Week 6: Two Sample Dependent t test & Statistical Errors Overview

Topics:

  1. The Two Sample Dependent t-test
  2. Types of Statistical Errors

Student Course Learning Objectives

4.  Choose, administer and interpret the correct tests based on the situation, including identification of appropriate sampling and potential errors

c.  Choose the appropriate hypothesis test given a situation

e.  Write the appropriate null and alternative hypotheses, including whether the alternative should be one-sided or two-sided

f.  Determine and calculate the appropriate test statistic (e.g. z-test, multiple t-tests, Chi-Square, ANOVA)

g.  Determine and interpret effect sizes.

h.  Interpret results of a hypothesis test

i.  Differentiate between Type I and Type II errors, explain each in the context of a situation, and describe how to decrease the chances of each

  1. Use technology in the statistical analysis of data
  2. Communicate in writing the results of statistical analyses of data

Video to Watch

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General Overview

Do you remember that the One Sample t-test compares a sample mean with a population mean? The Two Sample t-tests are also tests of means; however, they compare means from two different samples.

In the Two Sample Dependent t-test, the same subject participates in both samples. For example, we could try to determine whether pulse rates differ significantly depending upon whether an individual sits or stands. If we were in a classroom, I could randomly assign my students to either sit or stand. We could count pulse rates for 60 seconds and record them. I could then have my students take the opposite posture...those that previously sat would now stand, and those that previously stood would now sit. We could count pulse rates for 60 seconds and then record them. Now, each subject has taken part in BOTH samples. So, even though two samples have been collected, this is a Dependent t-test.

The independent variable would be position (sitting or standing), and is qualitative. The dependent variable would be the pulse rate, in beats per minute, which is quantitative.

Errors are a fun topic.  With statistical tests, we actually NEVER know if an error was committed.  We will only be able to say, "If an error was made, it was..."  There are two types of statistical error, Type I and Type II.  Whether you reject or retain your null hypothesis is what will tell you with type of error you 'might' have made.