Practical & Maths Skills: Statistical Tests

Question 1

What are statistical tests?

Answer 1

• Statistical tests are used to analyse data mathematically
• You can be more confident in your conclusions, if they’re based on results that have been analysed using statistical tests

Question 2

What kind of hypothesis do we have to use in statisical tests?

Answer 2

• You need to use a null hypothesis

- This hypothesis states that there is no significant difference or correlation between the things you’re investigating

Question 3

How are null hypothesises proved or disproved?

Answer 3

• With each statistical test, you calculate a critical value
• If the critical value is greater than the critical value at a probability (P value) of 5%, then you can be 95% confident that the difference is significant and not due to chance
• This is called a 95% confidence limit

Question 4

What is a Student’s t-test?

Answer 4

• Use the Student’s t-test when you have two sets of data you want to compare
• It tests whether there is a significant difference in the means of the two data sets
• If the value obtained from the t-test is greater than P value of 5%, then you can be 95% confident that the difference in means is significant and not due to chance

Question 5

What is a null hypothesis like for a Student’s t-test?

Answer 5

• There is no significant difference between X1 and X2

Question 6

What are conclusions like for a Student’s t-test?

Answer 6

• t < CV

• Accept null hypothesis – no sig. diff. between X1 and X2
• With 5% chance of error

• t > CV

• Reject null hypothesis – is sig. diff. between X1 and X2
• With 5% chance of error

Question 7

What is a chi-squared test?

Answer 7

• Use chi-squared test when you have categorical data and you want to know whether your observed results are statistically different from your expected results
• If your result is larger than the critical value at P = 0.05, you can be 95% certain the difference between the difference between observed and expected results is significant and not due to chance

Question 8

What is a null hypothesis for a chi-squared test like?

Answer 8

• There is no significant difference between the observed and expected values for all the categories

Question 9

What are conclusions like for a chi-squared test?

Answer 9

• X^2 < CV

• Accept null hypothesis – no sig. diff. between O and E
• With 5% chance of error

• X^2 > CV

• Reject null hypothesis – is sig. diff. between O and E
• With 5% chance of error

Question 10

What is a correlation coefficient?

Answer 10

• A correlation coefficient allows you to work out the degree to which two sets of data are correlated
• The Spearman’s rank correlation coefficient is an example
• It is given as a value between 1 and -1
• A value of 1 indicates a strong positive correlation
• 0 means there is no correlation
• -1 means there is a strong negative correlation

Question 11

How do we evaluate the Spearman’s rank correlation coefficient?

Answer 11

• If your result is higher than the critical value at P = 0.05, you can be 95% confident that the correlation between the two sets of data is significant and not due to chance

Question 12

What is a null hypothesis for the Spearman’s rank correlation coefficient like?

Answer 12

• rs < CV

• Accept null, the positive/negative correlation is not sig. and due to chance
• With 5% chance of error

• rs > CV

• Reject null, the positive/negative correlation is sig. and not due to chance
• With 5% chance of error

Question 13

How do we compare p-values to significance levels?

Answer 13

• Compare p-value to significance level
• If p-value is lower than significance level, reject null hypothesis
• If p-value is higher than significance level, we fail to reject null hypothesis