11 Correlations and Chi square test

Transcription

1 11 Correlations and Chi square test We are now approaching the final statistical tests that you will learn in this course, Correlations and the Chi square test. Correlations Correlations are used to look for a relationship and not a difference between two groups. Data have to be organised in the same way as for a timepoint comparison (e.g. each measurement in the same row). For correlations, I will introduce another decision tree, however both the main correlations are found in the same place in SPSS: Apart from the two statistical tests, the only new point in this decision tree is the small sample size decision. We will learn later what is considered a small and what is a large sample size (there is no formal test for this). Experimental data (for Exercise ): We have measurements of sugar levels and BMI for each of our patients and we want to know if there is a relationship between these two factors. 1

2 Exercise 11.1: 1. In the Excel spreadsheet Excercises_4, select the tab Pearson Correlation I. 2. Copy and paste the raw data into the SPSS Data View tab. 3. Label the data appropriately in the Variable View tab. 4. In the menu, go to Analyse->Correlate->Bivariate (see screen shot). 5. A new window called Bivariate Correlations opens up. You can see that the box for Pearson is ticked and that there is also a tick box for Spearman. 6. Using the blue arrow, transfer sugar and BMI over into the box called Variables (see screen shot). 7. Select OK. 2

3 8. From the table in the SPSS output window (which shows each correlation twice) you will need two numbers. The p-value, which tells you if there is a relationship yes or no (the p- value has to be<0.05 for the answer Yes) and the Pearson Correlation value, which tells you how strong the correlation between the two variables is (see screen shot). The Pearson (or any other correlation) has a value between 0 and 1 (or -1 and 0, if the correlation is negative). The closer the number is to 1, the stronger is the correlation. If the number is <0.3, we talk of this being a weak correlation. If the number is >0.75, we talk of this being a strong correlation. In our example, the correlation is weak (0.315). However, this does not really fall into account as the p-value (0.054) is not significant and hence in fact there is no relationship between the BMI and sugar level at all. Exercise 11.2: 1. In the Excel spreadsheet Excercises_4, select the tab Pearson Correlation II. 2. Repeat exercise 11.1 with this new dataset. Solution Exercise 11.2: This time, the correlation is highly significant (p<0.001) and also rather strong (0.662). 3

4 Exercise 11.3: 1. In the Excel spreadsheet Excercises_4, select the tab Spearman Rank I. 2. Copy and paste the raw data into the SPSS Data View tab. 3. Label the data appropriately in the Variable View tab. 4. In the menu, go to Analyse->Correlate->Bivariate and untick the box for Pearson and select the box for Spearman (see screen shot). 5. Select O.K. In our example, the correlation (here called Spearman s rho) is weak (0.211) and not significant (p=0.204). Exercise 11.4: 1. In the Excel spreadsheet Excercises_4, select the tab Spearman Rank II. 2. Repeat exercise 11.3 with this new dataset. 4

5 Solution Exercise 11.4: We have a strong (0.658), highly significant (p<0.001) correlation between sugar levels and BMI. Chi square test The Chi square test is a very simple statistical test for datasets in which only Yes-No answers exist (it is a non-parametric test) and is often used in the clinical field to evaluate if patient groups are matched. For example, it is used for comparisons of gender, races, or blood groups. Experimental data (for Exercise ): We want to know if there is a difference in the number of males and females or in the number of blood groups A and B in two study populations. Exercise 11.5: 1. In the Excel spreadsheet Excercises_4, select the tab Chi Square I. 2. Copy and paste the raw data into the SPSS Data View tab. 3. Label the data appropriately in the Variable View tab. 4. In the menu, go to Analyse-> Nonparametric tests->legacy dialogs-> Chi square (see screen shot). 5

6 5. In the window called Chi Square test that opens up, use the blue arrow to transfer Gender over into the box called Test Variable List (see screen shot). 6. Select OK. 6

7 The Output Window shows a table called Test Statistics, where we find the p-value of the test. In this case, the p-value is not significant (p=0.763), meaning that there is no difference in the proportion of genders. Exercise 11.6: 1. In the Excel spreadsheet Excercises_4, select the tab Chi Square II. 2. Repeat exercise 11.5 with this new dataset. Solution Exercise 11.6: This time, the p-value is significant (p<0.05), meaning that there is a difference in the number of cases with blood group A and blood group B. 7