Psychology: Research methods 21 (Calculated and critical values)

What are calculated and critical values

Once the statistical test is selected, the test is carried out (by hand or computer). From this a calculated value is produced. This calculated value is then compared with the critical value. 

What do we need to know to find the critical value

1) One-tailed or two-tailed tests - If the hypothesis made was directional then a one-tailed test is used, if the hypothesis was non-directional (because there was no previous research) then a two-tailed test is used. It is harder to get a significant result with a two-tailed test as the minimum probability is halved to cover each tail.  

2) Significance level – this will usually be the 0.05 level. However, sometimes a more stringent (e.g., 0.01) level is needed e.g., if an incorrect conclusion could be a risk to life. 

3) Value of N – this is the number of participants in the study. In some tests this is calculated as the degrees of freedom. 

What do the values indicate

For some tests the calculated value must be more than the critical value (TCPs) for the result to be significant, whereas in others the calculated value needs to be less than the critical value (S(b)MW):  

If the calculated value is higher or lower (depending on the test) then the probability that the result (difference/correlation) occurred by chance is less than 5% (p<0.05) and the alternative hypothesis is accepted.

When do we use the sign test

We use the Sign test when: 

• We are looking for a difference between two sets of data 

• The design was related (repeated measures or matched pairs) 

• Data is nominal (in categories)

What are the steps of doing a sign test

Step 1 – convert data into nominal data (increase (+), decrease (-) or no change (0)) 

 

Step 2 – Add up the signs 

 

Step 3 – Total the number for the less frequent sign. This is the calculated value 

 

Step 4 – Compare the calculated value with the critical value found in the table. You need to have the following information: 

• Was the hypothesis directional or non-directional hypothesis  

• The significance level (usually 0.05) 

• The number of participants (N) 

 

Step 5 – If the calculated value is less than or equal to the critical value, then the probability that the results occurred by chance is less than 5% so the alternative hypothesis can be accepted. 

Give an example

 

Example –Hypothesis (directional): The number of people who are happier after a holiday will be significantly higher than the number who were happier before 

 

Happier before	Happier after	No change
2	10	2

Table: Number of people who are happier before or after a holiday 

 

Calculated value = 2.  Now find the critical value. 

Critical value table 

Level of significance for a one-tailed test
	.05		.025		.01		.005
Level of significance for a two-tailed test
N	.10	.05		.02		.01
11	2	1		1		0
12	2	2		1		1
13	3	2		2		2

1) Hypothesis is directional so a one-tailed test is used 

2) Look at the column for  

p < 0.05 

3) N = 12 (ignore participants with no change) 

 

The calculated value must be less than or equal to the critical value  

Calculated value = 2                                              Critical value = 2  

Check that the results go in the correct direction i.e. people are happier after a holiday than before 

The calculated value is less than the critical value at p<0.05, therefore the probability that the results occurred by chance is less than 5%. The alternative hypothesis is accepted.