Statistical Tests

Psychology Statistical Test

Some examples of statistical tests include the chi-square test, Pearson’s correlation or the Sign Test.

There are parametric (for when data is normally distributed) and non-parametric (for when our data is non-evenly distributed).

Statistical Test Importance

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 the findings are significant, the alternative hypothesis should be accepted, and the null hypothesis should be rejected.

Statistical tests allow researchers to identify if the results are due to chance or if they are a result of the study and will enable the researcher to compare to previous findings.

Parametric Statistical Tests

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.

Types of Statistical Tests

Statistical tests are either parametric or non-parametric.

Some examples of parametric tests are as follows:

And some examples of non-parametric tests are as follows:

Psychology Statistical Tests: Types of Parametric Tests

There are several types of parametric tests, and the one that is used depends on what the researcher is trying to investigate:

Non-Parametric Tests

Non-parametric tests can be used when data is not normally distributed. There are several non-parametric tests. One we will be looking at here is the sign test.

Statistical Tests: Sign Test

The sign test is used for within-group studies (only one group of participants). However, two groups of participants could be used under a ‘matched-pairs’ design. The sign test assesses the difference between two conditions used on categorical data.

Statistical Tests: Sign Test Calculation

Let us look at how to calculate a sign test step-by-step with an example.

Here are the study results:

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).

2. Add the total number of ‘+’ and ‘-’. Ignore the data where there is no difference (i.e., the difference of 0).

For our data, we have the following:

+ = 3

- = 4

3. The less frequent sign is the ‘S-value’.

Here the S-value = 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 S-value to the critical value to determine if it is significant. A critical values table will always be given to you in an exam.

• Is the test one-tailed or two-tailed? In our example, our study is two-tailed as we wanted to see if there was a difference either way (positive or negative).
• What is the significance level? Unless specified, the significance level is always .05
• How many participants are there? The N-value. For our example, it is 7.

From the table, our critical value is 0.

The calculated value (S-value) 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 insignificant.

S(3) > 0 (critical value)

Errors in Hypothesis Testing

Researchers can sometimes make a Type 1 or Type 2 error when conducting research. When either error occurs in research, then it lacks validity.