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UMass Amherst PSYCH 240 - Hypothesis Testing

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PSYCH 240 1st Edition Lecture 11Hypothesis Testing-Goal: to establish the major principles of hypothesis testing-We'll use a simplified example so we can focus more on the concepts themselves Dog Problem-You work for an eccentric trillionare (Mr. Burns), and he wants to get a new set of guard dogs-You get a purchase order for a bunch of dogs - it's a mixture of bulldogs and German shepherds-Mr. Burns does not want the bull dogs, but all you have on the purchase order are the dogs' names and weights oYou tell Mr. Burns that you'll go though the list dog by dog, and you'd only order a dog if you have evidence that it is NOT a bulldogoThe evidence will be each dog's weight. German shepherds weigh more than bulldogs on average. So if a given dog is very heavy, then that is evidence that it is not one of the bulldogsoMr. Burns is not impressed oYou say that you'll pick a weight so heavy that it will be unlikely that any dog above that weight is just a fat bulldog. You say you'll make sure that there is no more than a 5% chance that a bulldog would be above your cutoff weight-For each dog, there are two hypotheses.oThe dog is a bulldogoThe dog is NOT a bulldog-Mr. Burns will let you order when you have evidence from the second hypothesis-You have assured him that the evidence you use will be specific-Evidence for a hypothesis is specific if the evidence would be unlikely to be observed if the hypothesis was false-Now you need a way to make sure that our evidence is as specific as Mr. Burns demandsoYou can do this by carefully setting your standard for "probably too heavy to be a bulldog"-You call the kennel and they tell you that bulldog weights are normally distributed with a mean of 55 pounds and a standard deviation of 5 pounds. So this is tour comparison distribution. New samples that you test might or might not belong to this distribution. oIf a dog has a weight near the center of this distribution, then it has a weight that is very typical for bulldogs, that would mean that it might actually be a bulldog, and we certainly don’t have any evidence that it is NOT a bulldogoIf a dog has a weight that is many standard deviations away from the center of this distribution, then we have some evidence that the dog is NOT a bulldogThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.-The only dogs on our list that aren't bulldogs tend to be heavier than bulldogs, so we will only focus on weights that are unusually high for a bulldogoWe need to set a cutoff that only 5% o the scores in out comparison distribution fall above (and 95% fall below). The value is 63.22-In R you can find this by entering qnorm(.95,55,5)--If the dog is above 63.22 pounds, you can buy it.oThis is a very common statistical practice in many fields of research. Just substitute "publish your result" for "order the dog", "journal editor" for "Mr. Burns", and "experimentalresults" for "dog weights" Hypothesis Testing-Null Hypothesis Significance Testing (NHST): we use this technique when we want to provide evidence against the null hypothesis and in favor of an alternative hypothesisoThe null and alternative hypotheses are defined in reference to a comparison populationoThe goal of the null hypothesis significance testing is to make sure that the evidence provided for the alternative hypothesis is specificoThere are 5 steps you will have to use each time you use this test1. State the null and alternative hypothesis Comparison Population: a population of scores with a known distribution. The new sample that we are testing might or might not belong to this populationNull Hypothesis: the sample you are testing belongs to the comparison population-One variable has no effect on another variable or that a new observation is just another instance of a process that is already well understood- Alternative Hypothesis: the sample you are testing does NOT belong to the comparison population-One variable has an effect on another variable or that a new observation is an instance of a new process that was not previously understood-Usually more interesting; you can think of it was the one we "want" to support with evidence2. Specify the characteristics of the comparison distributionLike in the example, getting the information from the kennel is what allowed us to define 3. Determine the critical value(s)State if test is one- or two-tailed (directional or non-directional)-One-tailed Test: we are only looking for evidence against the null hypothesis in one direction, so there is only one critical value-Two-tailed Test: we are looking for evidence against the null hypothesis in either direction, so there are two critical two critical valuesState the alpha value-Alpha: probability of concluding that we have good evidence forthe alternative hypothesis when it is actually false-Researchers typically use alphas of .05 or .01Report the critical value(s)-Significant Test: you achieved evidence for the alternative hypothesis that is specific enough for your desired alpha value-Non-significant Test: you failed to do this-Critical Value(s): once we have an alpha value, we use it to figure out where to place the cutoff(s) that we will use to separate significant results from non-significant results-We will always set the critical value(s) so that a proportion of scores equal to our alpha value is more extreme than the critical value(s) in the comparison distribution-Any result more extreme than the critical value(s) is deemed significant, so this makes sure that our chance of getting a significant test if the alternative hypothesis is false equals alpha-When alpha decreases, the critical values should get farther from the center of the comparison distribution4. Calculate the sample score on the comparison distributionLike in the example, we did this by simply looking at weight of the dog we were testing5. State your conclusionsState whether the test result was significant or non-significantExplain what this means for the particular research scenario that you were givenoIf the example is more extreme than the critical value(s), then you have some evidence for the alternative hypothesis1. If not, you can’t make confident conclusion about either hypothesis; results are inconclusiveoEven if you have evidence for the alternative, it still might be falseoIt is common to say a significant result means you should


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