Psychological Stats Exam 3
How much do grades change for every one-unit change in cheating? -.22 -.18 <.001 .02
-.22
We ran a regression analysis using the BYU Student Survey data, looking at how ACT predicted college GPA. Below is the regression formula. Please "plug and chug" to figure out the predicted college GPA for someone with a 29 ACT, which is the current average at BYU. Y^=0.03X+2.87 2.90 3.50 3.74 3.90
3.74
Which of the following yields more power for correlation? A larger correlation (r). Smaller sample sizes. Larger population standard deviation. Larger standard error.
A larger correlation (r).
Which of the following yields more power for regression? Smaller sample sizes. Greater population variability. Larger standard error. A larger regression coefficient.
A larger regression coefficient
SSregression
A number indicating the amount of variance in a dependent variable that can be explained by the variance in one or more associated independent variables. It thus describes how well a particular model fits the observed data.
What makes up the sampling distribution for the correlation? All possible means of a given sample size drawn from the null population. All possible average change scores from samples of a given sample size drawn from the null population (where on average there is no change). All possible differences between means from two samples, of two given sample sizes, drawn from the same population. All possible correlations between the two variables based on a given sample size drawn from the null population.
All possible correlations between the two variables based on a given sample size drawn from the null population.
What makes up the sampling distribution for the regression? All possible means of a given sample size drawn from the null population. All possible differences between means from two samples, of two given sample sizes, drawn from the same population. All possible regression coefficients (β) linking the two variables, based on a given sample size, drawn from the null population. All possible correlation coefficients (r) between the two variables, based on a given sample size, drawn from the null population.
All possible regression coefficients (β) linking the two variables, based on a given sample size, drawn from the null population.
Standard error of prediction
Average distance Y scores are from Y-hat regression line. Standarad deviation of Y scores around the regression line. 68% of scores within 1 standard error of regression line. 95% of scores within 2 standard error of regression line. 99% of scores within 3 standard error of regression line. Multiverate outliers are scores outside of 3 standard errors.
Standard error (for correlation)
Average size of correlation coefficient r given null hypothesis
Effect size Cramer's V for chi-square tests of independence is interpreted like which other effect size, but for nominal variables? A) d B) R2 C) r D) OR
C) r
Which of the following is NOT one of the three characteristics of associations between ordinal/ratio variables? Direction Strength Causality Shape
Causality
What do you conclude from these results? Cheating was a non-significant but small negative predictor of grades. Cheating was a significant but small negative predictor of grades. Cheating was a non-significant but large negative predictor of grades. Cheating was a significant but large negative predictor of grades.
Cheating was a significant but small negative predictor of grades.
What do the top and bottom of the t-test formula for regression represent? The regression coefficient you might expect to get if the null hypothesis were true over the regression coefficient you got in your data. The regression coefficient you got in your data over the regression coefficient you might expect to get if the null hypothesis were true. The regression coefficient you got in your data over the true regression coefficient in the alternative hypothesis population. The regression coefficient you got in your data over the regression in the null population.
The regression coefficient you got in your data over the regression coefficient you might expect to get if the null hypothesis were true.
Which of the following possible studies of gender and depression would most likely involve chi-square test of independence? Compare males and females with depression on level of depression symptoms. Examine the role of gender as a predictor of depression. Examine whether people diagnosed with depression are more likely to be male or female. Examine gender differences in likelihood of a depression diagnosis.
Examine gender differences in likelihood of a depression diagnosis.
Which of the following possible studies of gender and depression would most likely involve chi-square goodness-of-fit analyses? Compare males and females with depression on level of depression symptoms. Examine the role of gender as a predictor of depression. Examine whether people diagnosed with depression are more likely to be male or female. Examine gender differences in likelihood of a depression diagnosis.
Examine whether people diagnosed with depression are more likely to be male or female.
Which of the following is the hypothesis test for the set of predictors? F-test R-squared t-test Standardized regression coefficient (β)
F-test
What is the most fitting interpretation of the predictors based on the information provided? Family and peer religiousness were both significant and medium-sized predictors of church attendance, controlling for age and gender. Family and peer religiousness were both significant predictors of church attendance, controlling for age and gender, but the role of family small while that of peers was medium. Family and peer religiousness were both medium-sized but non-significant predictors of church attendance, controlling for age and gender. Family and peer religiousness were both small-sized but non-significant predictors of church attendance, controlling for age and gender.
Family and peer religiousness were both significant and medium-sized predictors of church attendance, controlling for age and gender.
What is the unit of analysis for chi-square? Means Differences between means Variance Frequencies
Frequencies
Which variable was NOT a significant predictor of church attendance? Age Gender Family religiousness Peer religiousness
Gender
Control variable
In multiple regression, regression coefficients for every predictore are interpreted controlling for the predictors in the model. Any predictor(s) included in a regression model other than your key predictors of interest.
Inferential statistics
Inferential statistics is a statistical method that deduces from a small but representative sample the characteristics of a bigger population. In other words, it allows the researcher to make assumptions about a wider group, using a smaller portion of that group as a guideline.
Which of the following is true regarding correct interpretation of a statistically significant regression coefficient? X causes Y. Y causes X. X and Y are bidirectionally linked (both cause each other). It could be any of the above, we can't tell.
It could be any of the above, we can't tell.
Which of the following is true regarding the correct interpretation of a statistically significant correlation. X causes Y. Y causes X. X and Y are bidirectionally linked (i.e., they both cause each other). It could be any of the above, we can't tell.
It could be any of the above, we can't tell.
What is the standard error of the sampling distribution for a correlation? It is the average distance sample means are from the mean of the null hypothesis population. It is the average distance means of change are from zero. It is the average distance differences between means are from zero. It is the average distance correlations are from zero.
It is the average distance correlations are from zero.
How is effect size R-squared interpreted for correlations? It is the proportion of overlapping variance between the two variables. It is the distance between the correlations in the null and alternative hypothesis populations, in standard deviation units. It is the strength and direction of the relationship between the two variables. It is the probability of rejecting the null when there is indeed a correlation in the population.
It is the proportion of overlapping variance between the two variables.
How is effect size R-squared interpreted for regressions? It is the distance between the regression coefficients in the null and alternative hypothesis populations, in standard deviation units. It is the proportion of overlapping variance between the two variables. It is the strength and direction of the relationship between the two variables. It is the probability of rejecting the null when there is indeed a link between X and Y in the population.
It is the proportion of overlapping variance between the two variables.
Which of the following is typically true for the mean of the sampling distribution for correlation hypothesis testing? It's estimated from the sample correlation. It's assumed to be zero because the null hypothesis is that there is no correlation. It is the same as the correlation in the general population. It is assumed to be one because that alternative hypothesis is that there is a correlation.
It's assumed to be zero because the null hypothesis is that there is no correlation.
Which of the following yields more power for chi-square? More cells/categories Smaller sample sizes Smaller difference between Os and Es Larger difference between Os and Es
Larger difference between Os and Es
What kind of relationship between variables does correlation assume? Strong Positive Linear Causal
Linear
Which of the following is the best interpretation of the control variables (age and gender) in the model? Age contributed a lot to the model, but gender did not. Gender contributed a lot to the model, but age did not. Both age and gender contributed a lot to the model. Neither age nor gender contributed much to the model.
Neither age nor gender contributed much to the model.
What kind(s) of variables are needed to run a chi-square? Only nominal variables Only ordinal variables Only ratio variables. One nominal and one ratio variable.
Only nominal variables
Which variable was the strongest predictor of church attendance? Age Gender Family religiousness Peer religiousness
Peer religiousness
What are appropriate implications we can draw from these results? Getting good grades prevents cheating. Cheating hurts academic performance. There is no clear association between cheating and grades. People who cheat more tend to get lower grades.
People who cheat more tend to get lower grades.
What is the regression line made up of (i.e., it is a line of what)? Predicted Ys Actual Ys Intercepts Slopes
Predicted Ys
Which of the following is the interpretation of R-squared regression? Ratio of the variance in the outcome explained by the set of predictors to the variance unexplained by them. Proportion of the total variance in the outcome that is explained by the set of predictors. Ratio of the size of your regression coefficient to the size of coefficient you might expect if the null were true. The strength and direction of relations b
Proportion of the total variance in the outcome that is explained by the set of predictors.
R-squared
Proportion overlapping variance. Is interpreted as small is .01, medium is .06, and large is .14.
Which of the following is the effect size for the set of predictors? F-test R-squared t-test Standardized regression coefficient (β)
R-squared
Which of the following is the interpretation of the individual t-tests in regression? Ratio of the variance in the outcome explained by the set of predictors to the variance unexplained by them. Proportion of the total variance in the outcome that is explained by the set of predictors. Ratio of the size of your regression coefficient to the size of coefficient you might expect if the null were true. The strength and direction of relations between that X and the Y variable, controlling for the other Xs.
Ratio of the size of your regression coefficient to the size of coefficient you might expect if the null were true.
Which of the following is the interpretation of the F-test in regression? Ratio of the variance in the outcome explained by the set of predictors to the variance unexplained by them. Proportion of the total variance in the outcome that is explained by the set of predictors. Ratio of the size of your regression coefficient to the size of coefficient you might expect if the null were true. The strength and direction of relations between that X and the Y variable, controlling for the other Xs.
Ratio of the variance in the outcome explained by the set of predictors to the variance unexplained by them.
What is the unit of analysis for hypothesis tests of regressions? Correlation coefficient (r) Standard deviation Variance Regression coefficient (β)
Regression coefficient (β)
The standard error of prediction is the standard deviation around the: Mean of Y Mean of X Regression line (Y-hat) Mean of the sampling distribution for the regression coefficient.
Regression line (Y-hat)
What kinds of research questions are correlations used to answer? Research questions involving comparing groups. Research questions involving associations between two ordinal/ratio variables. Research questions involving prediction. Research questions involving associations between two nominal variables.
Research questions involving associations between two ordinal/ratio variables.
What kinds of research questions are chi-square goodness of fit analyses used to answer? Research questions involving associations between ordinal/ratio variables. Research questions involving prediction between ordinal/ratio variables. Research questions involving particular univariate frequency distributions. Research questions involving associations between two nominal variables.
Research questions involving particular univariate frequency distributions.
What kinds of research questions are regressions used to answer? Research questions involving comparing groups. Research questions involving associations between ordinal/ratio variables. Research questions involving prediction between ordinal/ratio variables. Research questions involving associations between two nominal variables.
Research questions involving prediction between ordinal/ratio variables.
Which of the following possible studies of meditation and psychological well-being would most likely involve regression analysis? Researchers compared psychological well-being between people who took a meditation workshop and people who didn't. Researchers examined meditation as a predictor of psychological well-being. Researchers compared the psychological well-being of frequent meditators to national norms on psychological well-being. Researchers examined the association between meditation and psychological well-being.
Researchers examined meditation as a predictor of psychological well-being.
Which of the following possible studies of meditation and psychological well-being would most likely involve correlation analysis? Researchers compared psychological well-being between people who took a meditation workshop and people who didn't. Researchers examined meditation as a predictor of psychological well-being. Researchers compared the psychological well-being of frequent meditators to national norms on psychological well-being. Researchers examined the association between meditation and psychological well-being.
Researchers examined the association between meditation and psychological well-being.
You wonder whether people who cheat do better in school, since they have an unfair advantage. So, using the NSYR dataset, you run a regression of cheating predicting grades. Here's what you found, b = -.22, β = -.18, p < .001. Which of the following best characterizes the relationship between cheating and grades? Significant and positive Significant and negative Non-significant and positive Non-significant and negative
Significant and negative
How would you evaluate the size of the relationship between cheating and grades? Small Medium Large Significant
Small
Which of the following is the effect size for each individual predictor? F-test R-squared t-test Standardized regression coefficient (β)
Standardized regression coefficient (β)
Regression line
Summarizes linear relationship between X and Y. Is line of predicted Y values for every possible X vlaue, based on the regression formula (the formula for the regression line). Minimizes prediction errors (residuals). Intercept not always a possible value. Can generate manually by "plugging and chugging" two numbers, then drawing line. Can also generate in software.
Which of the following is a correct interpretation when the X variable is significantly correlated with Y in correlation, but is not a significant predictor in regression? The correlation between X and Y is misleading. That X did not account for significant unique variance in the outcome when controlling for the other predictors. That X was not correlated with any other X variables in the model. The correlation between that X and the Y must have been small.
That X did not account for significant unique variance in the outcome when controlling for the other predictors.
What do the top and bottom of the t-test formula for correlation represent? The correlation you got in your data over the correlation you might expect to get if the null hypothesis were true. The correlation you might expect to get if the null hypothesis were true over the correlation you got in your data. The correlation you got in your data over the true correlation in the alternative hypothesis population. The correlation you got in your data over the correlation in the null population.
The correlation you got in your data over the correlation you might expect to get if the null hypothesis were true.
What does the typical null hypothesis look like for chi-square goodness-of-fit? The frequencies are equally distributed across groups in the population. The percentage of people are not equally distributed across groups in the population. The two nominal variables are independent. The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).
The frequencies are equally distributed across groups in the population.
Which of the following is the interpretation of the standardized regression coefficient (β) in regression? Ratio of the variance in the outcome explained by the set of predictors to the variance unexplained by them. Proportion of the total variance in the outcome that is explained by the set of predictors. Ratio of the size of your regression coefficient to the size of coefficient you might expect if the null were true. The sign and strength of relations between that X and the Y variable, controlling for the other Xs.
The sign and strength of relations between that X and the Y variable, controlling for the other Xs.
Standardized regression coefficient
The standardized regression coefficient is β in the standardized regression coefficient. It is the slope of line that minimizes errors in predicting Y (regression line). Standard deviation change in Y associated with one standard deviation change in X. Rise over run. Since based on standardized data, interpreted like correlation coefficient r, as sign and size of relationship between X and Y. Identical to r if only one predictor.
How is an Odds Ratio of 1.0 interpreted in a chi-square test-of-independence? The two nominal variables are perfectly associated. The two nominal variables are independent. A one-unit change in one nominal variables in linked to a one-unit change in the other. It is not statistically significant.
The two nominal variables are independent.
What does the typical null hypothesis look like for chi-square test of independence? The frequencies are equally distributed across groups in the population. The percentage of people are not equally distributed across groups in the population. The two nominal variables are independent. The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).
The two nominal variables are independent.
What does the typical alternative hypothesis look like for chi-square test of independence? The frequencies are equally distributed across groups in the population. The percentage of people are not equally distributed across groups in the population. The two nominal variables are independent. The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).
The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).
What do the top and bottom of chi-square formula represent? The pattern of frequencies you observed over the pattern of frequencies you would expect to get if the null hypothesis were correct. The chi-square coefficient you got in your data over the true chi-square coefficient in the alternative hypothesis population. The chi-square coefficient you got in your data over the chi-square in the null population. The difference between your sample mean and the mean in the population, over the difference expected if the null hypothesis were correct.
The pattern of frequencies you observed over the pattern of frequencies you would expect to get if the null hypothesis were correct.
What does the typical alternative hypothesis look like for chi-square goodness-of-fit? The frequencies are equally distributed across groups in the population. The percentage of people are not equally distributed across groups in the population. The two nominal variables are independent. The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).
The percentage of people are not equally distributed across groups in the population.
We wanted to examine predictors of church attendance among youth in the NSYR dataset (a nationally-representative study of U.S. teens). We included age and gender as controls, and then family religiousness and peer religiousness as our key predictors. Here are the results for the model, F(4, 3313) = 176.80, p < .001, R2 = .18. Here are the results for each predictor: Age, b = -.01(.004), β = -.04 (p = .01) Gender, b = .007(.01), β = .01 (p = .55) Family religiousness, b = .04(.003), β = .23 (p < .001) Peer religiousness, b = .03(.002), β = .28 (p < .001) Which of the following is true about the model? The predictors explained a small and non-significant amount of the variance in church attendance. The predictors explained a significant but small amount of the variance in church attendance. The predictors explained a large but non-significant amount of variance in church attendance. The predictors explained a significant and large amount of the variance in church attendance.
The predictors explained a significant and large amount of the variance in church attendance.
The Foundations researchers wanted their sample to be 50% Latter-day Saint families and 50% families of other religious identifications. They created a dichotomous nominal variables coded as 0 = Other (N = 809), 1 = LDS (N = 882), and ran a chi-square goodness-of-fit test on it, χ2(1) = 3.15, p = .08. What can be concluded from this chi-square goodness-of-fit test? There are significantly more LDS families in the dataset than other families. There are significantly fewer LDS families in the dataset than other families. The proportion of LDS families is not significantly different from that of the other families. The researchers did not achieve their goal of roughly equal distribution of LDS vs. other religious identifications in their sample.
The proportion of LDS families is not significantly different from that of the other families.
What does the typical alternative hypothesis look like for correlation? Our sample is lower/higher on average than the known population. Our sample decreases/increases on average over time. One group is lower/higher than the other group. There is a negative/positive correlation between the two variables.
There is a negative/positive correlation between the two variables.
When you retain the null hypothesis in a chi-square, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of chi-square coefficient, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of chi-square coefficient, with your number of cells and people, if the null hypothesis were true.
There is greater than a 5% chance of getting your size of chi-square coefficient, with your sample size, if the null hypothesis were true.
When you retain the null hypothesis in a correlation, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true.
There is greater than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true.
When you retain the null hypothesis in a regression, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true.
There is greater than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true.
When you reject the null hypothesis in a chi-square, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of chi-square coefficient, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of chi-square coefficient, with your number of cells and people, if the null hypothesis were true.
There is less than a 5% chance of getting your size of chi-square coefficient, with your number of cells and people, if the null hypothesis were true.
When you reject the null hypothesis in a correlation, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true.
There is less than a 5% chance of getting your size of correlation, with your sample size, if the null hypothesis were true.
When you reject the null hypothesis in a regression, how do you statistically interpret the results? There is greater than a 95% chance that the null hypothesis is true. There is less than a 5% chance that the alternative hypothesis is true. There is greater than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true. There is less than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true.
There is less than a 5% chance of getting your size of regression coefficient, with your sample size, if the null hypothesis were true.
What does the typical null hypothesis look like for correlation? Our sample is not different on average from the known population. There is no change on average over time. The groups are not different. There is no correlation.
There is no correlation.
Which of the following is true of non-parametric statistics? They do not involve estimating population parameters (mean and standard deviation). They rely on the same assumptions about the population as do parametric statistics. They focus on ordinal or ratio variables. They include all the stats we have learned thus far.
They do not involve estimating population parameters (mean and standard deviation).
Which of the following is a valid interpretation of t-scores for correlation? They directly correspond to the p-value, so larger t-scores mean larger p-values. They tell you the ratio of your correlation to the correlation you might expect if the null hypothesis were true. They tell you the size of difference between your sample correlation and that in the null hypothesis population. They tell you the proportion overlapping variance between the two variables.
They tell you the ratio of your correlation to the correlation you might expect if the null hypothesis were true.
Unstandardized regression coefficient
This is the b in the unstadnardized regression formula. It is the slope of line that minimizes errors in predicting Y (regression line). It is also the amount of difference in Y associated with one-unit difference in X. It is the rise/run.
Which of the following is NOT a use of multiple regression? To compare various predictors of an outcome. To control for demographics. To control for confounding variables. To establish causality.
To establish causality.
What does it mean to "control for" a variable in a multiple regression analysis? To experimentally manipulate it To make sure it is left out of the regression analysis To Winsorize it prior to inclusion in the regression analysis To include it as an additional predictor on the regression analysis
To include it as an additional predictor on the regression analysis
SSY-total
Total variability in Y (sum of squared deviations of scores on Y around the mean of Y). The sum of (Y-My)2.
SSresidual
Total variabliity in Y not accounted for by X. How much we still don't know about Y. It is the sum of (Y-Y')2. Difference between the observed, or actual value of the variable, and the estimated value, which is what it should be according to the line of regression. Shows the amount of variance not explained by a regression. In the case of a perfect fit, the residual (or error) would be 0, meaning the estimated value is the same as the actual value. The lower the value, the better line of regression fits the data. A high residual sum would demonstrate that the model poorly represents the data.
What kind(s) of variables are needed to run a regression? An ordinal or ratio/interval variable, assessed at two occasions. A nominal variable and an ordinal or ratio/interval variable. Two or more ordinal or ratio/interval variables. Two or more nominal variables.
Two or more ordinal or ratio/interval variables.
What kind(s) of variables are needed to run a correlation? An ordinal or ratio/interval variable, assessed at two occasions. A nominal variable and an ordinal or ratio/interval variable. Two ordinal or ratio/interval variables. Two nominal variables.
Two ordinal or ratio/interval variables.
Which of the following is true regarding unstandardized and standardized regression coefficients? Both are interpreted in the same way. Unstandardized is interpreted in terms of change in Y for every one-unit change in X, while standardized is interpreted in terms of size. Standardized is interpreted in terms of change in Y for every one-unit change in X, while unstandardized is interpreted in terms of size. They are interpreted differently, but neither of them can tell us about how strongly X predicts Y.
Unstandardized is interpreted in terms of change in Y for every one-unit change in X, while standardized is interpreted in terms of size.
Which of the following CANNOT be interpreted in terms of size? r R-squared Standardized regression coefficient (β) Unstandardized regression coefficient (b)
Unstandardized regression coefficient (b)
What is the underlying logic of hypothesis tests of correlations? We are trying to figure out the probability of getting a correlation as large as ours, with our sample size, if there is no correlation in the population. We are trying to figure out the probability of getting a correlation as large as ours, with our sample size, if there is a correlation in the population. We are trying to figure out the probability that the two variables are correlated in the population. We are trying to figure out the probability that the two variables aren't correlated in the population.
We are trying to figure out the probability of getting a correlation as large as ours, with our sample size, if there is no correlation in the population.
What is the underlying logic of hypothesis tests of regressions? We are trying to figure out the probability of getting a regression coefficient as large as ours, with our sample size, if X is a predictor of Y in the population. We are trying to figure out the probability of getting a regression coefficient as large as ours, with our sample size, if X is not a predictor of Y in the population. We are trying to figure out the probability that X predicts Y in the population. We are trying to figure out the probability that the two variables aren't linked in the population.
We are trying to figure out the probability of getting a regression coefficient as large as ours, with our sample size, if X is not a predictor of Y in the population.
What is the underlying logic of hypothesis tests for chi-square goodness-of-fit? We are trying to figure out the probability of getting the univariate frequency distribution we observed if the null hypothesis is correct and there is a particular (usually equal distribution across cells) expected distribution in the population. We are trying to figure out the probability of getting the bivariate frequency distribution we observed if the null hypothesis correct and the two nominal variables are unrelated in the population. We are trying to figure out the probability of getting two ordinal or ratio variables this strongly associated, with this sample size, if the null hypothesis is correct and they are unrelated in the population. We are trying to figure out the probably of getting this size of differences between means, with these sample sizes, if the null hypothesis is correct and there are no group differences.
We are trying to figure out the probability of getting the univariate frequency distribution we observed if the null hypothesis is correct and there is a particular (usually equal distribution across cells) expected distribution in the population.
How are 95% confidence intervals interpreted for Correlations? There is a 95% chance that the true population lies within that interval. There is a 95% chance the research hypothesis is true. With repeated sampling, 95% of the time the true population correlation will lie within that interval. With repeated replication, 95% of studies will end up rejecting the null, if the alternative hypothesis is true.
With repeated sampling, 95% of the time the true population correlation will lie within that interval.
How are 95% confidence intervals interpreted for regression? Answer based on the most accurate and true interpretation of 95% CIs. There is a 95% chance that the true population regression coefficient lies within that interval. With repeated sampling, 95% of the time the true population regression coefficient will lie within that interval. There is a 95% chance the research hypothesis is true. With repeated replication, 95% of studies will end up rejecting the null, if the alternative hypothesis is true.
With repeated sampling, 95% of the time the true population regression coefficient will lie within that interval.
What does the typical alternative hypothesis look like for regression? Our sample is lower/higher on average than the known population. X is lower/higher than Y in the population. X is negatively/positively correlated with Y in the population. X is a negative/positive predictor of Y in the population.
X is a negative/positive predictor of Y in the population.
What does the typical null hypothesis look like for regression? Our sample is not different on average from the known population. X is not different from Y. X is not correlated with Y. X is not a predictor of Y.
X is not a predictor of Y.
Which of the following is the hypothesis test for each individual predictor? F-test R-squared t-test Standardized regression coefficient (β)
t-test
Regression Line Formula
y=bx+a
What is the key difference between goodness-of-fit and tests-of-independence? You need to calculate the Es (expected frequencies) for each cell as part of tests of independence, but not goodness-of-fit analyses. Larger chi-square values indicate greater mismatch between observed and expected frequencies for goodness-of-fit analyses, but not for tests of independence. Chi-square goodness-of-fit analyses involve one nominal variable, while chi-square tests of independence involve two nominal variables. Chi-square goodness-of-fit analyses are non-parametric statistics, while chi-square tests of independence are parametic.
Chi-square goodness-of-fit analyses involve one nominal variable, while chi-square tests of independence involve two nominal variables.
What is the unit of analysis for hypothesis tests of correlations? Mean Standard deviation Variance Correlation coefficient r
Correlation coefficient r
Which of the following is a true similarity or difference between correlation and regression? Correlation is about association, while regression is about prediction. You get more information with correlation analysis than regression analysis. Both correlation and regression are limited to one X and one Y variable. Correlation assumes a linear shape of the relationship between X and Y, while regression does not.
Correlation is about association, while regression is about prediction.
Descriptive statistics
Descriptive statistics describe, show, and summarize the basic features of a dataset found in a given study, presented in a summary that describes the data sample and its measurements. It helps analysts to understand the data better
Regression formula (don't write out and label the formula, just define it)
Descriptive, inferential, and applied statistic for examining the unstandardized linear relationship between an ordinal/ratio predictor and an ordinal/ratio outcome. It can include the unstandardized regression forumula which involves Y', x, b, and a variables; or it can include the standardized regression formula which involves the predicted or estimated value of standardized Y, standardized predictor variable, and β.
Sampling distribution (for correlation)
Distribution of r's (a t-distribution). All possible r's between X and Y, of samples of our sample size, from the null population. Use the t-test to locate our r in the distribution of all possible r's.
Sampling distribution (for regression)
Distribution ofβ's. All possible β's linking X to Y, of samples of our sample size. from the null population. Standard error is the average distance β's are from zero, in standard deviation units. You use the t-test to locate our β in the distribution of all possible β's.
