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113 Cards in this Set
- Front
- Back
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sampling distribution
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distribution of all possible values of a statistic (a picture of the null hypothesis in hypothesis testing)
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statistic
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a value summarizing a measurable characteristic of a sample (mean of sample, SD of sample, etc.)
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parameter
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a number that represents the characteristics of a population (mean of population, SD of population, etc.)
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sampling distribution of the mean
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distribution of all possible means of samples of a given size taken from a population (tends to be normal in shape no matter what the shape is of the original distribution, especially for n>30)
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binomial distribution
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sampling distribution for events that have two equally likely possibilities (ex: coin flip)
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sampling error
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amount of error that exists between a sample statistic and a population parameter
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standard error of the mean
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standard deviation of the means in the sampling distribution of the mean (estimate of the amount of variability in the expected sample means in the sampline distribution of means)
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null hypothesis (Ho)
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the assumption that observed data reflect only what would be expected from the sampling distribution (no effect of treatment, no relationship b/w variables, no difference b/w means, etc.)
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research (alternative) hypothesis (H1)
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a prediction regarding the relationship b/w or among two or more variables
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observed value
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value of inferential test statistic based on observed data
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p-value (probablility value)
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probability of obtaining an observed value (test statistic) as extreme or more extreme if the null is true
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critical value
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value of test statistic associated with alpha level (defines criticial region)
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critical region
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region that identifies values of the test statistic associated with statistically significant outcomes (if the observed value falls in critical region, the null is rejected; if not, the null is not rejected)
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alpha level (significance level)
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probability of obtaining an observed value in the critical region even if the null were true
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statistically significant
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the conclusion to reject the null hypothesis, made when the p-value is smaller than alpha
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statistically nonsignificant
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the conclusion to not reject the null hypothesis made when the p-value is great than alpha
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effect size
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a statistic that indexes the size of a relationship
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one-sided (one-tailed) p-values
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p-values that consider only the likelihood that a relationship occurs in the predicted direction
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two-sided (two-tailed) p-values
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p values that consider the likelihood that a relationship can occur either in the expected or in the unexpected direction (more commonly used)
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steps in hypothesis testing
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1. develop research hypothesis, 2. set alpha (usually a=.05), 3. collect data, 4. calculate test statistic (observed value) and corresponding p-value, 5. compare p-value to alpha
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p < a (p<.05)
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reject null
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p > a (p>.05)
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fail to reject null
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type I error
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("false alarm") occurs when we reject a true null (conclude a coil is unfair when it is fair) probability=a
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type II error
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("miss") occurs when we fail to reject a false null (conclude a coin is fair wen it is unfair) probability=b
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correct decision I
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occurs when we fail to reject a true null (conclude a coin is fair when it is fair) considered a "boring" result. probability=1-a
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correct decision II
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("hit") occurs when we reject a false null (conclude a coin is unfair when it is unfair) *known as POWER (the ability of a test to fnd a difference when there really is one) probability=1-b
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relationship between a and b
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when a is lower (probability of making a type I error is lower) then b is higher (probability of making a type II error is higher)
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trade off between type I and type II errors
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most researchers believe it is worse to make a type I error than a type II error so alpha is ALMOST ALWAYS set lower than beta
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t-test (for independent samples)
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population mean and SD is unknown
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statistical significance
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effect size x sample size
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sampling distribution
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distribution of all possible values of a statistic (a picture of the null hypothesis in hypothesis testing)
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statistic
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a value summarizing a measurable characteristic of a sample (mean of sample, SD of sample, etc.)
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parameter
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a number that represents the characteristics of a population (mean of population, SD of population, etc.)
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sampling distribution of the mean
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distribution of all possible means of samples of a given size taken from a population (tends to be normal in shape no matter what the shape is of the original distribution, especially for n>30)
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binomial distribution
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sampling distribution for events that have two equally likely possibilities (ex: coin flip)
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sampling error
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amount of error that exists between a sample statistic and a population parameter
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standard error of the mean
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standard deviation of the means in the sampling distribution of the mean (estimate of the amount of variability in the expected sample means in the sampline distribution of means)
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null hypothesis (Ho)
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the assumption that observed data reflect only what would be expected from the sampling distribution (no effect of treatment, no relationship b/w variables, no difference b/w means, etc.)
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research (alternative) hypothesis (H1)
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a prediction regarding the relationship b/w or among two or more variables
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observed value
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value of inferential test statistic based on observed data
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p-value (probablility value)
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probability of obtaining an observed value (test statistic) as extreme or more extreme if the null is true
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critical value
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value of test statistic associated with alpha level (defines criticial region)
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critical region
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region that identifies values of the test statistic associated with statistically significant outcomes (if the observed value falls in critical region, the null is rejected; if not, the null is not rejected)
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alpha level (significance level)
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probability of obtaining an observed value in the critical region even if the null were true
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statistically significant
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the conclusion to reject the null hypothesis, made when the p-value is smaller than alpha
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proportion of explained variability statistic
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(in the DV) is indicated by the square of the effect size statistic
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t-test
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(for independent samples) population mean and SD is unknown
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assumptions of a t-test
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a. scores have been sampled randomly from the population, b. sampling distribution of the mean is normal, c. within-groups variances are homogeneous
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example of t-test from book
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Haney, 1984 two sample experiment on whether death-qualifying a jury affects how simulated jurors perceive a criminal defendant
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z-test
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inferential statistics with one sample compared to a population (with a known SD)
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increasing sample size results in..
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increase statistical significance of a relationship whenever the effect size is greater than zero
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p-value is not a good indicator of a size of a relationship because..
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it is strongly influenced by a sample size, so smaller p-values do not mean there is a stronger relationship, just means the results are even less likely due to chance
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effect size is the best index of the strength of a relationship because..
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it is not influenced by the sample size. it stays the same regardless of the sample size.
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Pearson Correlation coefficient (r)
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used to evaluate direction and strength of relationship b/w two variables (measured on an interval or ratio scale)-ranges from +1 to -1 and represents effect size statistic for correlation. p-value of r can be determined and t-test used to analysis of data.
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linear relationship
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a relationship b/w two variables that can be approximated with a straight line
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nonlinear relationship
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relationship b/w variables that cannot be approximated with a straight line
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positive correlation
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as one variable increases, the other variable increases; as one variable decreases, the other variable decreases
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negative correlation
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as one variable decreases, the other variable increases
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no correlation
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r=0
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independent-no correlation
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no relationship b/w the two variables (can't use one variable to predict the other)
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curvilinear-no correlation
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relationships b/w two variables that change direction, and thus are not described by a single straight line (ex. stress and performance)
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coefficient of determination (r squared)
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proportion of variance in one variable explained by the other variable (ex. an r of .6 would have a coefficient of determination of .36)
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restriction of range
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size of r most likely decreases if there is a restriction of range (occurs when most participants have similar scores on one of the variables being correlated)
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linear regression
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a statistical technique for analyzing a research design in which only one predictor variable is used to predict a single outcome variable
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regression line
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line that best represents or fits the data (can be described mathematically by equation for straight line)
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regression line y variable
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outcome variable
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regression line x variable
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predictor variable
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null hypothesis in correlational research
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r=0, no relationship between the two variables
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alternative (research) hypothesis of correlational research
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r doesn't equal zero; there is a relationshpi between the to variables
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significant r
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indicates linear relationship that can be used to predict one variable from the other
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spearman correlation coefficient
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used to measure relationships between two variables measured on ordinal scales. uses rankings to compute correlation coefficient.
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chi-square statistic
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used to assess the relationship between two nominal variables
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chi square test of independence
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tests the likelihood that two variables are independent (when the frequency distribution for one variable is NOT related to the categories of the second variable). (ex. can measure relationship b/w political affiliation and atttitudes toward nuclear power)
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contingency table
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displays the number of individuals in each of the combinations of the two variables
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null hypothesis for chi-square
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the frequency distribution for one variable will have the same shape (same proportion) for all categories of the second variable (ex. the proportion of democrats and republicans will be the same for all categories of attitudes toward nuclear power)
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alternative (research) hypothesis for chi-square
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the frequency distribution for one variable will have a different shape (different proportion) for all categories of the second variable (ex. the proportion of democrats and republicans will not be the same for all categories of attitudes toward nuclear power)
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chi-square analysis
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compare contingency table of observed values to expected values (if the null were true). if difference is big enough (statistically significant chi-square) then reject the null and conclude there is a relationship between the two variables)
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multiple regression
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a statistical technique for analyzing a research design in which more than one predictor variable is used to predict a single outcome variable (tested with an F-test)
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zero-order correlations
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correlations (r values) b/w each of the predictor variables and the outcome variable
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beta weights (regression coefficients)
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statistics that indicate the relationship between each of the predictor variables and the outcome variable holding constant the effects of the other predictors
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multiple correlation coefficient R
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(effect size statistic for multiple regression) - a statistic that indicates the extent to which all of the predictor variables in a regression analysis are able together to predict the outcome variable
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R squared
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represents the proportion of variance in the outcome variable explained by all of the predictor variables together
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path analysis
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(often used with longitudinal research designs) assesses the relationships among a number of variables and examines the possible causal directions among the set of correlated variables
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path diagram
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a graphic display of the relationships among a number of variables (results of the path analysis displayed visually)
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Reverse causation
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(directionality problem – does x cause y or does y cause x?) – the possibility that the outcome variable causes the predictor variable rather than the predictor variable causing the outcome variable
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Reciprocal causation
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the possibility that the predictor variable causes the outcome variable AND the outcome variable also causes the predictor variable
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Third (common-causal) variable
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variables that cause both the predictor variable and the outcome variable
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Spurious relationship
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a relationship between two variables that is produced by a common-causal (third) variable
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Extraneous variables
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variables other than the predictor variable that cause the outcome variable but that do NOT cause the predictor variable
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Mediating variables (mediator)
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a variable that is caused by one variable that in turn causes another variable
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Correlation matrix
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a table showing the correlations of many variables with each other
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Panel studies (longitudinal research designs)
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research in which the same individuals are measured more than one time and the time period between the measurements is long enough that changes in the variables of interest could occur
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Cross-sectional research design
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research in which comparisons are made across people from different age groups, but all groups are measured at the same time
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Structural equation analysis
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a multivariate statistical procedure that tests whether the actual relationships among a set of collected variables conform to a theoretical prediction about how those variables should be related
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Latent variables
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the conceptual variables or factors in a structural equation analysis
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experimental condition(s)
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the level of the independent variable in which the situation of interest was created (can have more than one experimental condition)
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control condition(s)
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the level of the independent variable in which the situation of interest was NOT created (can have more than one control condition; some experiments do NOT have a control condition at all [e.g., imagery vs. rote rehearsal])
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Levels of an IV
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the specific situations created by the experimental manipulation
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conditions
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a term used to describe the levels of an experimental manipulation in one-way experimental designs
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Participant variables
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a variable that represents differences among individuals on a demographic characteristic or a personality trait (e.g., ethnicity, gender)
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Between-participants designs
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experiments in which the comparison of the scores on the dependent variable is between the participants in the different levels of the independent variable and each individual is in only one level (each participant participates in only ONE level of the IV)
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Within-participants (repeated-measures) designs
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experiments in which the same people participate in more than one condition of an experiment, thereby creating equivalence, and the differences across the various levels are assessed within the same participants (each participant participates in ALL the levels of the IV)
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random assignment
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a method of ensuring that the participants in the different levels of the independent variable are equivalent before the experimental manipulation occurs
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within-participants design
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repeated measures
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matched-groups design
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research design in which participants are measured on a variable of interest before the experiment begins and are then assigned to conditions on the basis of their scores on that variable
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Hypothesis testing in one-way experimental designs with Two-groups (two levels of IV)
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t-test
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t-test advantages and disadvantages
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advantages – simple to conduct, analysis is easy; disadvantage – doesn’t tell you about function of relationship
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Hypothesis testing in one-way experimental designs with Three or more groups (more than 2 levels of IV)
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ANOVA
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advantages and disadvantages for ANOVA
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advantage – tells you about function of relationship (e.g., can identify curvilinear relationships between variables); disadvantages – more difficult to conduct, analysis is harder
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Between-groups variance
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a measure of the variability of the dependent variable across the experimental conditions in ANOVA (called mean-square between). treatment effect + individual differences + experimental error
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F ratio – in ANOVA
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a statistic that assesses the extent to which the means of the experimental conditions differ more than would be expected by chance
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Within-groups variance
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a measure of the variability of the dependent variable across the participants within the experimental conditions in ANOVA (called mean square within). individual differences + experimental error
C. F ratio – in ANOVA – a statistic that assesses the extent to which the means of the experimental conditions differ more than would be expected by chance |
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Degrees of freedom
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number of values that are free to vary given restrictions that have been placed on the data
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