Midterm: Halfway through

Throwback . . .

Different types of data

Descriptive method of describing data

Normal distribution of data

Introduction to hypothesis testing: Paired t-test

Comparing two groups: the paired data situation

Hypothesis testing: the null and alternative hypotheses

Relationships between confidence intervals and hypothesis testing when comparing means

p-values: definition, calculations, and more information Section A

Are the population #means different? (continuous data)

Paired design:  Before-after data Twin data (Matched case-control)

Two independent sample design Randomized trial

Paired design t-test

Paired Design—Example: Before vs. After Why pairing? -  Control extraneous noise -  Each observation acts as a control -  Good way to get preliminary data/estimates to be used to develop further research

Ten non-pregnant, pre-menopausal women 16–49 years old who were beginning a regimen of oral contraceptive (OC) use had their blood pressures measured prior to starting OC use and three-months after consistent OC use1

Example of Paired design t-test

The goal of this small study was to see what, if any, changes in average blood pressure were associated with OC use in such women

In essence, what we have done is reduce the BP information on two samples (women prior to OC use, women after OC use) into one piece of information: information on the differences in BP between the samples

This is standard protocol for comparing paired samples with a continuous outcome measure

95% confidence interval for mean change in BP in population of women taking oral contraceptives, after starting OC use compared to before OC use

What’s the Confidence interval…?

  Location

  1 2 3 4 5 6 7 8 9 10

Zincconcentration inbottom water

.430 .266 .567 .531 .707 .716 .651 .589 .469 .723

Zincconcentration insurface water

.415 .238 .390 .410 .605 .609 .632 .523 .411 .612

Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs of data were taken measuring zinc concentration in bottom water and surface water.

1.) Does the data suggest that the true average concentration in the bottom water exceeds that of surface water? 2.) Calculate the 90% confidence interval of the data.

Pair Training No training

1 95 90

2 89 85

3 76 73

4 92 90

5 91 90

6 53 53

7 67 68

8 88 90

9 75 78

10 85 89

11 90 95

Twenty sixth graders were randomly selected from a school district. Then, they were divided into 11 matched pairs, each pair having equal IQ's. One member of each pair was randomly selected to receive special training. Then, all of the students were given an IQ test. Test results are summarized below.

1.) Does the special training effective?2.) What is the 95% Confidence interval?

zz

Two different physicians assessed the number of palpable lymph nodes in 65 randomly selected male sexual contacts of men with AIDS or AIDS-related conditions

What is the 95% CI for difference in mean number of lymph nodes of Doctor 2 compared to Doctor 1? Is it significant? Provide a conclusion to your answer.

Type I error -  Claim HA is true when in fact H0 is true The probability of making a Type I error is called the alpha-level ( α -level) or significance level

Comparing Means among Two (or More) Independent Populations

“A Low Carbohydrate as Compared with a Low Fat Diet in Severe Obesity”*

-132 severely obese subjects randomized to one of two diet groups

-Subjects followed for a six month period

Comparing Two Independent GroupsComparing Two Independent Groups

Comparing Two Independent Groups: Diet Types Study

T-test (UNPAIRED)

independent groups w/smaller

sample size

< 2 independent groups