ttests Quantitative Data One group 1 sample ttest

t-tests • Quantitative Data • One group 1 -sample t-test • Two independent groups 2 -sample t-test • Two dependent groups Matched Pairs t-test t-Tests Slide #1

A Full Reality • No longer know what s is!!!!! • What should be used instead? – Our best guess at s s • Changes details, not the big picture t t-Tests Slide #2

Student’s t-distribution Compared to a standard normal (Z): • Similarities 10521 df – symmetric about 0 – approximately bell-shaped • Differences -4 -2 0 Z or t – more probability in the tails – less probability in the center – Exact shape depends on degrees-of-freedom (df) 2 4 • See HO for R work t-Tests Slide #3

1 -sample t-test • Ho: m = mo (where mo = specific value) • Statistic: • Test Statistic: df = n-1 • Assume: – s is UNknown – n is large (so that the test stat follows a t-distribution) • n > 40, OR • n > 15 and histogram is not strongly skewed, OR • Histogram is approximately normal • When: Quantitative variable, one population sampled, s is UNknown. t-Tests Slide #4

A Full Example • In Health magazine reported (March/April 1990) that the average saturated fat in one pound packages of butter was 66%. A food company wants to determine if its brand significantly differs from this overall mean. They analyzed a random sample of 96 one pound packages of its butter. Test the company’s hypothesis at the 1% level. Variable n %Sat. Fat 96 Mean St. Dev. 65. 6 1. 41 Min 60. 2 t-Tests . . . Slide #5

Practical Significance • Is there a real difference between 66% and 65. 6% saturated fat? • If the sample size is large enough, any hypothesis can be rejected. t-Tests Slide #6

R Handout t-Tests Slide #7