PSYCH 240 1st EditionExam # 2 Study Guide Sections: 6 - 10 Section 6: Hypothesis Testing- Null Hypothesis Significance Testing (NHST): we use this technique when we want to provide evidence against the null hypothesis and in factor of an alternative hypothesis- Specific Evidence: evidence for a hypothesis is specific if the evidence would be unlikely to be observed if the hypothesis was false- When alpha decreases, the critical values should get farther from the center of the comparison distribution- The sampling distribution gets less variable as sample size increases (increasing the sample size is helpful because it makes it more likely that you will get a significant result if the alternative hypothesis is true)Section 7: Central Limit Theorem Central Limit: tells us how to derive the shape, mean, and variability of the distribution of meansgiven a distribution of scores and a sample sizeo Shape: usually normal (when some assumptions are met) If the distribution of scores is any other shape besides normal, then the distribution of means will still be very close to normal if the sample size is30 or greater (the shape can be far from normal for smaller sample sizes)o Mean: the distribution of means has the same mean as the distribution of scores (μM = μ)o Variability: σ2M = σ2/NσM = σ/sqrt(N)-σ2M: variance of the distribution of means- σ2: variance of the distribution of scores- σM: standard error of the mean- σ: standard deviation of the distribution of scores- N: sample size Three types of means:o Comparison Mean: the population mean of the comparison distributiono True Mean: the mean of the population from which your data were sampledo Sample Mean: the one mean for the one sample you happened to get for your study Z-score for the sample mean of the sampling distribution of the meano z = M- μM/σM z: z-score M: sample mean μM: population meanThese 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. σM: standard error of the meanSection 8: Single Sample T Tests T-distributions:o T-distributions are constructed like this: Randomly sample from a population of scores that follow a normal distribution with a mean equal to the value specified in the null hypothesis Compute a t-value using the mean and standard deviation of each sample After you do this a bunch of times, the t-values will follow a t-distributiono A t-distribution is symmetrical, unimodal, and bell-shaped like a normal distribution, but it has fatter tailso T-distributions get closed to a normal distribution as sample size increaseso Knowing the t-distribution lets us figure out where to place the critical values to achieve the desired alpha value Single Sample T-Test:o Step 1: state the null and alternative hypotheses Comparison Population: a population of scores with a known distribution Null Hypothesis: the sample you are testing that belongs to the comparison population Alternative Hypothesis: the sample you are testing that does NOT belong to the comparison populationo Step 2: specify the characteristics of the comparison distribution N= sample size Degrees of Freedom (df)= N-1o Step 3: determine the critical value(s) One- or two-tailed test?- One-Tailed Test: we are only looking for evidence against the null hypothesis in one direction (one critical value)- Two-Tailed Test: we are looking for evidence against the null hypothesis in either direction (two critical values) Alpha: probability of concluding that we have good evidence for the alternative hypothesis when it is actually false (this is given to you) Critical Value(s): the cutoff(s) that we will use to separate significant results from non-significant results (find this by using the chart)o Step 4: calculate the sample score on the comparison distribution SM = S/sqrt(N)- SM: standard error of the mean- S: standard deviation- N: sample size t = (M-μM)/SM- t: T-score- M: sample mean- μM: population meano Step 5: state your conclusions Significant Test: you achieved evidence for the alternative hypothesis that is specific enough for your desires alpha value Non-Significant Test: you failed to do soo Assumes that scores are normally distributed in the population T-Tests in journals:o Example: t (18)= 4.11, p<.05 The value in parenthesis is the df The value after the “=” is the t value for the test P-Values: the probability that you would get misleading evidence for the alternative hypothesis ifthe significance region started at your sample valueo A p-value is what alpha would be if the critical value(s) were set such that your result fell right on the edge of the significance regiono Whatever result you get, you assume the critical value(s) were placed there and then you backtrack to see what alpha would have been if you had run the test like that If p is less than the acceptable chance of erroneously claiming to have evidence for the alternative hypothesis (alpha), then the test is significantSection9: Dependent Sample T-Tests Dependent v. independento Dependent Sample T-Test: used when the scores in one sample are related in some way to the other scores in the other sampleo Independent Sample T-Test: used when the scores in one sample have no relationship tothe scores in the other example Within-subjects design v. between-subjects designo Within-Subjects Design: every participant contributes data to all of the conditions/samples Dependent sample t-testo Between-Subjects Design: each subject contributes data to only one of the conditions Independent sample t-test Dependent sample t-test:o Step 1: state the null and alternative hypotheses Null Hypothesis: the two samples come from an identical population, so the difference scores come from a population with a mean of zero  Alternative Hypothesis: the two samples come from different populations, so the difference scores come from a population with a mean other than zeroo Step 2: specify the characteristics of the comparison distribution N= number of DIFFERENCE scores Degrees of Freedom (df)= N-1o Step 3: determine the critical value(s) One- or two-tailed test?- One-Tailed Test: we are only looking for evidence against the null hypothesis in one direction (one critical value)- Two-Tailed Test: we are looking for evidence against the null hypothesis in either direction