{"id":616,"date":"2015-07-20T13:29:32","date_gmt":"2015-07-20T17:29:32","guid":{"rendered":"http:\/\/sites.berry.edu\/vbissonnette\/?page_id=616"},"modified":"2016-06-24T08:16:08","modified_gmt":"2016-06-24T12:16:08","slug":"spearman-correlation","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/spearman-correlation\/","title":{"rendered":"Spearman Correlation"},"content":{"rendered":"

Example homework problem:<\/h3>\n

You work for an automotive magazine, and you are investigating the relationship between a car’s gas mileage (in miles-per-gallon) and the amount of horsepower produced by a car’s engine. You collect the following data:<\/p>\n\n\n\n\n\n
Automobile:<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n7<\/td>\n8<\/td>\n9<\/td>\n10<\/td>\n<\/tr>\n
Horsepower:<\/td>\n95<\/td>\n135<\/td>\n120<\/td>\n167<\/td>\n210<\/td>\n146<\/td>\n245<\/td>\n110<\/td>\n160<\/td>\n130<\/td>\n<\/tr>\n
MPG:<\/td>\n37<\/td>\n19<\/td>\n26<\/td>\n20<\/td>\n24<\/td>\n30<\/td>\n15<\/td>\n32<\/td>\n23<\/td>\n33<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Is there a significant correlation between horsepower and MPG (alpha = .05)?<\/p>\n

Note that these are the same data that we worked with when you were working with the Pearson correlation procedure<\/a>. This will allow you to compare and contrast the results of the two procedures.<\/p>\n

\n

Enter these data into the first two columns of Stats Homework’s <\/i>data manager and rename the variables. Your screen should look like this:<\/p>\n

\"corr6\"<\/a><\/p>\n

Make sure to double-check and save your data. To conduct your analysis, pull down the Analyze<\/b> menu, choose Non-Parametric Tests<\/b>, and then choose Spearman Correlation<\/b>. You will be presented with this dialog:<\/p>\n

\"spearman1\"<\/a><\/p>\n

Select horsepower and gas mileage as your variables. Check the option to output our difference scores to your data, and click\u00a0Compute<\/strong>.<\/p>\n

Before we look at the output produced by this procedure, let’s take a look at the variables that have been created by it and written back into your data:<\/p>\n

\"spearman2\"<\/a><\/p>\n

Note that the Spearman procedure has ranked each of your variables and has put these ranks into two new variables, Rank_X and Rank_Y. Also, it has computed the difference between each pair of ranks (Diff), and the squares of these differences (Diff\u00b2).<\/p>\n

We use the sum of the squared differences (\u03a3D\u00b2) to compute the Spearman correlation. Now, the output will be easy to figure out:<\/p>\n

\"spearman3\"<\/a><\/p>\n

Rank Statistics<\/b>.<\/p>\n