MSE 600 Descriptive Statistics Chapter 11 & 12 in 6 th Edition (may be another chapter in 7 th edition)

Hypothesis testing Scientific method tests the Null Hypothesis – That there is NO difference We reject or accept the null hypothesis

In experimental research we test the Null Hypothesis. Should we accept it or not? In any study – 3 possible situations 1. In reality there IS a difference or a relationship between variables (e.g., cause-effect) 2. Sampling error or alternative explanations masks the truth 3.There is NO difference in reality (see page 99)

Don’t Fix it Engine does NOT have a problem Fix it Engine has a problem Good Waste Money Breaks- down What kind of error will you accept?

Null H is True No difference Null H is False; There is a difference Accept the Null H (fail to reject) Reject the Null H Good Type II Type I What kind of error will you accept? Science does not want to make a Type I error

Defendant Innocent Defendant Guilty Accept Innocence (Not Guilty Verdict) Reject Innocence (Guilty Verdict) Good Type II Type I What kind of error will you accept? Science does not want to make a Type I error Justice System

Null H is True No difference Null H is False; There is a difference Accept the Null H (fail to reject) Reject the Null H Good Type II Type I What kind of error will you accept? Science does not want to make a Type I error

Significance Testing Do we keep the Null H or not? In inferential statistics We use tests of significance Basically a ratio of treatment difference to sampling error. Treatment error divided by sampling error Difference due to treatment sampling error

Difference due to treatment sampling error If the treatment error or difference is large enough then we will reject the Null H We will say there is a difference between the groups or will accept a relationship exists.

Tests of Significance.05 is conventional level p<.05 (italicized lower-case p) 5 times out of 100 we are willing to make a Type I error We are willing to make a mistake and say there is a difference when in reality there is no difference

Testing for a statistical significant difference Want to minimize the occurrence of a Type I error If the difference between the means of two groups is “significant enough” – we reject the NULL Hyp That is, we say there is a difference Conventional value of significance is when the probability of a significance test will occur 5% of the time or less.

Statistical significance vs Practical Significance

5% increase in number of people who live by using aspirin.

A Difference that Doesn’t Make a Difference (Figure 12.2)