Qualitative variables are ones for which we cannot calculate averages. The variables have categories, and we can count how many cases fall in each category. Examples of such variables are: sex, voting behaviour, attitude, marital status, employment status, occupation, religious affiliation, etc.

 

In all of the following cases we will be dealing with two variables.

·        The independent variable, or cause, will be qualitative.

·        The dependent variable will be qualitative.

 

We will start with a simple quasi-experimental design – a before and after experiment with no control group. We have written a manual that provides instructions on how to change a bicycle tire. We want to know if the manual helps people learn how to change a bicycle tire. Our independent variable is the presence or absence of the instruction manual. Our dependent variable is whether people learn how to change a tire successfully. Each variable has only two values: presence or absence of the manual, and success or failure in changing a tire.

 

Each individual in a random sample of 40 people is given a bicycle with a flat tire, spare parts and various tools. Each person is given twenty minutes to change the tire. Eleven (12) of the individuals successfully change the tire. We then give everyone the manual to read. After 10 minutes we again give each individual a bicycle with a flat tire. After twenty minutes we find that 30 of the individuals have successfully changed the tire.

 

In order to see if there is an improvement, we compare the proportion who could change a tire after reading the manual to the proportion who could change it before the manual. When the dependent variable is qualitative, we compare the proportions before and after, not the actual number.

 

Diffexp = Posttestexp – Pretestexp

Diffexp = 30/40 – 12/40 = 0.75 – .30 = .45.

We see that .75, or 75% of the individuals could change a tire after reading the manual, compared to only .3 or 30% who could change it without reading the manual. This is an increase of 45%.

 

While there is an increase in the proportion of people that can change a bicycle tire, we cannot be sure that these individuals wouldn’t have improved anyway. Those who were unsuccessful the first time may have just needed more time to figure it out. They may have learned from their mistakes during the pretest. To get around this problem, the researchers use a control group. The control group receives the pre-test, but not the training manual. The results are as follows:

 

 

Sample size

Pretest

Stimulus

Posttest

Experimental

40

12

Training manual

30

Control

40

12

None

20

 

 

 

Pretest

Stimulus

Posttest

Experimental

.30

Training manual

.75

Control

.30

None

.50

 

The following calculations are made to determine if there is an experimental effect:

 

Diffexp = Posttestexp – Pretestexp       =      .75 – .30 = .45

Diffcontrol = Posttestcontrol – Pretestcontrol      =      .50 – .30 = .20

Effect = Diffexp – Diffcontrol            =      .45 – .20 = .25

Interpretation: On average the 25% more individuals in the experimental group than the control group could change a tire. We attribute this to the training manual.

 

For those of you with a background in statistics, we would carry out a statistical test to determine if the differences between the two groups are statistically significant.

Example

 

Hypothesis: Does the drug Antabuse reduce drinking among recovering alcoholics? Antabuse is a drug that makes people feel sick when they drink alcohol. They throw up.

 

A sample of recovering alcoholics is asked if they had any alcoholic drinks in the previous week. The individuals in the sample then receive the drug. A week later they are asked if they had any alcoholic drinks in the previous week. During the same period a control group of alcoholics is also asked if they had any alcoholic drinks during each period. The results are recorded below:

 

Experimental group

 

Control group

ID

First week

(before receiving Antabuse)

Second week

(after receiving Antabuse)

 

ID

First week

 

Second week

 

1

Yes

No

 

 

Yes

No

2

No

No

 

 

Yes

Yes

3

Yes

Yes

 

 

No

No

4

No

No

 

 

Yes

No

5

Yes

No

 

 

No

Yes

6

Yes

No

 

 

No

No

7

No

No

 

 

Yes

Yes

8

Yes

Yes

 

 

No

No

9

No

No

 

 

Yes

Yes

10

Yes

Yes

 

 

Yes

Yes

 

 

Results:

·        Proportion that drank prior to treatment:      6/10 = .6

·        Proportion that drank after treatment:      3/10 = .3

·        Diffexp = Posttestexp – Pretestexp       =.3 –.6 =    -.3

 

Thirty percent (30%) fewer of the experimental group didn’t drink.

This may be due to the Antabuse.

It could be due to other factors that we haven’t controlled for.

 

To check this we compare changes in the experimental group to changes in the control group.

·        Proportion that drank prior:      6/10 = .6

·        Proportion that drank post:      3/10 = .5

·        Diffexp = Posttestexp – Pretestexp       =.5 –.6 =    -.1

 

Fewer people in the control group drank. There was a 10% drop.

Effect = Diffexp – Diffcontrol            =      -.3 – -.1  = -.2

Antabuse reduced the proportion of people drinking by .2, or 20%.

 

 

 

Case 1

 

Case 2

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.57

.53

 

.57

.53

Control

.56

.52

 

.55

.55

 

Case 1:            Experimental effect is zero.

 

Case 2:            Experimental effect is -.04 or a drop of 4%.

 

 

 

Case 3

 

Case 4

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.37

.42

 

.14

.27

Control

.37

.35

 

.13

.19

 

Case 3: The net experimental effect is an increase of .07, or 7%.

 

Case 4: The net experimental effect is an increase of .07, or 7%.

 

 

 

Case 5

 

Case 6

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.07

.19

 

.38

.35

Control

.11

.12

 

.37

.26

 

Case 5: The experimental effect is an increase of .11.

 

Case 6 The experimental effect is an increase of .08.

 

 

Experimental group

 

Control group

ID

First week

(before receiving Antabuse)

Second week

(after receiving Antabuse)

 

ID

First week

 

Second week

 

1

Yes

No

 

 

Yes

No

2

No

No

 

 

Yes

Yes

3

Yes

Yes

 

 

No

No

4

No

No

 

 

Yes

No

5

Yes

No

 

 

No

Yes

6

Yes

No

 

 

No

No

7

No

No

 

 

Yes

Yes

8

Yes

Yes

 

 

No

No

9

No

No

 

 

Yes

Yes

10

Yes

Yes

 

 

Yes

Yes

 

 

 

 

 

 

Case 1

 

Case 2

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.57

.53

 

.57

.53

Control

.56

.52

 

.55

.55

 

 

 

 

 

 

Case 3

 

Case 4

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.37

.42

 

.14

.27

Control

.37

.35

 

.13

.19

 

 

 

 

 

 

Case 5

 

Case 6

 

Pretest

Posttest

 

Pretest

Posttest

Experimental

.07

.19

 

.38

.35

Control

.11

.12

 

.37

.26