Psychology Notes > Statistics (2nd year) Notes

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GENERAL

4 questions, 1 each on:

2 way independent ANOVA

Mixed ANOVA

Regression (Stepwise)

Factor Analysis (PCA)

You will have to work out the diff between 2 way and mixed ANOVA regression and PCA will say

One or Two-Way

Independent ANOVA

Multiple regression

Factor analysis

Repeated Measures

(RM) ANOVA

Mixed ANOVA

Used to study differences in group means (along with interaction effects)

Used to study relationship between variables (whether certain variables predict an outcome variable)

Used to explore whether they is any meaningful pattern in data (no p values)

Used when there are more data points than Ps

And when you have 1 or more IV in a RM design

Used when you have some IV(s) which are of ind design, and some IV(s) which are RM design

Which ANOVA?

Ask:

What are the IVs? What is the DV?

How many IVs are there?

How many conditions of each IV?

Between subjects, within subjects, or both?

1.1 = small effect size

0.06 = medium effect size

0.14 = large effect size

Case:Variable 25:1, preferably 40:1

Checks for multicollinearity

A tolerance statistic of less than 0.1 is a serious problem

A tolerance statistic of less than 0.2 is a potential problem

Post hoc tests (work similar to t tests)

= tells us the direction of the differences between groups

If the main effect from the omnibus test is not sig you do not need to do any post hoc tests

If the main effect of the omnibus test is sig we do need to follow up with post hoc tests

Write out all descriptive stats just copy out SPSS table

ONE-WAY INDEPENDENT ANOVA = when IVs are in groups/conditions

= determines differences between groups when you have more than 2 conditions

SPSS instructions:

Analyse Compare mean 1-way ANOVA

IV in Factor box

DV in dependent list

Options select

Descriptive

Homogeneity of variance test

Welch ( test which corrects for unequal variance)

Means plot

Post Hoc select

Scheffe

Games-Howell

Continue OK

Step 1

Is the data suitable for a one way independent ANOVA?

More than 2 conditions

One nominal IV (more than 2 groups or categories)

One interval/ratio DV (on a continuous scale)

Step 2

Is the sample suitable for a one way independent ANOVA?

Roughly equal group sizes largest group size should be no more than twice the smallest group size

At least 30 cases in total

At least 10 cases in each group

(If you fewer cases than this, still run an ANOVA, just mention to be cautious about interpretation. If p values are in the region of .05 to .10, and/or the effect size is large, it is more likely that the result is not significant purely because of a lack of statistical power).

Step 3

Are there equal variances between the groups?

Check the Levene's statistic.

If not significant, groups have equal variance use the table which reports the standard F statistic.

If significant, it indicates that the groups differ significantly in their variance (ie unequal variance) use the table with Welch's F statistic.

Step 4

What do the results of the overall ANOVA tell us?

Report: F(df1, df2) = _ , p = _ , η² = _

η² = eta squared (the effect size). In the exam just write 'eta squared'.

Eta squared = (Between groups Ps) / (Total Ps) x100 to get % Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?

the p needs to be less than 0.05 to be sig

Step 5

Run post hoc tests (if the main effect of the ANOVA is significant)

If the Levenes test was not significant: Use the Scheffe test

If the Levenes test was significant: Use the Games-Howell test

Report mean scores for the groups

Look at p values from post hoc tests Interpret these ie if sig or not

TWO-WAY INDEPENDENT ANOVA

= when IVs are in groups/conditions = more than 1 IV

SPSS instructions:

Analyse General Linear Model Univariate

IV in Factor box

DV in dependent list

Plots select

Put first IV in horizontal axis

Put other IV in separate lines

Add

Do the same but reverse variables

OK

Options

Move all factors from L to RH side into 'display means for' box

From display section choose

Descriptive stats

Estimates of effect size

Homogeneity tests

Post Hoc

Select both variables from Factors box put into Post Hoc Tests for box

Scheffe

Continue OK

Step 1

Is the data suitable for a Two Way independent ANOVA?

More than 1 nominal IV (2 groups or more per IV)

1 interval/ratio DV (on a continuous scale)

Step 2

Report descriptive statistics (means, standard deviations) for each subgroup

Step 3

Is the sample suitable for a Two way independent ANOVA?

Roughly equal group sizes largest group size should be no more than twice the smallest group size

At least 30 cases in total

At least 10 cases in each group

(If you fewer cases than this, still run an ANOVA, just mention to be cautious about interpretation. If p values are in the region of .05 to .10, and/or the effect size is large, it is more likely that the result is not significant purely because of a lack of statistical power)

Step 4

Are there equal variances between the groups?

Check the Levene's statistic.

If not significant, groups have equal variance use the table which reports the standard F statistic. If significant, it indicates that the groups differ significantly in their variance (ie unequal variance) use the table with Welch's F statistic.

Step 5

What do the main effects of the ANOVA tell us?

Report: F(df1, df2) = _ , p = _ , η² = _ for each main effect

η² = partial eta squared (the effect size). In the exam just write 'eta squared' SPSS calculates this

Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?

the p needs to be less than 0.05 to be sig

What does the interaction effect tell us?

Report: F(df1, df2) = _ , p = _ , η² = _

Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?

Step 6

The next step will depend on the results of the main effects and interaction effect:

Significant main effects?

YES: Interpret the direction of the main effects (use the mean scores ignoring the effect of the other IV). If there are more than 2 groups, use the post hoc tests to work out the group differences

NO: If neither of the main effects is significant then move on to the interaction effect no need to interpret the direction of the effect if it's not significant in the first place

Significant interaction effect?

YES: Conduct simple effects analysis using either T tests or One Way ANOVA. Interpret the results.

NO: Focus on the significant main effects need to interpret the plot if the interaction is not significant in the first place.

When the interaction is sig SIMPLE EFFECTS/FOLLOW UP ANALYSIS

Data Split file

Compare groups place the IV with 3 conditions in box OK

analysis will now be done on each separate group

Running t tests:

Analyse Compare Mean Ind t test

Place IV that you HAVE NOT split into Grouping variables box

Place DV in Test Variable box

Define groups Enter coding from variable view into group 1 and 2

OK

Report Levene's for each

Don't need to report each group if they are all sig/non-sig, just state as such

Step 7

Give a general conclusion/summary regarding the results

REPEATED MEASURES ANOVA Used when there are:

More than 2 conditions of an IV

More than 1 IV

SPSS instructions:

Analyse General Linear Model Repeated Measures

In RM Design box:

Replace factor1 with the variable name

Input number of conditions into Number of Levels

Add Define

Select each level of the variable and use right arrow to put them into the Within Subjects variables

Options Desc Stats

OK

Step 1

Is the data suitable for a RM ANOVA?

DV measured on an interval/ratio scale

More than 1 IV

Normal distribution of scores on the DV

Step 2

Report descriptive statistics (means, standard deviations) for each subgroup

Step 3:

Is the sample suitable for a RM ANOVA?

Minimum of 10 Ps In a RM design, fewer Ps are usually required

Step 4: Mauchly's Test of Sphericity

Are there equal variances between differences in condition means?

Similar to Levenes

We need at least 3 conditions for this to be an issue

If not significant, differences have equal variance sphericity is assumed

Step 5: Tests of Within-Subjects Effects table

What does the overall main effect of the ANOVA tell us?

If Mauchly test is non-sig, use the rows labelled Sphericity Assumed

If Mauchly test is sig, use the rows labelled Greenhours-Geisser this changes the df, thus the assoc

Mean Squares

Report: F(df1, df2) = _ , p = _ , η² = _ for main effect

η² = partial eta squared (the effect size). In the exam just write 'eta squared' SPSS calculates this

Interpret: Was the p value significant? What was the effect size? Is this a small/medium/large effect?

Step 6: Post hoc tests

Where do the differences lie? use post hoc tests to determine the specific difference

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