Correlation Coefficient
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When would we use “correlation coefficient” statistical test?
• Two continuous variables (ie. variables that are measured.) • Investigating whether correlation between two variables is significant.
Within what range will the correlation coefficient (rs) value be between, what would the values within the range show?
Between -1 and +1. - 1 shows strongest negative correlation. +1 shows strongest positive correlation.
What do we do with our calculated correlation coefficient/ rs value to see whether there is a significant correlation between 2 continuous variables?
• Compare to critical value at P(0.05)
What is the P value in relation to correlation coefficient?
• P value is probability that correlation is due to chance.
Critical value table. You have seven pairs of data, how would you find the critical value in table?
• Look for value w/ “7 pairs of data”, P (0.05.)
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?
• 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.
What is meant when we say a critical value at P (0.05) is the threshold value?
• The rs value needs to be equal to / higher than critical value to prove that there is a signicant correlation between 2 continuous variables.
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?
• 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.