Correlation Coefficient

Question 1

When would we use “correlation coefficient” statistical test?

Answer 1

• Two continuous variables (ie. variables that are measured.)
• Investigating an association/ link between the two measurements.

Question 2

Within what range will the correlation coefficient (rs) value be between, what would the values within the range show?

Answer 2

Between -1 and +1.
- 1 shows strongest negative correlation.
+1 shows strongest positive correlation.

Question 3

What do we do with our calculated correlation coefficient/ rs value to see whether there is a significant correlation between 2 continuous variables?

Answer 3

• Compare to critical value at P(0.05)

Question 4

What is the P value in relation to correlation coefficient?

Answer 4

• P value is probability that correlation is due to chance.

Question 5

Critical value table. You have seven pairs of data, how would you find the critical value in table?

Answer 5

• Look for value w/ “7 pairs of data”, P (0.05.)

Question 6

Investigation: effect of temperature on rate of enzyme-controlled reaction.
What is the null hypothesis?
I have calculated an rs value of 0.616 and the critical value at P(0.05) is 0.6786, what does this show?
Reject/ accept null hypothesis?

Answer 6

• Null hypothesis: there will be no significant correlation between temp and enzyme rate of reaction.
• rs value doesn’t exceed critical value, which is threshold value.
• This means there is MORE than 5% probability that correlation is due to chance.
• Accept null hypothesis: increase temp didn’t always result in increase in rate of enzyme-controlled reaction.

Question 7

What is meant when we say a critical value at P (0.05) is the threshold value?

Answer 7

• The rs value needs to be equal to / higher than critical value to prove that there is a signicant correlation between 2 continuous variables.

Question 8

Refer to graph on Miss Estruch video: 14.44.

Student conluded more glucose you add, the more bacteria there will be. Do you agree with this conclusion, use all information provided?

Answer 8

• Graph shows positive correlation between no of bacteria and concentration of glucose.
• However:
• The results overlap. For same conc of glucose, multiple different results for no of bacteria. This shows range in effect.
• Corelation coefficient shows 50% probability that it was due to chance so, not significant correlation, it must be less than 5% probability that it was due to chance.