Experiments We wish to conduct an experiment to see the effect of alcohol (explanatory variable) on reaction time (response variable).

Factors and Treatments The manipulated factor will be the amount of alcohol consumed. There will be two treatments No alcohol (Control group – drink grape punch) Alcohol (Treatment group – drink grape punch spiked with grain alcohol)

Experimental Design The twelve participants will be split, at random, into two groups of 6. Each participant will drink two 8 ounce glasses of grape punch in half an hour. Reaction time of each participant will be measured after drinking the punch.

Experimental Design Control of outside variables. Each participant drinks grape punch. Each participant has reaction time measured in the same way.

Experimental Design Randomization Replication Participants are randomly assigned to treatment groups. Replication There are 6 participants in each treatment group.

Natural Variation Participants will vary in terms of their natural reaction time. Randomization spreads this variation evenly across the treatment groups.

Data 1. Control Group 2. Treatment Group

Analysis of Results The data gathered from this experiment can be analyzed using the methods presented in Chapter 24 (Lectures 33 and 34). Two independent samples.

Natural Variation We cannot control the natural variation in reaction time, i.e. make each participant have the same reaction time to begin with. We can account for this natural variation by introducing a blocking variable.

Block Design Have each participant serve as a block. Each participant will experience both treatments (no alcohol, alcohol) in a random order.

Block Design There is no variation in the natural reaction time within a block (it is the same person within a block). Therefore we can better assess the effect of alcohol on each person’s reaction time.

Data With this block design we will get a pair of observations (reaction time after grape punch and reaction time after grape punch with alcohol) for each participant.

Two Independent Samples Two separate sets of individuals. One value of the response variable for each individual.

Paired Samples One set of individuals. Two values of the response variable (a pair of values) for each individual.

Know the Difference It is important to know the difference between data arising from two independent samples and data arising from paired samples.

Example Alcohol and Reaction Time Experiment run as a block design with participants as blocks. A pair of reaction times (seconds) for each participant.

Participant No Alcohol Alcohol Difference Alc – No Alc 1 6.7 7.4 0.7 2 7.0 0.0 3 7.7 4 7.3 7.5 0.2 5 7.2 –0.2 6 7.6 7 6.2 1.2 8 6.4 1.1 9 6.6 0.6 10 –0.3 11 12 6.5 0.9

Summary of Differences

Conditions & Assumptions Randomization Condition Paired data Nearly Normal Condition The differences could have come from a population whose distribution is a normal model.

Difference

Confidence Interval for

Table T df 1 2 3 4 11 2.201 Confidence Levels 80% 90% 95% 98% 99%

Confidence Interval for

Interpretation We are 95% confident that the population mean difference in reaction time is between 0.102 and 0.748 seconds. On average, a person’s reaction time increases from 0.102 to 0.748 seconds after drinking this amount of alcohol.

Test of Hypothesis for Step 1: Null and Alternative Hypotheses. Step 2: Check Conditions See earlier slides.

Test of Hypothesis for Step 3: Test Statistic and P-value

Test of Hypothesis for Step 4: Use the P-value to make a decision. Because the P-value is small, reject the null hypothesis.

Test of Hypothesis for Step 5: State a conclusion within the context of the problem. The population mean difference in reaction time, with and without alcohol, is not zero.

Comment This agrees with the confidence interval. Zero was not in the confidence interval and so zero is not a plausible value for the population mean difference.

JMP Data in two columns Create a new column of differences Reaction time with no alcohol. Reaction time with alcohol. Create a new column of differences Cols – Formula

JMP Analysis – Distribution JMP Starter – Basic Differences Matched Pairs

Analysis - Distribution

Matched Pairs