Pick appropriate weights

Must first confirm that the hypothesis are independent, then test them using planned comparisons. For example the following 3 hypothesis:

1. The analogue recording differs in realism from the digital recordings.

2. The digital compact disc recording differs in realism from the digital file types.

3. The two digital file types differ in realism from one another.

These would become… Appropriate Weights

The null hypotheses corresponding to each of the above hypotheses are:

Null Hypothesis 1:

Null Hypothesis 2:

Null Hypothesis 3:

Assign weights to conditions on left side of hypothesis that up to +1

Assign weights to condition on the right side that add up to -1

For Hypothesis 1, only the Vinyl Disc is on the left side of the hypothesis, so it gets a weight of +1. Compact Disc, Mp3 and wav are on the right side of the hypothesis, so they each get a weight of -1/3.

SPSS only allows you two decimal places when you enter a negative weight. We can get round it by multiplying all the weights for the hypothesis by an integer that makes them round numbers. So when we come to run the analysis on SPSS we will actually use the weights +3, -1, -1 and -1 rather than +1, -1/3, -1/3 and -1/3.)

Appropriate weights for the three hypotheses are:

VD CD mp3 wav Hypothesis 1 1 -1/3 -1/3 -1/3

(For SPSS 3 -1 -1 -1)

Hypothesis 2 0 1 -1/2 -1/2

Hypothesis 3 0 0 1 -1

Then Check For Independence…

The comparisons are all independent of each other (the sum of the products of the weights for each pair is zero):

Hypotheses 1 and 2: (1 x 0) + (-1/3 x 1) + (-1/3 x -1/2) + (-1/3 x -1/2) = 0 - independent

Hypotheses 1 and 3: (1 x 0) + (-1/3 x 0) + (-1/3 x 1) + (-1/3 x -1) = 0 - independent

Note that the above two calculations still yield 0 when the SPSS weights are used for Hypothesis 1.

Hypotheses 2 and 3: (0 x 0) + (1 x 0) + (-1/2 x 1) + (-1/2 x -1) = 0 - independent

If data doesn’t come to 0 must try again… probably entered data wrong…

Next use the t-test approach (taken by SPSS)

First we enter all the scores into a column of the SPSS Data Editor and name the column realism.

Alongside, we enter ten 1s, ten 2s, ten 3s and ten 4s to represent the different recording methods.

We’ll name this column method, and label its values Vinyl Disc, Compact Disc, mp3 and wav. The data look like this:

Run the data on SPSS

Analyse>Compare means>One way ANOVA

SPSS refers to Planned Comparisons as Contrasts..

Click on Options and request Descriptive (statistics):

Click on Continue and then on Contrasts to open the One Way Anova: Contrasts dialogue box:

SPSS requires that you specify the weights for each comparison. It allows only 3 decimal places for a positive weight and 2 decimal places for a negative one

If you have weights like 1/3, 1/6, etc. it’s probably better to multiply all the weights for the comparison by a value that makes them all whole numbers

So, instead of using 1, -1/3, -1/3, and –1/3 for the first hypothesis, it is better to use 3, -1, -1, and –1.

Enter coefficient in the coefficients box then click Add, allows you to enter the remaining three coefficients for the first comparison: -1, -1, -1. The window will now look like this:

That has set up the coefficients for the first hypothesis. You now have to click on Next, and enter the coefficients for the second hypothesis, 0, 1, -.5, and .5.

Note that for the second hypothesis we had to give the first condition a weight of 0 quite explicitly….

When all are entered… click continue and okay… follow for output

How to report descriptives

Descriptives

realism

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

Vinyl

10

46.0000

9.12871

2.88675

39.4697

52.5303

30.00

60.00

CD

10

60.9000

7.46027

2.35914

55.5632