{"id":5135,"date":"2016-06-26T14:32:53","date_gmt":"2016-06-26T19:32:53","guid":{"rendered":"http:\/\/www.thejuliagroup.com\/blog\/?p=5135"},"modified":"2016-06-26T14:37:22","modified_gmt":"2016-06-26T19:37:22","slug":"data-analysis-by-example-thats-funny","status":"publish","type":"post","link":"https:\/\/www.thejuliagroup.com\/blog\/data-analysis-by-example-thats-funny\/","title":{"rendered":"Data Analysis by Example: That’s funny …"},"content":{"rendered":"

In the last post, I used SAS Enterprise Guide<\/a> to filter out a couple of ‘bad’ records that came from test data, then I created a summary table of the number of questions answered and the percentage correct. Then, I calculated the mean percentage correct for the\u00a0\u00a0around 84%. That seemed a bit high to me.<\/p>\n

Having (temporarily) answered the first question regarding the number of individual subjects and the average percent of correct answers from the 424 subjects, I turned to the next question:<\/p>\n

Is there a correlation between percentage correct and the number of questions attempted? That is, do students who are getting the answers correct persist more often?<\/em><\/strong><\/p>\n

Since I had both variables, N and the mean correct (which, since this was score 0= correct, 1= incorrect gave me the percentage correct) from the summary tables I had created in the previous step, it was a simple procedure to compute the correlation.<\/p>\n

I just went to the TASKS menu, selected MULTIVARIATE and then CORRELATIONS<\/p>\n

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

Under ANALYSIS VARIABLES correct_ N for the ‘correct’ variable, which is a variable that holds whether the\u00a0 student answered correctly, 0(= no) or 1(=yes).\u00a0 Under CORRELATE WITH I dragged correct_mean, which has the percentage each student answered correctly.<\/p>\n

\"Variables<\/a>Since it is just a bivariate correlation and the correlation of X with Y = the correlation of Y with X , it would make absolutely no difference if I switched the spots where I dragged the two variables.<\/p>\n

I click run and I get a somewhat unexpected result, you can see here, with a correlation of -.07<\/a>.<\/p>\n

I also note that the minimum number of answers attempted is 1. Now, I have done (and published) analyses of these data elsewhere, as this is an on-going project.<\/p>\n

 <\/p>\n

\n

Other analyses from this same project can be found in:<\/p>\n

Telling Stories with Your Data<\/a> and<\/p>\n

Yes, PROC FREQ Does That!<\/a><\/p>\n

\n

Because of these analyses of ‘Fidelity of Implementation’, that is the degree to which a project is implemented as planned, I am pretty sure that these data include a large proportion of students who only had the opportunity to play the game once.<\/p>\n

So … I decided to run a scatter plot and check my suspicion. This is pretty simple. I just go to the TASKS menu and select GRAPH then SCATTER PLOT.<\/p>\n

I selected 2-D Scatter Plot<\/p>\n

\"2D<\/a><\/p>\n

Then, I clicked on the DATA tab, dragged correct_Mean under Horizontal and Correct_N and vertical, then clicked RUN.<\/p>\n

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

This produced the graph below.<\/p>\n

\"scatter3\"<\/a>Now, this graph isn’t fancy but it serves its purpose, which is to show me that there IS in fact a correlation of mean correct and the number of problems attempted. Look at that graph a minute and tell me that you don’t see a linear trend – but it is pulled off by the line of 1.0 at the far end.<\/p>\n

This did NOT fit my preconceived notion, though, that the lack of correlation was due to the players who played once, and so there would be a bunch of people who had answered 1 or 2 questions and got 100% of them correct. Actually, those 100-percenters were all over the distribution in terms of number of problems attempted.<\/p>\n

This reminds me of a great quote by Isaac Asimov,<\/p>\n

The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ (I found it!) but ‘That’s funny …’<\/p><\/blockquote>\n

Well, we shall see, as our analysis continues …<\/p>\n

 <\/p>\n

\n

Want to see these data at the source?<\/a><\/p>\n

Check out our game, playable on Mac or Windows. Download Spirit Lake or Fish Lake\u00a0 to play, or for Forgotten Trail, just click on the link provided, no download required.<\/a><\/p>\n

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

You can also follow the link above to donate a copy of the game to a school or give as a gift.<\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

In the last post, I used SAS Enterprise Guide to filter out a couple of ‘bad’ records that came from test data, then I created a summary table of the number of questions answered and the percentage correct. Then, I calculated the mean percentage correct for the\u00a0\u00a0around 84%. That seemed a bit high to me….<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9,11,8],"tags":[],"class_list":["post-5135","post","type-post","status-publish","format-standard","hentry","category-software","category-statistics","category-technology"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/5135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/comments?post=5135"}],"version-history":[{"count":4,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/5135\/revisions"}],"predecessor-version":[{"id":5144,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/posts\/5135\/revisions\/5144"}],"wp:attachment":[{"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/media?parent=5135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/categories?post=5135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.thejuliagroup.com\/blog\/wp-json\/wp\/v2\/tags?post=5135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}