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1. Spearman’s Rank Order Correlation Coefficient What is it and when is it used? Spearman’s Rho is used when we are trying to find a ____________________ between two ____ _____________________. The two sets of data have to be _______________. The level of measurement also has to produce ______________data. Examples Is there a relationship between the cost of chocolate and the taste? Hypotehsise! Experimental: ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ Null: ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ Probability level I am willing to accept is_____ Table to show___________________________ Graph to show______________________________________ __________________________________________ ___________________________________________________ (Complete with scores)
2. What do your descriptive results tell you? ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ (If we didn’t have a correlation, let’s pretend we did for the purposes of the next bit!) Now for the inferential stats! How does it work? We need to rank two sets of data, compare the rank of each data set, and then using this to find a correlation co-efficient. The closer the rank of the two sets of data, the stronger the relationship. How do we use it? Using this test will give us an observed value (called a correlation co-efficient) between __________ and __________, which shows the strength of the relationship. 1) 1) First calculate the sum of differences squared (⅀d²) 2) However, to know whether or not the result is significant, we need to look up our result on a table of critical values. To do this we need two pieces of information. a. Did you write a directional (one tailed) or non directional (two tailed) hypothesis? b. How many ___________________ were in the study? This number is called N (number of chocolates in our case!). Using this information, we compare our observed value with the _______________ value on the table. If our observed value is equal to or higher, we reject our _______________ hypothesis and accept the _________________ hypothesis. #cho c a) Price per 100g b) Mean Taste score c) Rank for column (a) d) Rank for column (b) Diff = d (ra-rb) d² 1 2 3 4 5 ⅀d² Now the calculation Σd2 = _______ N = _____ CV(5) = ______ )1( 6 1 2 2 − Σ −= NN d rs )1_____(____ ____6 1 2 − × −=sr _______ ______ 1 −=sr sr = 1 - _______ sr = ________ this is a positive / negative correlation.
3. If however, we predicted a positive correlation, but we found a negative correlation (or the vice versa), we would still reject the _________________ hypothesis as the correlation was in the wrong direction. We then use this information to state our conclusion. OUR RESULTS: The calculated correlation coefficient of ________ is higher than/ less than the critical value of ______ where N = ________ for a ____-tailed test. There is/is not a significant correlation at p<0.___. Therefore I need to __________ the experimental hypothesis and _______________ the null hypothesis because…. __________________________________________________________________________________________________ __________________________________________________________________________________________________ Extra practice! For the following, look up the critical value and write an appropriate conclusion A. There will be a relationship between how many burgers a person eats and their self esteem. Participants: 18 students. Observed value: +0.494 B. There will be a positive relationship between a person’s height, and their reaction time. Participants: 7 men. Observed value: +0.699 C. There will be a negative correlation between the number of friends a person has on Facebook, and the hours spent revising for an exam. Participants: 29 year 8 students. Observed value +0.458
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