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Suppose you are a researcher and you want to find out if there is a difference between the anxiety levels of patients before and after 12 weeks of cognitive behavioural therapy. How would you know if the results you obtained are significant? Does cognitive behavioural therapy make a significant difference in anxiety levels? This is where statistical tests come in.
Hypothesis testing statistics is when statistical tests are used in experimental research to identify if the alternative or null hypothesis should be accepted in research. If findings are significant, the alternative hypothesis should be accepted, and the null hypothesis rejected.
Statistical tests in psychology are tests that analyse data from experiments.
Let us look at the types of statistical tests in psychology. These are parametric (for when data is normally distributed) and nonparametric (for when our data is nonevenly distributed).
Parametric tests are a type of statistical test used to test hypotheses. A criterion for the data needs to be met to use parametric tests. The criteria are:
Data must be normally distributed.
Homogeneity of variance – the amount of ‘noise’ (potential experimental errors) should be similar in each variable and between groups.
There should be no extreme outliers.
Independence – the data from each participant in each variable should not be correlated. Measurements from a participant should not be influenced or associated with other participants.
There are several types of parametric tests, and the one that is used depends on what the researcher is trying to investigate:
Parametric test  What it measures?  Example research scenario 
Correlation  The relationship (strength and direction) between two variables  The relationship between fitness test scores and the number of hours spent exercising 
Paired ttest  Compares the mean value of two variables obtained from the same participants  The difference in depression scores in a group of patients before and after treatment 
Unpaired ttest  Compares the mean value of a variable measured from two independent (different groups)  The difference between depression symptom severity in a placebo and drug therapy group 
Oneway Analysis of Variance (ANOVA)  Compares the mean of two or more independent groups (uses a betweensubject design and the independent variable needs to have three or more levels)  The difference in average fitness test scores of individuals who exercise frequently, moderately, or do not exercise 
Oneway Repeated Measures (ANOVA)  Compares the mean of three or more conditions when the participants are the same in each group (uses a withinsubject design and the independent variable needs to have three or more levels)  The difference in average fitness test scores during the morning, afternoon and evening 
Nonparametric tests can be used when data is not normally distributed. There are several nonparametric tests. One we will be looking at here is the sign test.
The sign test is used for withingroup studies (only one group of participants). However, two groups of participants could be used under a ‘matchedpairs’ design. The sign test assesses the difference between two conditions used on categorical data.
Let us look out how to calculate a sign test stepbystep with the use of an example.
A researcher aims to identify a difference between patients’ anxiety scores before and after 12 weeks of cognitive behavioural therapy (CBT).
Here are the study results:
Participant  Anxiety score before CBT  Anxiety score after CBT 
1  25  22 
2  36  21 
3  20  24 
4  40  30 
5  17  19 
6  20  20 
7  26  23 
8  27  34 
9  25  25 
10  28  28 
1. Work out the difference between the two sets of data (it doesn’t matter which column is added/subtracted from which, the data will still end up with the same results).
Participant  Anxiety score before CBT  Anxiety score after CBT  Difference 
1  25  22  3 
2  36  21  15 
3  20  24  +4 
4  40  30  10 
5  17  19  +2 
6  20  20  0 
7  26  23  3 
8  27  34  +7 
9  25  25  0 
10  28  28  0 
2. Add up the total number of ‘+’ and ‘’. Ignore the data where there is no difference (i.e., the difference of 0).
For our data, we have:
+ = 3
 = 4
3. The less frequent sign is the ‘Svalue’.
Here the Svalue = 3 (the + was the less frequent sign, and the + had a total of 3)
Find out the N value (number of participants, not including those with a difference of 0).
Here the N value is 10  3 = 7 (we had 10 participants minus the 3 that had a difference of 0)
4. Compare the calculated Svalue to the critical value to determine if it is significant. A critical values table will always be given to you in an exam.
Level of significance for a onetailed test  
 .05  .025  .01  .005  
Level of significance for a twotailed test  
 .10  .05  .02  .01  
N 



 
5  0 


 
6  0  0 

 
7  0  0  0 
 
8  1  0  0  0  
9  1  1  0  0  
10  1  1  0  0  
11  2  1  1  0  
12  2  2  1  1  
13  3  2  1  1  
14  3  2  2  1  
15  3  3  2  2  
16  4  3  2  2  
17  4  4  3  2  
18  5  4  3  3  
19  5  4  4  3  
20  5  5  4  3  
25  7  7  6  5  
30  10  9  8  7  
35  12  11  10  9 
From the table, our critical value is 0.
The calculated value (Svalue) must be equal to or less than the critical value to be significant.
Our results are insignificant because the calculated value (3) is greater than the critical value (0).
You could write your answer up as:
The calculated value (S=3) is greater than the critical value of 0. Therefore, the difference in anxiety scores before and after cognitive behavioural therapy is not significant.
S(3) > 0 (critical value)
What makes a test statistically significant?
Significance tests provide researchers with a statistical value used to measure how likely the results from research are due to chance. If the value is lower than .05, then the results are statistically significant.
Researchers can sometimes make a Type 1 or Type 2 error when carrying out research. When either error occurs in research, then it lacks validity.
Type 1 error: rejecting the null hypothesis when it is true (false positive), which happens when the researcher identifies that their data is significant when it is not.
Type 2 error: mistakenly accepting the null hypothesis and rejecting the alternative hypothesis when it is true.
The type of statistical test used for analysis depends on:
Statistical tests are tests used to analyse data from experiments.
There are two types of statistical tests, parametric and nonparametric tests.
The type of statistical test used depends on:
Significance tests provide researchers with a statistical value used to measure how likely the results from research are due to chance. If the value is lower than .05, then the results are statistically significant.
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