GVPT100: Final Exam Review (Chapters 6-9)a. Sample and Populationi. Two key concepts:1. Population—the universe of subjects the researcher wants to describea. N= Population Size2. Sample—a number of cases or observations drawn from a populationa. n= Sample Sizeii. Leads to two different values:1. Population parameter—actual valuea. Ex.—number of people who voted for John McCain2. Sample statistic—estimate of the population parametera. Ex.—number of people taking exit poll who said they votedfor John McCainb. Inferential Statistics: set of procedures for deciding how closely a relationship we observe in a sample corresponds to the unobserved relationship in the population from which the sample was drawnc. Sampling Termsi. Random Sample: Every member of the population has an equal chance ofbeing chosen for the sample ii. Sampling Frame: Method for defining the population the researcher wants to study iii. Selection Bias: Some members of the population are more likely to be included in the sample than others iv. Response Bias: Some members of the population are more likely to respond than others d. Error and Samplesi. Selection/sampling bias—some individuals are more likely to be includedin the sample than others. Wrong sampling frame. ii. Response bias—some individuals are more likely to be measured than othersiii. Random sampling error—the extent to which a sample statistic differs by chance from the population parametere. Other Approaches other than Random Samplingi. Quasi-random sampling—or “cluster sampling” 1. Example—picking specific localities, and then randomly selecting individuals in relation to them2. Can minimize costs of conducting face to face interviewsii. Purposive sampling:1. Over representing some groups to make comparisons:2. Example—comparing college students with adults generally3. Important—only allows for comparing groups, not for generalizingto overall populationiii. Sampling Error1. Sample Sizea. Bigger sample, smaller errorb. Smaller sample, bigger error2. Variation in population characteristic being measureda. Bigger variation, bigger errorb. Smaller variation, smaller erroriv. Standard Deviation1. Stepsa. Calculate each value’s deviation from the mean. b. Square each deviation. c. Sum the squared deviations. d. Calculate the average of the sum of the squared deviations = variance. e. Take the square root of the variance = standard deviation. 2. As Standard deviation goes up, so does standard error3. Standard Error = Standard deviation / √nv. Central Limit Teorem1. If we were to take an infinite number of samples of size n from a population of N members, the means of these samples would be normally distributed.vi. Z-score1. Z= (deviation from mean)/(standard unit) 2. Stepsa. Find the value’s deviation from the meanb. Divide it by the standard deviationvii. Confidence Intervals1. 95% confidence interval a. The interval within which 95% of all possible sample estimates will fall by chance b. range in which we are 95% confident that the population parameter falls withinviii. t-Distribution1. A probability distribution that can be used for making inferences about a population mean when the sample size is smallix. Degrees of Freedom = n – 1x. Significance Tests1. Significance: an observed relationship b/w an independent variableand a dependent variable really exists in the population and is unlikely the product of chance2. Null Hypothesisa. No relationship between IV and DVb. Any relationship that does appear is the product of chance.c. Ho: null hypothesis “there is no difference”d. Ha: alternative hypothesis hypothesis “there is a difference” 3. Type I and Type II ErrorsRelationshipin oursampleRelationship in PopulationYes NoYes Correct Type I ErrorNo Type II Error Correcta. Type I Error:b. Type II Error:xi. Hypothesis Testing1. Confidence Interval Methoda. Researcher uses standard error to determine the smallest plausible mean difference in the population. If the smallest plausible difference is greater than 0, then the nullhypothesis can be rejected. If the smallest plausible difference is equal to or less than 0 then the null hypothesis cannot be rejected2. P- Value Methoda. Researcher determines the exact probability of obtaining the observed sample difference, under the assumption that the null hypothesis is correct. If the probability value (p-value) is less than or equal to .05 then the null hypothesis can be rejected. If the p-value is greater than .05 the null hypothesis cannot be rejectedxii. Two Tailed vs. One Tailed1. Two-tailed: a. Looking at both sides of the distribution.b. Use with non-directional hypothesis2. One-tailed: a. Only look at the “tail” you care about. b. Use with directional hypothesisxiii. Χ21. Purpose: looking for whether the observed dispersion of cases differs significantly from the expected dispersion of cases2. Stepsa. Find expected frequency for each cell.b. Subtract expected from observed.c. Square the difference.d. Divide by expected frequency.e. Add up all the numbers from the cells. 3. Things to knowa. Smaller values of Χ2 mean you are less likely to reject the null. Larger values mean you are more likely to reject.b. But we need a more precise figure. So we look up the Χ2 critical value for the level of confidence we want.c. Note: just like the t-distribution, the Χ2 distribution also depends on n and dfxiv. Lambda1. Lambda = Prediction error w/o IV – prediction error w/ IV2. Meaninga. Weak = Less than or equal to .1b. Moderate = Between .1 and .2c. Moderately strong = Between .2 and .3d. Strong = Greater than .3xv. Somers’ dyx1. Tells you whether the direction of the difference between cases on the IV helps predict direction of the difference on the DV 2. Termsa. Concordant pairs: pairs that are consistent with a positive relationshipb. Discordant pairs: pairs that are consistent with a negative relationshipc. Tied pairs: pairs that are tied on the dependent variable.3. Somers’ dyx = (C-D)/(C+D+Ty)xvi. Regression1. What is ita. A way to estimate the effect of an IV on a DV.b. Tells you the direction of the relationship, the magnitude/strength, and significance2. Termsa. Beta/coefficient (Β):i. Estimate of size and direction of effect of X on Yb. Standard Errori. Our confidence in our estimate of B.ii. (We can also express this as a Z- or t-score!)c. P-valuei. Tells us how likely it is that we would have observed that relationship by