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Statistical Tests

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Statistical Tests

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 non-parametric (for when our data is non-evenly distributed).

Parametric 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 parametric tests

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

Parametric testWhat it measures? Example research scenario
CorrelationThe relationship (strength and direction) between two variablesThe relationship between fitness test scores and the number of hours spent exercising
Paired t-testCompares the mean value of two variables obtained from the same participantsThe difference in depression scores in a group of patients before and after treatment
Unpaired t-testCompares 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
One-way Analysis of Variance (ANOVA)Compares the mean of two or more independent groups (uses a between-subject 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
One-way Repeated Measures (ANOVA)Compares the mean of three or more conditions when the participants are the same in each group (uses a within-subject 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

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.

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.

Steps of the sign test

Let us look out how to calculate a sign test step-by-step 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
12522
23621
32024
44030
51719
62020
72623
82734
92525
102828

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).

ParticipantAnxiety score before CBTAnxiety score after CBTDifference
12522-3
23621-15
32024+4
44030-10
51719+2
620200
72623-3
82734+7
925250
1028280

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 ‘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.

Level of significance for a one-tailed test

.05

.025

.01

.005

Level of significance for a two-tailed 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

  1. 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).
  2. What is the significance level? Unless specified, the significance level is always .05
  3. 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 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.

Types of errors in hypothesis testing

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.

Statistical Tests - Key takeaways

  • Statistical tests are tests that are used to analyse data from experiments.
  • There are two types of tests; parametric and non-parametric tests. Parametric tests are used on normally distributed data, and non-parametric tests on data that is not normally distributed.
  • The sign test is non-parametric.
  • 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.

Frequently Asked Questions about Statistical Tests

The type of statistical test used for analysis depends on:

  • Whether the data meets the assumption for parametric or non-parametric tests 
  • The type of information the researcher wants to find from data, e.g., a correlation would be used if the researcher wants to identify if there is a relationship between two variables.

Statistical tests are tests used to analyse data from experiments.

There are two types of statistical tests, parametric and non-parametric tests. 

The type of statistical test used depends on: 

  • Whether the assumptions are met or violated of parametric and non-parametric tests
  • What the hypothesis aims to measure, e.g., a correlation when the research aims to measure the association between sunlight exposure and growth of plants.

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. 

Final Statistical Tests Quiz

Question

What is a type 1 error? 

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Answer

A type 1 error is when the researcher rejects the null hypothesis when it is true (false positive).

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Question

What is a type 2 error? 

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Answer

A type 2 error is when the researcher mistakenly accepts the null hypothesis and rejects the alternative hypothesis when it is true.

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Question

Why is hypothesis testing used in psychology research?

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Answer

Hypothesis testing is a statistical test used in experimental research to identify if the alternative or null hypothesis should be accepted in research. 

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Question

Which hypothesis should be accepted if significant findings are found? 

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Answer

Significant findings mean the alternative hypothesis should be accepted and the null hypothesis rejected.

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Question

Which hypothesis should be accepted if insignificant findings are found? 


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Answer

Insignificant findings mean the null hypothesis should be accepted, and the alternative hypothesis rejected.

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Question

Why is hypothesis testing used as an analysis method?

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Answer

Results are more likely to be valid

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Question

Which of the following is the definition of the null hypothesis?

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Answer

The researcher predicts there will be no difference in the results found between the groups (e.g., control versus experimental).

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Question

Which of the following is the definition of the alternative hypothesis?

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Answer

The researcher predicts there will be no difference in the results found between the groups (e.g., control versus experimental).

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Question

Which of the following describes what a one-way ANOVA measures?

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Answer

The relationship (strength and direction) between two variables

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Question

Which of the following tests should be used when researching the difference in average fitness test scores during the morning, afternoon, and evening?

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Answer

One-way Analysis of Variance (ANOVA)

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Question

What is the difference between paired t-tests and unpaired t-tests?

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Answer

A paired t-test analyses data from the same participants but in different conditions, e.g., different times. Whereas, unpaired t-tests compare the mean of participant’s scores from two different groups.

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Question

What information can researchers get when carrying out a correlation to identify the relationship between variables? 

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Answer

The information researchers can get when using a correlation is the strength and direction of the relationship between two variables.

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Question

What are the assumptions of parametric tests?

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Answer

  • Data must be normally distributed 
  • Homogeneity of variance
  • No extreme outliers 
  • Data should be independent

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