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