PSYCH 240 1st Edition Exam# 3 Study Guide Section 11: Independent-Sample T-Tests- Step 1o Null Hypothesis: The two groups come from populations with the same mean.o Alternative Hypothesis: The two groups come from populations with different means.- Step 2o df1=N1-1o df2=N2-1o dfTOT=df1+df2- Step 3o One- or two-tailed?o Alphao dfTOTo Tcv (from chart) For a directional test always make sample 1 the condition that is hypothesized tohave a higher mean (which is not necessarily the one with a higher sample mean), if you do this then you will always need to use a positive critical value- Step 4o UDIFF: population mean of the distribution of differences between means if the null hypothesis is true (0)o SDIFF: estimated standard deviation of the distribution of differences between means assuming that the null hypothesis is true- Step 5o Significant/non-significantThese 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.o The test produced/failed to produce specific evidence for the alternative hypothesis- Central Tendency: if we take both samples from the same population, then mean 1 will be higher than mean 2 on a random half of the sample and vice versa on the other halfo So the mean of the distribution of differences between means, μDIFF, is zero- Shape: if the original population of scored is normal, then the distribution of differences between means will be normalo If the sample sizes for both samples are above 30, then the distribution of differences between means will be very close to normal regardless of the shape of the distribution of scores- Variability: how you find the population standard deviation of the distribution of differences between means - Which test to use:oIf the problem gives you two sample means (M) and to sample standard deviations (S), then you need to do an independent-samples t testoIf the problem only gives you one sample mean (M) and one sample standard deviation (S), then you either need to do a single-sample t test or a dependent-samples t testIf the problem says something about difference scored then it’s a dependent-samples t testIf not, then it’s a single-sample t test-Independent T assumptions:oNormality: the test assumes that the original scores follow normal distributionsoEqual Variance: the test assumes that the populations for both groups have the same variability-Within v. between:oIf the alternative hypothesis is true, you are more likely to find a significant result in a with-subjects design than a between-subjects designThis is because the within-subjects design removes subject-level variability oIf the null hypothesis is true, you are equally likely to find a significant result in a within-subjects design and a between-subjects designSection 12: Bayesian Statistics- Bayes Theorem:oop(H|D) - probability that the hypothesis is true given the observed dataop(H) (prior probability) - the overall probability that the hypothesis is true given what you already know before new evidence is offered for or against the hypothesisop(D|H) - the probability of observing the new evidence given that the hypothesis is trueoLikelihood: the probability of observing data under a given hypothesisoNumerator - overall chance that the hypothesis will be true AND you will observe the dataoDenominator - the overall probability of observing the data regardless of whether or not the hypothesis is true or false (probability of the data)p(H) x p(D|H) - the probability that the hypothesis is true and you will observe the datap(~H) x p(D|~H) - the probability that the hypothesis is FALSE and you will observe the dataoThe probability that the hypothesis is false will always be 1 - the prior probability that the hypothesis is true p(~H) = 1-p(H)Problems will only give you p(H)-Plausibility of the Claim: probability that the claim/hypothesis would be true given what you know before you get new evidenceo"Plausible" means that p(H) is high and p(~H) is low-Sensitivity of the Evidence: probability that the new evidence would be observed if the claim was true o"Sensitive" evidence means that p(D|H) is highoThe evidence offered is something you would expect to observe if the hypothesis was really true-Specificity of the Evidence: probability that the new evidence would be observed if the claim was false o"Specific" evidence means that p(D|~H) is lowoThe evidence offered is something you would NOT expect to observe if the hypothesis was really falseoNHSTs use only this. NHSTs funnel conclusions into two categories - significant or non-significant. Bayesian statistics quantify the degree of support for a hypothesis on a continuous scale so the probability that a hypothesis is true can be anything between 0%and 100%-Likelihood Ratio (LR): the probability of having the evidence if the hypothesis was true divided by the probability if the hypothesis was falseooLR of 1 means that the evidence is irrelevant to the hypothesisThe evidence is equally likely to be observed regardless of whether the hypothesis it true or falseoLR above 1 means the evidence favors the hypothesis, with higher values meaning stronger evidenceLR value of 2 means the evidence is twice as likely to be observes if the hypothesis is true, 10 means 10 times more likely, etc.oLR value below 1 means the evidence goes against the hypothesis, with lower values meaning stronger evidence againstLR value of 1/2 means the evidence is twice as likely to be observed if the hypothesis is FALSE, 1/10 means 10 times more likely,