Using Chapters 12+ of the book, provide a clear and concise answer to each question below making sure to address each part of the question. Answer each question in sentence form using correct spelling and grammar. Then, submit the file (appropriately named) with your answers, including any graphs created, through the assignment link in this course space. Be sure that your answers are a different color font (ideally red) than the questions. Show your work and clearly label where each number is coming from. If you have to use a formula to get an answer, make sure to clearly write down the formula you are using. Credit is given both for right answers as well as based off of work shown/steps taken.
What does the sign and the actual number tell you in a correlation?
Provide some details for the following examples based upon you answer above using a significance value of .05 (sign, number, and significance).
r = .03 (p>.05)
r= .99 (p<.05)
r= -.8 (p<.05)
You are speaking with a friend who informs you that they have observed that when trees are taller in their neighborhood the birds at their house often “sing” more frequently. Your friend tells you that this must mean that taller trees result in birds singing more often. What might you tell your friend about this observation and their conclusion based upon what we know about correlations?
Below is a screenshot of a correlation between two quiz scores, Quiz 1 and Quiz 2. These are not real data (I made them for this example), but if they were what might you tell me about the results (.05 significance value)? Please also provide a brief description of the mean and standard deviation as well (under “descriptive statistics”). For an excellent example of how to interpret a correlation table see the following link created by ASK Brunel (2012/13): https://www.youtube.com/watch?v=pgQ9T_SdzoQ
Suppose I provide you with the following information to calculate a correlation coefficient.
COVxy = 0.14
Sx * Sy = 0.22
Please calculate the correlation:
Based on this correlation, provide an interpretation:
Why might it not have been the best idea to immediately calculate a correlation such as this before doing anything else with the data?
After reading the below scenario, write out which statistical test you would use.
“A researcher prepares a set of 20 different photographs of Dakota’s dogs playing at the park, with 10 mounted on a white background and 10 mounted on red. One picture is identified as the test photograph and appears twice in the set, once on white and once on red. Each participant looks through the entire set of photographs and rates how amazing each dog photo is on a 10-point scale (0 = awesome and 10 = super amazing). Are the ratings for the test photograph significantly different when it is presented on a red background compared to a white background?”
What statistical test should you use to answer this question and why?
Below is a screenshot of a data set I made up in Excel:
The first step is you will need to open an Excel document and type in the data in the screenshot as shown. Then watch the attached link to a YouTube video. This will explain how to run a correlation in Excel. It is a straightforward function so likely will not be too confusing once you watch the video.
You do not need to enable anything/download anything to run a correlation other than just having Excel. Excel on Mac will work too. I am not sure if Numbers for Mac allows this to be ran by default, but it might. You are also welcome to just hand calculate it if you would like if you do not have the above programs/would rather just do this.
Once you run a correlation, please write a one sentence description stating how to interpret the correlation (along with the actual number you got, you can round to the first decimal) if we were to find this correlation statistically significant. Your sentence should discuss the direction and magnitude, and then describe what this means in more general terms (i.e., in relation to the two variables you see in my screenshot, food dropped and dogs going outside to go potty).
Here is a screenshot of the data set:
