Each year I always have to decide what to do after the AP Stat Exam. Should I dive into ANOVA tests? Watch Moneyball? I never seem to have a clear plan in mind. Twitter found me this year’s project.
Microsoft recently announced its age-predicting algorithm How-Old.net. I submitted my own picture, was a bit shocked, and then moved on.
(For the record I’ll be 30 in September. My dad will 60 next year!)
I would have been happy to feel a little depressed and move on if it weren’t for @giohio’s Twitter post.
So I begrudgingly convinced 7 fellow colleagues to submit a photo and reveal their true age. Could a measly sample size of 8 determine the accuracy of Microsoft’s algorithm?
The table provided is the summary statistics for Actual Age – Predicted Age. With a mean difference of -5.625, one might believe that the algorithm does overestimate the age of individuals. However, a large standard deviation exists that suggests taking a look at the shape of the distribution as well.
The box plot indicates a distribution that is skewed to the left. This is good news for me, as my picture was one of the larger overestimates in age. A skewed distribution may indicate that the median may be the more representative measure of center. With a median difference of 0.5, evidence may now suggest the algorithm does well at predicting the age of individuals. Even with all the variation in predictions, do we have evidence to claim that that Microsoft’s algorithm is inaccurate?
Consider the scatterplot of predicted age versus real age.
Our least-squares regression equation is: predicted age = 62.08 – .257(real age). This would indicate the older you are, the younger the algorithm believes you to be. Maybe Microsoft is just secretly trying to boost self-esteem of our older generations while putting youth back in line?
While the sample size is very small (n = 8), the residual plot seems to indicate that this model is appropriate.
Consider a 1-Sample T-test for the following hypotheses:
Null: μ = 0 , we believe there to be no difference between the actual and predicted ages.
Alternative: μ ≠ 0, we believe there is a difference between the actual and predicted ages.
(Again, a small sample size leads to missing conditions for the test. But here are the results.)
We are provided with a t-score of -1.0637 and p-value of .3228. This means we fail to reject the null hypothesis, and evidence suggests there is no difference in actual ages and predicted ages of faculty members in the sample.
When my students tackled the problem, I encouraged them to identify their population of interest. Some groups chose the student body, but not all did. One group tackled the characters from Game of Thrones. Did the actor’s age match the actual age for the show and the books. Another student set out to see if the students in the Breakfast Club were actually predicted to be high school age. This project was a fun way to wrap up the year and pose a task that can be answered in multiple ways.
Any suggestions for revisions or questions, please let me know.