Chapter 10

# Chapter 10 - Chapter 10 Inferences Involving 2 Populations...

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Chapter 10 Inferences Involving 2 Populations

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Previously… We focused on 1-sample tests We took 1 sample from 1 population and compared a sample statistic to “Some Value” of interest Examples: Does the Population mean = 10 cm? Does the Population Proportion = 55%? Is the Population Variance = 2.3 gms?
µ = ? σ 2 =? p = ? σ known σ not known z -test t -test z test χ 2 test One population tests

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Now we will start talking about sampling 2 populations Goal is to compare between 2 populations Can be experiments or surveys
Comparing 2 Populations From EACH population, take 1 ‘good sample’ Example: Who studies more – UVA or UMD students? Randomly sample UMD students – get a sample mean Randomly sample UVA students – get a sample mean Compare sample means statistically Make inference back to populations

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Experiment with 2 populations Use randomization to assign mice to either Drug A or Drug B Run experiment for 2 weeks Measure something on each mouse to look at drug effect Compare the mean for mice with Drug A to the mean for mice given Drug B Make inference to Drug effects
What is Randomization? Using some aspect of chance to assign treatments to EUs randomly Twins for a study. Look at 1 twin, flip a coin, if coin is heads – that twin goes to Treatment A and other twin goes to Treatment B

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Randomization vs. Random Sampling Random sampling = Randomization = Which used in surveys? Which used in experiments?
Comparing 2 populations To know which statistical test to use we still need to know 1 more thing: Are experiment units Independent OR Dependent This is a Study Design Element

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Dependent vs. Independent Samples You want to contrast the ability of 2 suntan lotions to prevent sunburn study : randomly assign people (EUs) to a treatment (lotion A vs. lotion B) study: randomly assign the left side of each EU’s body to one lotion and the right side of the body to the other lotion (same person gets both treatments) why 2 populations if on same person?
Another example Want to know the effect of a good night’s sleep on exam score : use randomization to assign EUs to either 8 hours sleep treatment or 4 hours sleep treatment then administer exam : use randomization to assign each EU to a sleep treatment and then administer exam, then a week later have the same EU complete the OTHER treatment and compare results for each EU (same person gets both treatments)

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Key question…. . When there are 2 treatments, ask if Experimental Units are Paired ? can be a powerful statistical tool! e.g., for the suntan lotion study, by doing both treatments on same person --- any difference in amount of burning should be just due to the type of lotion used -- NOT due to genetic variability between people Not Paired Paired (on same person)
Statistical Test on Means Previous chapters we compared the mean from one population to some ‘known’ value Ho: μ = 0 Used the t-distribution to determine probability associated with the Ho df of test = n -1 n s x t μ - = Chapter 9

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Chapter 10 - Chapter 10 Inferences Involving 2 Populations...

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