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### 53 Cards in this Set

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 Hypothesis Testable statement about the nature of social reality; reasons for relationships. Measurement Assigning a unit of analysis to an attribute on a variable. Unit of analysis Person or thing from which data is collected. Variable Set of logical attributes that are of interest to the researcher. Conceptualization Process of formulating and clarifying concepts. Operationalization Describes the research operations that will specify value/category of variable on each case. Indicator Observable measure. Imperfect representation of concepts. Ratio Implied relation to 1. Proportions and Percentages fa/N fa/Nx100 Rates Make values comparable to each other. fa/D x 100,000 Inferential statistics Moving from description to explanation. Population Entire amount of subjects: large group actually interested in. Sample Selection from population - don't have access to entire population. Infer from samples to population. Should be representative. Hypothesis testing The extent to which samples reflect true numbers of population. Dependent variable What we are trying to explain. Variable that is measured. Depends on independent variable. Independent variable What is manipulated; what is causing dependent variable. Nominal Categories of this variable are mutually exclusive. No mathematical properties. Ordinal These variables can be logically ranked, but have no true mathematical properties. Interval These variable have true mathematical properties. No true zero point. Ratio These variables have mathematical properties and have a true zero point. Sampling distribution A hypothetical distribution of all possible sample outcomes for a statistic. Bridge between sample & population. Central Limits Theorem Many statistics have sampling distribution that is approximately normal. On average, the sample mean is the same as the population mean. Areas under the normal curve 68% within 1 standard deviation. 95% within 2 standard deviations. Statistical significance Unlikely it happened just by chance. Difference big enough/rare enough. Parameter Variable related to population. Two tasks of classical inference 1. Estimate magnitude of parameter. 2. Test specific claims about magnitude of parameter. Confidence Interval Estimate from standard deviation of statistic. 1.96 Point & interval estimation Using statistic as estimate of the parameter is risky. Unknown variability. Instead, create interval estimate. Alternatives to chi-square Phi: 2x2 table only Cramer's V Lambda: PRE measure Proportional Reduction of Error PRE measures compute prediction errors in two different situation: a) when only raw totals are used for prediction b) when an independent variable is used for prediction Concordant and Discordant pairs most PRE measures for ordinal variables based on assessment of pairs of cases. Con: same directionality Dis: opposite directionality Goodman & Kruskal's Gamma only uses cases with concordant and discordant pairs T-tests All types of t-tests are designed to compare sample means. Comparison of 2 "groups". Based on t distribution. Independent samples t-test What does "independent" mean? Score on test variable for members of 1st group are not dependent on scores of 2nd group. Standard form. Independent samples t test: assumptions 1. test variable is normally distributed in each of the 2 populations 2. the variances of the normally distributed test variable are equal 3. cases have been randomly samples from population 4. scores are independent Levene's test for equality of variances Tests assumption of equality of variances. Null=equal variances assumed. Paired sample t test What we use when assumption of independent samples is violated. Same person measured twice (per/post), or when pairs of subjects are matched in some way. Paired sample t test: assumptions 1. Difference scores are normally distributed. 2. cases have been randomly samples from population. 3. the difference scores are independent from each other (among sample) One sample t test Used when comparison mean is: a) unknown b) arbitrarily chosen Test Value Key consideration of one sample t test. a) midpoint of test variable b) average based on past research c) chance level of performance One sample t test: assumptions 1. Test variable normally distributed 2. cases have been randomly sampled 3. scores are independent of each other Mann-Whitney U test Nonparametric substitute for equal variance t test. Used when assumption of normality not valid. Significance testing Test specific claims about magnitude of parameter. Interested in parameters that indicate relationship. Idea of null hypothesis: reject or fail to reject. 0.05 alpha level Willing to risk 5% chance of wrong answer. If probability of observed relationship happening by chance is <5%, reject null. Type I Error Rejecting a null hypothesis that is true (saying there is a relationship when there is actually none). Type II Error Failing to reject a null hypothesis that is not true (saying there is not a relationship when there actually is). One-tailed test If we have directionality. Critical value is 1.64 Basic ideas of chi-square Are two variables related to one another? Null hypothesis: the two variables are independent. Logic of chi-square Observed and expected counts. Reject null if observed counts are sufficiently different from expected counts. How to conduct chi-square 1. Calculate marginals 2. Calculate expected counts 3. (observe-expected) ²/expected 4. then, sum across all cells 5. calculate degrees of freedom 6. compare observed w/ expected, determine if can reject null Calculation of expected counts row total x column total / grand total what we would expect to see if the two variables are independent of each other Degrees of freedom (chi-square) (row-1)x(column-1) How many pieces of information would I need in order to fill in the remainder of the cells? Limitations of chi-square Expected cell counts must be greater than 5. Often can't tell us relative strength of relationship.