2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Khan Academy – Shapes of distributions Video: 5:06 minutes Available at: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data- statistics/cc-6-shape-of-data/v/shapes-of-distributions

Please don’t be offended by the label, 6 th grade math!

How does the central limit theorem apply?

According to the central limit theorem, for sufficiently large samples (n = 30), the sample means will be distributed around the population mean approximately in a normal distribution. The sample mean of 30 observations is less variable and has a smaller standard deviation than an individual observation from the population.

This is true even if the population is NOT normally distributed. Woa.. talk about the power of math, right? (Quiz)

What are Z scores? A Z score is a way of standardizing so you can make comparisons. (Quiz)

Example: You are an admission counselor and students submit applications with both ACT or SAT tests as part of the process. After some research, you discover that the mean score of the ACT is 21 with a standard deviation of 4.7. The mean SAT score is 1,550 with a standard deviation of 110.

You want to compare students -

Student 1 - ACT score of 31

Student 2 - SAT score of 1,980

Use the "Z" score formula where:

"x" is the observed value, " " is the mean of the sample, and " " is the standard deviation z score

Equation 3: Formula to calculate a standardized score

Calculations for ACT Student 1 = (31-21) divided by 4.7 = 2.13

Calculations for SAT Student 2 = (1980 - 1550) divided by 110 = 3.91

The SAT (student 2) has the higher relative standing.

FYI - There is a formula in Excel called STANDARDIZE that returns a normalized value from a mean and standard deviation.

84