

Part 3

Independent Samples ANOVAIn SPSS

Independent Samples ANOVA in SPSS1. SPSS steps for an Independent Samples ANOVA:

2. Analyze ---> Compare Means ---> One Way ANOVA

3. “Depend List” = D.V. (from the list of variables)

4. “Factor” = I.V. (from the list of variables)

5. Options: “Descriptive Stats” & "Homogeneity..”

6. Post Hoc: “Scheffe” & “Tukey”

Independent Samples ANOVA in SPSS1. SPSS steps for an Independent Samples ANOVA:

2. Analyze ---> Compare Means ---> One Way ANOVA

3. “Depend List” = D.V. (from the list of variables)

4. “Factor” = I.V. (from the list of variables)

5. Options: “Descriptive Stats” & "Homogeneity..”

6. Post Hoc: “Scheffe” & “Tukey”