maths

Question 1

what is a correlation?

Answer 1

the process of establishing a relationship or connection between two or more things

Question 2

what statistical test do you need to do to see if there is a significant correlation between two variables?

Answer 2

spearman’s rank correlation

Question 3

what is the formula for spearman’s rank correlation coefficient?

Answer 3

rₛ = 1 - (6Σd² / (n (n²-1))

Question 4

what do the different aspects of spearman’s rank stand for?

Answer 4

• Σ = the sum of
• d = the difference in rank
• n = the total number of data pairs

Question 5

what do the results of spearman’s rank correlation mean?

Answer 5

• the result of the test will be a number between +1 and -1. if it isn’t you’ve done it wrong
• +1 means there is a perfect positive correlation (as one variable increases, so does the other)
  -1 means there is a perfect negative correlation (as one variable increases, the other decreases)
• 0 means there is no correlation

Question 6

what is the process of calculating spearman’s rank?

Answer 6

1. rank both sets of data, highest value for each value is given 1 and so on
2. work out the difference between the two values in each pair
3. square the difference
4. add them all up (Σ)
5. multiply by 6

Question 7

how do you work out if your value is significant in spearman’s rank?

Answer 7

• look at the critical value table for spearman’s rank (given)
• find the 95% confidence column (0.05)
• look at the number of data points used. this is your critical value
• compare your spearman rank value (ignore any minus signs)

Question 8

when you do you accept and reject the null hypothesis in spearman’s rank?

Answer 8

• if the spearman rank value is larger than the critical value, there is less than 5% probability the correlation is due to chance. we reject the null hypothesis
• if the spearman rank value is smaller than the critical value, there is greater than 5% probability the correlation is due to chance. we accept the null hypothesis

Question 9

what statistical test do you use to compare means to see for statistically significant differences?

Answer 9

student’s t-test

Question 10

how do you interpret the results of a student’s t-test?

Answer 10

• value of ≤ 0.05 means there is a significant difference between the means
• value of ≥ 0.05 means there is no significant difference between the means

eg. if your t-test value is ≥0.05, you have more than a 5% probability that the difference is due to change. we accept the null and reject the alternate hypothesis