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116 Cards in this Set
- Front
- Back
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What is Type I Error?
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We detect an effect (reject null) where none really exists.
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What is Type II Error?
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When you don't find an effect (fail to reject the null) but one really exists. Most common according to Cohen.
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What is it called when you have significance and an effect really exists?
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Power (reject null correctly)
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What is it called when you reject the null and there really is not an effect?
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The correct decision (fail to reject the null correctly)
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How would you know if a Type I Error has been made?
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We can never be certain but by setting appropriate alpha/significance level we can say, for example, that with a .05 alpha we are 95% certain that our test would not indicate a significant effect where none exists. The more conservative the alpha, the more confidence we can have in our statement (but more conservative also means more likely to make Type II error, the most common).
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What are the four levels of measurement? What are examples of each?
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Nominal- numbers at levels of categories (1=M, 2=F)
Ordinal- ordering categories on continuum based on rank (1= youngest, 2=middle, 3= oldest) Interval- ranking w/equal distances, arbitrary zero/ no inferences based on zero (1= 1981, 2=1982, 3= 1983) Ratio- absolute zero, equal distances between each item (height, weight) |
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What 2 types of data are measured?
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Quantitative- interval or ratio or ordinal
Qualitative- nominal or ordinal BOTH can be ordinal |
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What kind of general tests do you run with qualitative/nominal/ordinal DV(s)?
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Nonparametric tests- Chi square, logistic regression, discriminant analysis. Often have ranking but no actual values assigned (one to four stars)
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What kinds of tests do you run with quantitative/interval/ratio/ordinal DV(s)?
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Parametric Tests (more assumptions b/c probability of distribution parameters). Then, look at IV:
Qualitative IV - t-tests, ANOVA Quantitative IV- correlations, MR, multivariate analyses |
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What is HOV and HOVCVM?
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HOV- Homogeneity of variance- Levene's test tests the assumption that each group (category) of the independent)(s) has the same variance on an interval dependent. If the Levene statistic is significant at the .05 level or better, the researcher rejects the null hypothesis that the groups have equal variances. This is an assumption of analysis of variance (ANOVA). This is only a problem if there are unequal N in groups.
HOVCVM- Homogeneity of variance covariance matrices,same variance on an interval dependent and same relationships among DV's. Box's M test tests this, as required by MANOVA and some other procedures. When M is not significant, the researcher accepts the null hypothesis that groups do not differ. |
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What is Simple Linear Regression?
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Correlation! One continuous IV and one continuous DV. Age and SAT score
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What is multiple regression analysis (MR)?
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Do X & Y vary together? 2 or more continuous IV's, 1 continuous DV. Changes in age and weight effect SAT score?
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What is multivariate analysis?
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Simultaneous observation of two or more dependent variables:
MANOVA- 2 or more categorical IV's, 2 or more continuous DV's multiple regression w/ 2 continuous DV's (rather than just one) |
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What is r? What is R squared? What is xbar? What is ybar? What is μ? What is σ2?
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r- coefficient of linear correlation
Rsquared- coefficient of determination, variance explained in the model that you're using xbar- mean of sample values ybar- variance of sample values μ- mean of population values σ2- variance of population values |
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What is collinear? What is multicollinear?
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Collinear- very nearly correlated (technically perfectly correlated but this is usually not the way it's used)
Multicollinearity- used to talk about more than two variables being collinear, often people just say collinear. |
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What is effect size? What are some different effect sizes that we look at in statistics?
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Effect size- measure of the strength of the relationship b/w two variables. Descriptive statistic that conveys the estimated magnitude of a relationship, complements inferential statistics.
Different effect sizes: Pearsons r "r" Cohens d "d" F (ANOVA |
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What is σ?
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sample standard deviation (SD)
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What is the analytical perspective?
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If a differences in one variable (DV or Y) are the result of differences in another variable (IV X), then are the changes in DV/Y due to changes in IV/X. Do they vary together?
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What is the theoretical framework and what is its goal?
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The theoretical framework describes how theory always drives our statistics. We use hypotheses to determine which tests to use, and formalize hypotheses based on the scientific method (observable, measurable, empirical). Peer review lends credibility to this process.
Goal: to generalize beyond sample |
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What is range? What limits the ways we can use range?
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Measurement that includes the highest and lowest value ranges (highest-lowest+1=range). Highly influenced by outliers, sample size (difficult to compare 2 groups)
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What is Mean Deviation?
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Mean deviation is each score minus the groups mean score divided by # of scores
12, 9, 6 = group mean of 9 12-9=3 9-9=0 6-9=-3 3+0-3=0/3=0 Limit- Mean Deviation scores are always zero so you can't compare across samples. |
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What is variance conceptually and technically?
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Conceptually- a measure of how far a set of numbers are spread out from each other in a probability distribution. How far the numbers lie from the mean (expected value).
Technically- average of the sum of squared deviations. You have to find the square of each deviation score, sum them, and divide by number of scores (n) Limit- must use two different formulas for population and sample |
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What is covariance conceptually and technically?
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Conceptually- a measure of how much two variables change together or the degree to which two scores change relative to their means
Technically- sum of cross products deviations of pairs of x and y scores from their respective means divided by N-1 Note- if they change together a lot variance is small, if they change together a lot variance is large |
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What is the equation for a line?
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Y= a+bx
Y is the DV score PREDICTED a is the y intercept (where data falls on y axis, the higher the value, the higher the line & vice versa) b is the slope/beta weight. The slope tells you how many points Y will increase for any single point increase in X x is the actual data point/score (on IV) |
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What is the equation to find a score (using equation for a line)?
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y=a+bx+ e
e is error, the distance b/w predicted & obtained y (DV score), or what is NOT predicted by equation of line. The larger the error (deviation from the line), the worse the line fits the data |
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What is the statistical test of significance for simple linear regression? conceptually, what is it measuring?
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The F test
Conceptually, You are dividing the SS Regression divided by k (# of IV) and dividing that by the SS Residual (error) divided by (N-k-1). You compare this F value to a pre-determined F value. If less than this number you fail to reject the null. If larger than this number you reject the null. If F < 1 there is more unexplained than explained variance (no good). explained/error Limit- the larger the sample size, the more likely you are to get sig F |
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What is range restriction?
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It reduces the correlation that otherwise would be found, will be larger than overall samples. Example: correlation b/w HS GPA and college GPA when every student had the same HS GPA (Correlation would be 0)
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What are some assumptions of simple linear regression? What are the implications of violating these assumptions?
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IV level is fixed (use same X /IV values in replications)
IV measured w/out error Pop means of Y at each level of x are linear Y (DV) is a random variable Violating measurement errors in DV leads to less accuracy (errors don't bias regression in one direction) Violating msmt errors in IV leads to errors biasing regression, underestimating true regression. |
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What is an outlier? How do you detect outliers?
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An outlier is a data point that is distinct/deviant from the general trend of the data. Commonly due to either methodology or actual observed behaviors.
To detect: Standardized residuals (ZRESID): Look for values greater than 2 Studentized residuals (SRESID): better than zresid b/c does not assume all residuals have same variance. follows t distribution Studentized Deleted Residuals (SDRESID) The general idea here is that by including the outlier you are lowering the likelihood that it will be detected- SPSS will do this for us (running analysis on all data points) so we don't spend all day doing studentized deleted residuals Standard->Studentized->Studentized deleted! |
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Why do we need influence analysis?
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Sometimes data points have a larger influence on the regression coefficients than other data points- where an outlier pulls the data wider (lower correlation than there really is) an influential observation pulls the data longer (higher correlation than there really is). See page 49 in Pedhauzer for refresher if necessary.
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What are some different types of influence analysis?
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Leverage, Cook's D, DFBETA, Standardized DFBETA
Leverage- all things being equal the large an x score deviates from the mean the larger the average. A subjective comparison of one point to others- doesn't tell you how much. Cook's D- Look for large difference in Cook's D, doesn't tell you how much influence DFBETA- After deleting a data point you can see how much actual influence it has, still influenced by scale of msmt so can't use across studies Standardized DFBETA- Enables us to compare DFBETA across studies. Can see what costs of taking outlier out are, look at generalizability ALWAYS REPORT WHY YOU EXCLUDED OUTLIERS/INFLUENCE OBSV'S |
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What is the formula for Multiple Regression (R)? What is the formula doing?
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2 or more IV's & 1 DV
Y= a+b1x1+....+Bkxk+e b1=slope for IV1 X1=IV score for IV1 bk=Slope for last IV xk= IV score for last IV Predicts the DV from multiple IV's by minimizing the distance b/w all IV's in a regression line (best fit of data) |
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How would you notate a multiple regression situation where you had 4 IV's but only wanted to look at the first two and the last on a DV?
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Ry.124
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What information is contained in a regression equation?
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Prediction- maximizes prediction by optimally weighting each iv to get best fit and minimize error
Proportion of variance explained- total variance of ALL IV's, more confident in prediction w/more variance explained Test for Statistical Significance- R2 Relative importance-used to determine if any of the iv's are statistically sig- important to have indiv tests be sig so you can see where the variance is! |
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What are regression weights and how do you use them?
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There is b which is an unstandardized regression coefficient. You report this with raw scores or applied research.
Then there is Beta (fancy B) which is a standardized regression coefficient. You report this when dealing with standardized scores or theoretical research. |
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What does Rsquared tell you? How do you test for it?
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Rsquared is the variance of the DV accounted for by all the IV's (effect sizes). You test for R squared with the F test which tells if you all the variance accounted for in the IV's explains a significant amount of variance in the DV.
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Once you have your Rsquared (variance explained in DV by all IV's) how do you tell which IV's add significant variance? What are some things you should think about when looking at these results?
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You have to test the each IV's regression coefficients (regression weights) after controlling for the other IV's by partialling out the other IV's.
Things to think about: Intercorrelated IV's will lead to non-significant partial regression coefficients b/c of the overlap. It is possible that all the IV's together account for sig variance (Rsquared) but the individual IV's do not (beta weights). Will get same results with standardized vs unstandardized beta weights! |
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Describe confidence intervals and what you can do with them.
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CI= beta weight +or- Tcritical value times the standard error of the beta weight. Tcrit- cutoff value for either rejecting or failing to reject the null indicating the score is outside the normal t distribution.
Confidence intervals allow you to say "I am 95% certain the true score is between these two values". You can use CI's instead of p values to determine significance. |
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What is a t test? What would you set as an alpha level? How would you know if you could reject the null?
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A t-test is an inferential test that determines if there is a significant difference between the means of two data sets. In other words, a t-test decides if the two data sets come from the same population or from different populations.
Setting alpha- An alpha level represents the number of times out of 100 you are willing to be incorrect if you reject the null hypothesis. If you choose an alpha level of 0.05, 5 times out of 100 you will be incorrect if you reject the null hypothesis. You can look at tcrit or p value. If the tcrit is greater than the tstat then you can reject the null. If the p value is greater than alpha you can reject the null. |
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Can you determine relative importance from multiple regression? What part of your equation would define relative importance?
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You can determine relative importance to a degree with standardized beta weights. You cannot infer relative importance with unstandardized beta weights because they can be influenced by the scale of measurement. You can look at the b's sig level to see if it does account for variance but this does not tell you the relative importance of that IV on the DV.
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What are the two ways that we can exert control in scientific research? What are the implications of each (pos & neg attributes)?
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We can exert experimental/methodological control and statistical control. Experimental control is best because the xp controls the distribution of variance (b/c of theory). The nature of the construct remains unchanged but this takes longer to do and is not always possible.
Statistical control is easier and faster- takes place after the data is collected- you control the distribution of the variance with statistics (control by partialling). The more control you exert the more you fundamentally change the nature of the variables you're studying. You control for variables by partionalling (and semi-partialling) the unique variance one variable shares with the others (they are genuinely related but you're changing it so they appear to not share the same variance). |
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Statistical control is tantamount to partialling/controlling for variables. What are some of the different problems you can run into when controlling in this way?
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The ides of partialling is that you only want to look at the unique variance that two variables share, so you control for another variable that you think influences that relationship.
Some problems we might encounter are: We might identify spurious relationships through partial correlation. This is when two variables are only correlated b/c of the influence of a 3rd variable. There is no relationship after you partial out the MEDIATING variable. You may also find that a variable moderates the relationship between the two variables you're studying- affecting the zero-order correlation between two variables of interest. Mediator- tells you why two things are related (only b/c of 3rd variable) Moderator- tells you when two things are related (situational relationship) |
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What do we mean we talk about zero-order correlations between variables? What is an implication of using zero-order correlations?
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Zero-order correlations are the relationship between two variables, while ignoring the influence of other variables in prediction.
Implication: A simple correlation does not account for possible overlaps between independent variables (redundancy problem). |
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When looking at partial vs semi-partial correlation which one is going to be smaller? What are the advantages of partialling a "smaller" amount of variance? What are you giving up?
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Semi-partial correlations will always be smaller than partial correlations, which is good b/c you are measuring more of the actual construct (takes a smaller chunk of genuine variance out).
Unfortunately with semi's you will have a harder time finding significance b/c there is less variance accounted/controlled for/explained. |
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What is a suppressor variable? Why should they be identified? Possible causes?
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A suppressor variable enhances the correlation b/w two variables by increasing regression weights and, thus, increasing the predictive validity of other variables in a regression equation.
Suppressor variables can lead to results that do not reflect treatment on outcomes (instead of a drug leading to reduced symptoms vs control group the drug might appear to lead to more symptoms b/c of suppressor variable e.g. treatment setting) You can identify a suppressor variable by looking at the way your constructs are correlated- if an item is positively correlated to many things in the total model but demonstrates negative bivariate correlations than you would have a suppression suspect. Ideally you would plot your data so that suppressor variables would be more easily identified, thus improving your analysis to include more "true" information about the variables. Possible causes: collinear variables, small N, confounding/spurious variables |
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What does Pedazur have to say about prediction and explanation in scientific research?
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Prediction is useful for applied research (predictor, criterion), not interested in furthering theory but should be rooted in theory (clinical psych).
Explanation is useful for understanding, experimental research (IV, DV), interested in advancing theory |
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How can you detect a moderator? What would you do with it?
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You dummy code the suspected moderator (1 & 2), so then you take your first IV and multiply that by the dummy coded sex variable. This gives you 4 things: V1, Dummy coded variable, Dummy var*V1, and your DV. Regress your DV on the 2 IVs and the interaction term. If the beta weight for dummy*V1 is significant, this means you have differential prediction of V1 leading to DV on the Dummy coded variable... or in English, you have a moderator. From there you can look at levels of V1 for Dummy coded variable (mean +/- standard deviations)
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How could you use regression analysis in a selection situation?
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You could predict some criterion (like performance) by giving appropriate weights to several predictor variables (performance on work sample, personality test, etc). We don't care about saying why they predict, we just want the best candidates.
would use b (unstandardized) b/c it is applied research |
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What is shrinkage? How could you minimize shrinkage?
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Shrinkage occurs when your multiple regression equation is derived from zero-order correlations that are thought to be error free- this never happens so obtained Rsquared will be less than ideal.
Shrinkage depends on the # of predictors to sample size, and all things being equal, the smaller the ratio the smaller the shrinkage. Essentially, when you're trying to see how well a regression equation obtained in a sample performs in another sample from the same population you would cross-validate to estimate shrinkage. You can minimize by using fewer predictors. |
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What is cross validation? What is it used for?
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Your first sample is called a screening sample. Your second sample is called a calibration sample. You look at the DV when predicted with the regression equation you used in the first sample (this creates a cross-validity coefficient). If the difference between the previous Rsquared and the cross validity coefficient is small then it is appropriate to use in other situations w/the same conditions. This is used when you want to estimage how well a regression equation performs in a similar sample (including associated shrinkage).
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What are some methods for predictor selection and in what situations would you recommend them?
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All possible combo's- you want an informed choice. Adjusted Rsquared will probably be highest but you may exclude the best predictor (b/c it's not in the highest combo)
Forward selection- Start with highest zero order correlation, stop when your predictors stop adding adjusted R squared. Never use-redundancy Backward elimination- Start with all predictor combo Rsquared. Then, delete predictors so that this value remains the largest possible (deleting predictors that have smallest decrease in Rsquared). Use when you want max Rsquared and non-redundant predictors (may still have collinearity) Stepwise- Most common. start with highest zero order correlation, then 2nd, etc. at each step you make sure predictors are redundant. You look at FIN & FOUT. Gives you a parsimonious set of IV's. Blockwise- group predictors into blocks constructed based on theory, then stepwise block by block (order theoretically determined). Keep predictors in block that are not redundant and still predictive. Lock that block. You can reorder the blocks. Use when you want the most meaningful predictors from each. |
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Power table question- what are the four types of outcomes that we can find when looking at our statistics results?
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Power- Finding a significant effect when in fact there is one present (1-Beta)
Beta- Finding a non-signifcant effect when in fact one is present Type II Correct decision- Not finding a significant effect when there is none present (1-alpha) Alpha- Identifying a significant effect when none is present. Type I |
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What must be true of the null and alternative hypotheses? How do we notate these?
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H0: Null hypotheses
H1: Alternative hypotheses Hk: etc All hypotheses combined must be inverse and exhaust all possibilities. |
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What is the general idea behind hypothesis testing? Confidence Intervals?
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Hypothesis testing: We are 95% certain that when we do not identify an effect (failing to reject the null) none in fact exists (alpha level)
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What does a t-test do? What are the two kinds? Assumptions of both?
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A t-test makes inferences about the sample variance when the population variance isn't known.
Independent measures t-test: Two separate samples for each population or treatment. Repeated measures t-test: Looks at 2 sets of data from the same sample, with no variance due to individual differences (b/c same people). Assumptions: Normal populations, Values are independent, homogeneity of variance (linear, varying together) |
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What are the four goals of science? How do we implement these via statistics?
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Describe- Means, SD
Explain- Ultimate goal of science, ANOVA, Regression, as appropriate Predict- Attributable variance to IV's Control- Partioning variance, rigorous methods, scientific method (observable, empirical, measurable) |
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Two main ways that researchers approach research is for the sake of explanation for the sake of prediction. What are the two reasons for pursuing these different avenues and what statistical methods do they employ?
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Applied researchers are interested in prediction- they are concerned with treatment effects and practical outcomes such as employee selection. E.g. Using regression in selection with beta weighting for different predictors of performance.
Basic researchers are interested in explaining why relationships exist or why outcomes occur. They might use ANOVA to examine how variability between treatment conditions in a clinical study can be attributed to different IV treatment levels after controlling for between treatment variance (leaving only variance attributed to tx). |
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An undergraduate researcher comes to you with a study idea- she wants to see if category membership (M/F) predicts the outcome of number of close relationships. She suspects females have more close relationships than males. What would you advise her to do?
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She must dummy code the category membership of male and female (Female =0, Male =1). You then use these nominal variables in regression to compare each group on the outcome (# of close relationships). You should tell her to look at the F value, it gives the same information that it does in an ANOVA w/non-dummy coded variables (will say if there is a difference, but not where). If the null is rejected she should do post-hoc tests (Scheffe or Tukey, recommend Scheffe b/c it's conservative)
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What is a quasi-experimental design?
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You conduct research with no random assignment, b/c of practical or ethical issues, so your study results are harder to interpret (less control, less variance controlled for, less internal validity). Example: having cutoff scores for inclusion into a treatment condition for a clinical trial so that only those who need the tx the most are included. People who don't meet this cutoff are considered to be in the control group.
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Another undergrad comes up to you and asks for your advice on conducting a study where he wants to look at how interviewees may perform differently based on the information they receive from the recruiter before an interview. He is thinking that people will perform differently when they get no information, get basic company information and when they get basic company info + the job description. What would you recommend to him?
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Recommend using effect coding which is a code based on treatment effects. We are interested in seeing what the expected differences will be based on the manipulation (This procedure compares the groups to the overall mean). For example, he can enter the data as: Company info = -1, No info = 0 (control), Co. info + job desc = 1). This will give him an F test which will tell him if there's an overall distance but not where. If the null is rejected he should do post-hoc tests (Scheffe or Tukey, recommend Scheffe b/c it's conservative)
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What is an ANOVA? How does MS (mean square) fit into the ANOVA framework?
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An ANOVA, or analysis of variance, is similar to regression in that we are interested in the changes of an IV on a DV but we don't always have continuous data (ordinal, interval, ratio). For categorical data we must use ANOVA to examine the variance between groups of two or more treatment populations. Your IV is always going to be the factor and your DV is the level. MS or mean square is the variance between groups or levels (MS between), and the mean square within groups (MS within). Your significance test for ANOVA is the F test, and it looks at MSbetween(tx)/MSwithin(chance).
One factor (DV) = Single factor design 2+ factors = factorial design Look at interactions (moderators of relationships) first and then main effects (mean difference of DV based on level of IV). When you reject the null and you have 3+ tx groups you should follow up with pairwise comparisons while controlling experiment-wise alpha. Use Scheffe over Tukey because it is more conservative and uses less degrees of freedom. |
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What is an ANCOVA? What is an appropriate way to use ANCOVA?
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ANCOVA, or analysis of covariance, is an extension of ANOVA that examines potentially confounding variables (covariates), essentially controlling for them and making them part of what ANOVA treats as error. Error smaller = F ratio larger, easier to get significance.
ANCOVA adjust the means of the DV to what they would be if everyone got the same value on the cv's by estimating the linear impact of each cv on the dv and adjusting to remove this impact. Each CV costs a df. Assumes that the cv's are correlated with the DV, uncorrelated to each other, and measured consistently. Assumes random samples. Limited generalizability. You still look at the F statistic, but now you also must look at eta quared (η2) which is similar to R squared in ANOVA with one IV and partial η2 with multiple IV's. To use ANCOVA appropriately you must have categorical IV's, more than two treatments/populations, and want to control for some confounding factors or you suspect interactions and also confounding factors. You must also either have equal cell sizes or correct for the equal cell sizes. |
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What is eta squared (η2)?
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SS between/SS within
Effect size of F test in ANCOVA A measure of relationship: like a correlation coefficient it tells you on a scale 0 to 1 how much of variance in DV can be account for by each IV (analogous to r2 and can be thought of as a % on a scale 0-100). e.g η2= .36 = 36% variance explained in DV by IV. It is a useful addition to just being told if a relationship or difference is significant (F value does this). As an estimate of variance explained in the population it is upwardly biased (i.e., an overestimate). |
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In ANCOVA, how can you correct for unequal cell sizes? What are your options and what is your "best bet"?
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There are four options to deal with unequal cell sizes in ANCOVA, besides just collecting more data:
1. Randomly delete cases- conservative, costs power 2. Adjust all main effects & interactions for each other & for the effects of the covariates- preferred in xp research 3. Adjust observed effects for each others, tx unequal cell sizes as indicators of importance (emphasizing main effects over interactions- wrong) 4. Researcher decides relative importance of effects (subjective, hard to defend). |
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What are some assumptions of ANCOVA?
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No outliers- this violates the homogeneity of regression assumption
No collinearity- we do not want any relationship between CV's- test by running multiple Rsquare tests with each cv as a dv- drop if greater than .5 Normality and homogeneity of variance- usually the case when sample is greater than 30 anyways. |
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What is MANOVA?
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An ANOVA with multiple DV's
Categorical IV's, 2+ Continuous DV's Creates a COMPOSITE DV out of multiple DV's and asks if that combo varies based on treatment. COMPOSITE DV is a linear combo of all DV's that maximizes group differences A different composite is created for EACH main effect & interaction. If you ran multiple ANOVA's instead of a MANOVA you would miss out on seeing if the DV's are correlated and you would have redundancy in your DV's. DV correlation above .6 is a sign that you need to scrap your study and find uncorrelated DV's. MANOVA can be LESS POWERFUL than ANOVA b/c you're looking at more variables, but it is more useful b/c you need to know if there are effects of combo's of DV's! |
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What is MANCOVA? What test statistic would you use?
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Multivariate analysis of covariance.
Again, you have multiple DV's statistically combined into a composite DV, where you want to assess the effects of IV's, but now you also want to control for covariates (see if DV's are redundant/cv's of other dv's). You would use Stepdown analysis to look at contributions of individual DV'. Start with most important DV based on Lit Review, and then an ANOVA is performed as if that DV was the only one present. If sig then MANOVA treats that DV as a covariate. Next, add the next important DV against all the IV's w/ your new covariate. Keep up until you find a non-sig ANOVA! Test statistic: Use the F test still, and post hoc: Wilks' lambda which is a direct measure of the proportion of variance in the combination of DV's that is unaccounted for by the IV. |
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When looking at 1+ categorical IV's and multiple continuous DV's (MANOVA, MANCOVA), what are some limitations that you need to consider?
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You may end up over-assessing your DV's (redundancy- use MANCOVA),
Still have to decide which DV is most important (subjective) Unequal cell sizes are an issue, need more cases in your cells than you have DV's Must have multivariate normality (an extension of the normal distribution) Assumes no outliers present Assumes homogeneity of variance matrix is the same for every cell assumes absence of collinearity (must delete collinear DV) |
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What is the matrix method that we employ in looking at raw data?
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Briefly, the variance for a variable is a measure of the dispersion or spread of scores. Covariance indicates how two variables vary together.
The variance-covariance matrix is a compact way to present data for your variables. The variance is presented on the diagonal (where the column and row intersect for the same variable), while the covariances reside above or below the diagonal. |
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What is the idea behind variance partitioning? Is it empirical or theoretical? Does variance = importance?
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Variance partitioning is the idea that Rsquared tells you the total variance accounted for but not which IV accounts for what amount of variance and also, we can divide this variance (partitioning it) to figure out what variance is attributable to each predictor. This must not be confused with the importance of the IV, but rather what each IV adds beyond what we already know.
This is an empirical question and is only valid for prediction! E.g. what variance is attributed to gender, group membership or error? |
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What is incremental partitioning?
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Looking at effects of one IV when controlling for other variables, must have theoretical reason to do this!
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What are exogenous & endogenous variables? What is a direct effect? Indirect effect? Total effect?
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Exogenous- variable in which variability comes from outside the theoretical model- no attempt is made to control for these (assumed relationship).
Endogenous- variable in which variability comes from inside theoretical model (endo/attempts to explain relationship) AND outside the model (exo/does not attempt to explain relationship). MUST REFLECT THEORY Direct effect- causal link b/w var's Indirect effect- theoretical link b/w var's which goes through a mediator. Total effect- sum of direct & indirect (rsquared). |
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What is an effect?
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Influence of IV on DV, assumes you have control, removes other plausible alternative explanation (more control = causal statements).
Indicate average relations b/w IV's on DV but don't tell you HOW IV's lead to DV's. Predictive statement only. |
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What is the regression equation (review)?
What is the equation for an actual score? Formula for a line? |
Regression Equation:
Y = a + bX (Y= Score on DV; a= y intercept/ alpha/mean of population when x is zero; b=slope/regression coefficient in the population; X=value of IV/x score) Equation for actual score: Above, plus Error (e) |
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How do you find the slope of a regression equation?
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Slope (b) = regression coefficient in population (Sum of XY/Sum of xsquared)
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How do you find the y intercept in a regression equation?
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y intercept = mean of population (alpha)- Mean of Y (Ybar/average DV of sample)- slope * Mean of X (Xbar/average IV score of sample)
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What is a proxy? What two kinds of validity must you consider when selecting a proxy? Are proxies ever perfect?
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A stand in for a construct, your proxy is more easily measurable than construct (GRE for academic potential)
Must consider: construct validity- does it represent the construct? predictive validity- does your proxy predict successfully (ie to other proxies that have been validated, GRE on GPA). Can never be perfect or it would BE the construct. |
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What are specification errors? What are the four different kinds of specification errors? Which one is the hardest to detect?
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Specification errors are mistakes that you make when constructing your model, usually through inclusion/exclusion of variables and talking about how they're related. This leads to misinterpretation of the theory/results.
1. Omitting relevant variables (criterion deficiency) Biases slope upwards or downwards. 2. Including irrelevant variables (criterion contamination) You lose df, which increseases Standard Error of Estimate. 3. Nonlinearity- predictors not linearly related, not appropriate for regression equation. can fix by squaring one of the variables (quadratic term) 4. Nonadditivity- interactions are present (effect of 1 depends on the other) fix by multiplying together. Hardest to detect omitting relevant variables. |
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What is SEM?
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Standard error of the mean- standard deviation of test, if same person took the test infinity times they would get a standard deviation from the mean (SEM)
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What should we remember about measurement errors when looking at regression? What are three types of measurement errors?
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Regression assumes that measurement errors don't happen- but they do. They bias beta weights (standard and unstandardized), They bias Rsquared downward when in the DV
They bias Rsquared up or down when in the IV. 1. Conceptually measurement errors exist b/c our proxy will never match the construct 2. Consistent/systematic measurement errors indicate that all participants have same biasing experience 3. Random measurement errors are just the errors that vary across time & people. |
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What is collinearity, how can you diagnose it?
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Collinearity is the presence of highly correlated predictors which introduce redundancy into your model.
Reduces df and precision of regression coefficients. You can diagnose with the Variance Inflation Factor (VIF) which tells you how much variance in regression weights is overestimated by the predictors being correlated. You could also look at tolerance. Either way, being close to 1 for both means ='s lesl collinearity, closer to 0 = high collinearity |
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What is the main difference between unstandardized beta coefficients (b) and standardized beta coefficients (fancy B)? Which one would be more effected by the reliabilities of the measure? What do both have in common?
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b= can compare SAME predictor/criterion across groups, you don't lose any of the raw score information.
Fancy B= Looks at standard deviation of predictor and how that relates to the criterion. You can compare relative contribution of predictors. Ok to use across predictors that have scales w/different reliabilities across groups. Unfortunately it is affected by sample variability. BOTH REPRESENT CHANGE ON DV WHEN YOU HAVE ONE UNIT CHANGE IN IV!!! |
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What must we remember above all else when interpreting beta weights (both standardized and unstandardized)?
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You must look at theory/original model when interpreting beta weights!!
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What is Logistic Regression? What makes it different from ANOVA, MANOVA?
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The goal in Logistic Regression (LR) is to predict (discrete) categorical outcomes (like group membership) from categorical and/or continuous IV's... this creates a relatively continuous DV. Uses logit function/logistic (S-shaped) curve. Main difference is that we are now looking at Categorical DV's!
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What DOESN'T Logistic Regression assume? What DOES it assume? It is a parametric or non parametric test? What does that mean?
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LR does NOT assume:
Normal IV distribution(s) IV linearity Homogeneity of variance Linear IV-DV relationship B/c of these non-assumptions this is a LOW power test, always will be less powerful than multiple regression b/c of these. LR assumes/needs equal people in each condition! LR is still a non-parametric test b/c it does not have parameters, also look for CATEGORICAL DV's. A nonparametric test makes no assumptions at all about distribution. |
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What is a probability test and how does it relate to LR? How does LR make the DV continous?
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A probability test is essentially an odds ratio. In LR you look at the P (probability of occurring) and the 1-P (probability of not occurring).
Odds =P/1-P LR makes the DV continuous by considering natural logarithms (ln), or LOGIT in relation to probability Logit(P)= ln(P/(1-P)), extendes DV to +/- infinity (S shaped/logistic curve) |
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What is the clinch pin of LR in terms of the equation and outcomes? What would LR hypotheses look like?
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You can predict group membership (outcomes) because LR gives you relative weights for each predictors alongside a significance test. You can turn this around to get the probability of the actual odds of the outcome.
Logit (DV)= B1(IV1)+ B2 (IV2)+ constant (B0). H0: IV's not predictive of DV category H1: IV's are predictive of DV category |
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When would you use LR? What significance test would you use with LR?
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Your data does not meet the assumptions of discriminant analysis but you still want to predict category membership/dichotomous behavior/classification/etc.
You would use -2Log Likelihood (-2LL), a badness of fit test, close to 0= good model fit, close to 1 = good fit. You still can't talk about % of variance accounted for b/c DV is discrete/dichotomous. |
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What stat's would you use in following situations:
1. IV is continuous and DV is continuous 2. IV categorical, DV continuous 3. IV categorical, DV categorical |
1. bivariate correlation (continuous, continuous)
2. t-test (2 sets of data/categories, look at means) 3. Logistic regression (categorical DV) |
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What does chi square tell you?
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It looks at observed vs expected frequencies
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What is a bivariate correlation?
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It is just a correlation (bi=2, correlation b/w two variables)
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What are some examples of nonparametric tests? What do they all have in common?
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Chi square, discriminant analysis, logistic regression. Categorical dv's. Do not meet assumptions of parametric statistics.
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When would you use a bivariate correlation?
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When you have 1 continuous IV and 1 continuous DV and you're not controlling for any variables
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When would you use a partial correlation or hierarchical regression? How would you know you need to use hierarchical regression instead of stepwise?
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1 continuous DV
Continuous IV's Controlling for one or more variables Hierarchical regression is based on theory, stepwise is based on using the highest zero-ordered correlations first. |
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What is canonical correlation and when would you use it?
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Canonical correlation allows us to investigate the relationship between two sets of variables, it is an extension of Multiple Regression. Canonical analysis subsumes MR, DA & MANOVA.
Continuous IV 2 or more Continuous DVs |
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When would you use a t-test, what are the different types and when would you use them?
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A t-test has to have 1 continuous DV, and 1 categorical IV (w/only 2 levels)
One sample t-test- comparing sample to population mean Independent Samples t-test- comparing means of 2 independent groups Repeated measures t-test- one group tested twice Paired samples/Matched group- groups matched on single characteristic (e.g. age or IQ) |
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When would you use an ANOVA? What are the two types of ANOVA?
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Use ANOVA when 1 continuous DV and 2+ Categorical IV's or one IV with 3+ levels
Repeated measures ANOVA- W/in subjects design One way or two way ANOVA- Between subjects design and # of IV's |
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What are the differences b/w one way vs Two Way ANOVA?
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one way- testing b/w two or more independent groups, assessing treatment or time effect (only one factor).
two way- can assess both time and treatment in the same test, but also whether there is an interaction between the parameters. Assesses simultaneously. |
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When would you use MANOVA?
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2+ continous DV's
Any number of categorical IV's |
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When would you use Multiple Regression?
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2+ continuous IV's
1 Continuous DV not controlling for variables |
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Before entering a between subjects ANOVA into SPSS, what is it helpful to do?
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Draw out the matrix array for each (Gender * Group) Two genders x Low/Control/High groups (-1, 0, 1)
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When writing about significance and effect sizes how do you structure your sentence?
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The effect size (T/F/Wilks lambda/etc) produced a positive sign/non sig effect,
F(df)=effect size, p><=.05 (alpha level set), there is/isn't a significant effect b/w DV at time 1 (M=mean) and DV at time 2. (M=mean) |
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What is the difference between parametric vs. nonparametric statistics (what’s the difference and why do we care?)
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Parametric- based on normal (Gaussian) distribution
Non-parametric- not based on normal distribution nonparametric are used when: one ore more variables measured on nominal or ordinal scale, or even interval or ratio when parametric assumptions aren't met. You need to evaluate what is the best type of test for your data- some nonparametric tests may be more robust for some populations than parametric tests. |
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Why would we use discriminant function analysis (as opposed to logistic regression)? What part of the discriminant function do we look at to see how well the functions discriminate b/w groups? What is an issue with it?
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Similar to ANOVA or Regression (using linear relationship to predict outcome) but looks at CATEGORICAL DV (discrete group membership, often dichotomous). ASSUMES equal interval IV though.
We look at eigenvalues to tell us how well the functions differentiate- the larger the eigen the better the discrimination. A problem is that it has no upper limit. Logistic regression has more flexible assumptions but of course requires a higher N (use when IV is nominal or ordinal) |
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What is Factor Analysis and what are the things we can do to understand what factors we're measuring?
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Factor analysis is a data reduction technique used to help id underlying constructs. Can be explanatory or confirmatory. Groups items w/similar factors into structures (orthogonal or oblique).
You can understand the factors better by using one of these: Step 1: Extraction with Principal Component Analysis- pulls out potential factors in data, look at Eigenvalues to see which ones to keep. Step 2: Factor Rotation- Rotate factors to make them more interpretable: A. Orthogonal (forces/assumes uncorrelated factors). Default setting, not a common assumption but ppl use it anyways. Recommend: VARIMAX (most common) B. Oblique (allows/assumes factors are correlated) Looks at Loadings AND correlations b/w factors. Most practical. Recommend: PROMAX (gives best oblique structure). |
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What is a scales internal consistency reliability? What are some forms of internal consistency?
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just a correlation (unidimensionality), measure with cronbach's alpha :)
Forms: Split-half- one half to another Coefficient alpha- average of all the possible split half combo's KR-20 Version of alpha used with DICHOTOMOUS variables. |
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What is the difference between coefficient alpha and cronbach's alpha?
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Alpha level (also known as level of significance) is the probability of type I error. It is the probability of rejecting the null hypothesis when it is true. In hypothesis testing problems, this is usually assumed to be 0.05 (5%) or 0.01 (1%) even though any other percentage ( < 0.10) may be assumed.
This means 5% out of 100 times, we are likely reject the null hypothesis when it is true (if alpha = 0.05), that is to say we are 95% certain we will only find an effect if one in fact exists. Cronbach's alpha is a coefficient of reliability. |
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What is Item analysis? What are the two types of correlations you should look at? How would you know if you have a bad item?
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Item analysis test to see if all of the items individually do a good job of assessing the construct.
Look at these 2 correlations: Item-total correlations- correlation b/w each item and the score on the measure Inter-item correlation- correlations b/w items, should be high & positive for unidimensional test. You can tell if you have a bad item b/c when you delete it the analysis returns a higher alpha for the test. |
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What is a binomial Test? Why do you use it? What do you look at?
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Compares proportions of people or behaviors that fall into categories on a TWO-category variable.
You look at your base proportion- which is the null hypotheses that tells you how often a behavior happens in the population by chance. Heads or tails: .50 Then, compare observed proportion from xp to base proportion. You would use this when you suspect that there's a 50/50 chance but want to be certain. |
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What is a chi-square test? Why do you use it? What do you look at?
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Chi-square is the same as binomial except that it compares 2+ groups.
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What is Crosstabs/Contingency analysis?
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Contingency tables are used to assess whether a statistical relationship exists b/w 2 variables. E.g. are college males who tx young, middle aged and elderly women with disdain the same (or different from expected?).
Looks at FREQUENCIES of relationships among variables. |
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What are some nonparametric tests that you could use for independent samples?
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Mann-Whitney U (MW)- all scores b/w 2 groups converted to ranks and then compared
Kruskal-Wallis - same as MW but looks at 2+ samples Median Test- Creates a 2-way contingency table to see if there is a relationship b/w rows and performance. Good to use when neither the mean nor mode are appropriate. |
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What are some nonparametric tests that you could use for Related samples?
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McNemar- looks at pairs of data, dichotomizes data (not good), ignores tied scores
The Sign Test- only concerned with the direction of the difference b/w scores- ignores tied scores. The Wilcoxon- Ignores tied scores, ranks all the scores on absolute value (magnitude of difference) and then puts sign back on each difference score & compares the avg rank of pos vs neg difference scores |
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What is a K-related samples tests? What are two types?
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The K Related Samples tests are extensions of the McNemar & Wilcoxon tests, they can deal with more than two groups/samples. You use their predecessors as follow-up tests.
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What are some tests of validity? How would you demonstrate to a client that a measurement was valid?
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ALL OF THE FOLLOWING DEMONSTRATE CONSTRUCT VALIDITY!!
Content validity- check the operationalization against the relevant content domain for the construct. Face validity- you look at the operationalization and see whether "on its face" it seems like a good translation of the construct. Criterion-Related Validity- we make a prediction about how the operationalization will perform based on our theory of the construct (Concurrent, Predictive, concurrent, divergent). You can demonstrate validity of a measurement to a client by measuring the content against SME's (concurrent), ensuring face validity (procedural justice), etc. |
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What is multiple linear regression?
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2+ IV's, 1 DV
Minimizes the distance between all iv's in a regression line to find the best fit for multiple IV's with 1 DV Rsquared = proportion of variance explained by multiple IV's on one DV. F = effect test of multiple regression Equation looks at slopes/beta weights for each combined with IV score (optimal weighting) for each IV plus Error |
