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?
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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
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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
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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?
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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?
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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)
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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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