Advanced Statistics Final Exam

If a student gets a lower than desired score on a learning assessment, according to the syllabus, which of the following is LEAST likely to be helpful in improving future scores?
A. Increasing regular study and review of course material
B. Testing oneself to develop one's own judgment of learning
C. Figuring out which specific items were missed on the learning assessment
D. Increasing focus on big-picture concepts
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If a student gets a lower than desired score on a learning assessment, according to the syllabus, which of the following is LEAST likely to be helpful in improving future scores?
A. Increasing regular study and review of course material
B. Testing oneself to develop one's own judgment of learning
C. Figuring out which specific items were missed on the learning assessment
D. Increasing focus on big-picture concepts
C
An instructor gives cumulative tests in a class and requires students to make an appointment if they want to know which items they missed on a test. According to Dr. Sanford, in which of the following situations is the instructor likely to receive complaints from students about not being told which items they missed?
A. If the students are not given any study guides or any direction on how to study for tests.
B. If the students are given access to the entire pool of questions used to create the tests.
C. If student grades are determined by a very small number of tests so that they rarely receive feedback (for example, if grades are determined by just two midterm tests and a final exam).
D. If the instructor fails to give students tools that can be used so that students can do their own judgment of learning.
B
The syllabus describes a plan in which an answer key for the lecture study guide is NOT posted. Which of the following is a FALSE statement about this plan?
A. This plan provides a way for students to learn key concepts even if they choose to skip some videos.
B. This plan is intended to encourage students to focus on big-picture concepts rather than making excessive use of rote memorization.
C. With this plan, it is assumed that, in any class, there is always some risk that students could learn material incorrectly.
D. With this plan, if students are uncertain about answers after reviewing videos, one way to get correct answers is by asking questions during class meetings.
A
The syllabus describes several potential problems that could occur if students are told which specific items they missed after each learning assessment. Which of the following is NOT listed as a potential problem with telling students which items they missed?
A. It discourages students from testing themselves and doing their own judgment of learning.
B. It discourages students from focusing on understanding the important big-picture concepts.
C. It leads students to focus on a narrow set of missed items, when they should be focusing on following all the tactics for doing well in the course.
D. It encourages students to take an excessively holistic approach in viewing their learning assessment scores.
D
According to the syllabus, which of the following is true about the reliability of learning assessments?
A. At the beginning of the semester, a simple random error could drop a score from an A to a B+.
B. Tests at the beginning of the semester will be more reliable than tests at the end.
C. When a test is easy, it produces more reliable scores for students in the top portion of a class than for students in the bottom portion.
D. Tests at the beginning of the semester will be equally as difficult as tests at the end of the semester.
A
Professor Cid observed that, "the patient was in good condition, talked relevantly and coherently, and was correctly oriented." This is an example of ______ .
A. A quantified observation
B. An observation that has NOT been quantified
C. A variable
D. A categorical variable
E. A numerically scaled variable
B
A sample of patients were given scores on the Brief Psychiatric Rating Scale. This is an example of ______ .
A. Quantified observations
B. Observations that have NOT been quantified
C. A variable
D. A categorical variable
E. A numerically scaled variable
A, C, E
In a sample of patients, some were in a treatment group and others were in a control group. This is an example of ______ .
A. Quantified observations
B. Observations that have NOT been quantified
C. A variable
D. A categorical variable
E. A numerically scaled variable
A, C, D
Correctly spell the term that has to do with the extent to which the same amount of something always produces the same assessed numerical value regardless of when or how it is assessed.
reliability
Correctly spell the term that has to do with the extent to which a scale measures what it is supposed to measure.
validity
A study where scores for all the variables are determined by assessment and there are NO manipulated variables is called __________ research.correlationalA study that has at least one variable with scores determined by an assessment and at least one manipulated variable produced by the researcher forcing cases into groups is called __________ research.experimentalFifty people received a treatment for anxiety. Their level of anxiety was assessed both before the treatment and after the treatment. This is an example of ______ . A. A study using random assignment B. A type of research that was specifically described in class as being limited in its ability to determine cause. C. A type of research that was specifically described in class as being limited in its ability to explain natural phenomena. D. A study that includes a manipulated variable E. Correlational research F. A clinical trialB, EA researcher conducts a clinical trial. This is an example of ______ . A. A study using random assignment B. A type of research that was specifically described in class as being limited in its ability to determine cause. C. A type of research that was specifically described in class as being limited in its ability to explain natural phenomena. D. A study that includes a manipulated variable E. Correlational research F. A study that includes a categorical variableA, C, D, FCorrectly spell the term for a numerical value based on data from all the cases in a population that describes something about the population.parameterTo address the question, "how big is the effect?" we need to calculate an effect size. This will be a(an) __________ statistic.descriptiveTo address the question, "could the results be random chance?" we need to calculate a(an) __________ statistic.inferentialWhat is ei? A. The score you expect to get for case i. B. The actual score for case i. C. How much case i deviates from the mean. D. The mean of all the "e" values in the sample.CWhat is 𝑥̅? A. The score you expect to get for case i. B. The actual score for case i. C. How much case i deviates from the mean. D. The mean of all the "e" values in the sample.AWrite an alternate version for this linear equation that includes a term for the predicted score on x.xhat_i=xbarWrite an alternate version for this linear equation that does NOT use the "hat" symbol.x_i=xbar+e_iWrite the formula for the sum of squares of variable x.sum(x_i-xbar)^2Use the letters "ss" to indicate "sum of squares" and write the formula for a variance of variable x.ss/(n-1)Use the letters "ss" to indicate "sum of squares" and write the formula for a standard deviation of variable x.sqrt(ss/(n-1))In the process of computing a standard deviation, Zelda lost one degree of freedom. What did Zelda do that caused her to lose one degree of freedom? A. She omitted one person from the sample. B. She used a statistic that was smaller than its expected value. C. She used a biased formula to calculate the standard deviation. D. She divided the variance by n-1. E. She used squared deviations rather than absolute deviations. F. She calculated the meanFCorrectly spell the statistical term that is a single word and that goes in the blank. Bruno computed a standard deviation, but he accidentally used "n" rather than the degrees of freedom in his formula. This means that the value he obtains will be _______________ .biasedCorrectly spell the term used when the expected value is not equal to the parameter.biasCorrectly spell the term that indicates the average of all the values for a population of values from which a single value can be randomly sampled.expected valueWrite the formula for a z-score.(x_i-xbar)/sdUse the letter "z" to indicate a z-score and write the formula for a T-score.10z+50Write the formula for a centered score.x_i-xbarCorrectly spell the term for the thing that has a mean of 0 and a standard deviation of 1.z-scoreCorrectly spell the term for the thing that has a mean of 50 and a standard deviation of 10.t-scoreA z-score is equal to a _____ divided by a _____ . A. mean B. centered score C. difference score D. expected score E. standard deviationb, eIf scores in a sample are normally distributed, what is the probability of randomly selecting someone from the sample that has a z-score of 2 or lower?98If scores in a sample are normally distributed, what is the probability of randomly selecting someone from the sample that has a z-score of 1 or higher?16What is a numerical value based on data from a sample that indicates something about the sample?descriptive statisticWhat is the general term for a numerical value based on data from a sample (that may indicate something about the sample or something about the population)?statisticHow do you find variance from standard deviation?variance = sd^2What is the mean of e_i?zeroWhat commonly calculated statistic is essentially the mean of |e_i| ?standard deviationIn a normal distribution, what percent of cases fall between a score that is at the mean and a score that is one standard deviation above the mean?34In a normal distribution, what percent of cases fall between a score that is one standard deviation above the mean and a score that is two standard deviations above the mean?14In a normal distribution, what percent of cases fall above the second standard deviation?2Write the formula for a d-statistic.(xbar_1-xbar_2)/sd_pooledIn each figure, which letter is 1 standard deviation above the mean? (28)G, D, EIn each figure, which letter is 2 standard deviations above the mean? (29)H, G, IWhat is the value of the d-statistic depicted in this figure? (30)1Type a single word to fill in the blank. (31) This is a _____ effect.In each blank, type a 2-digit number (and nothing else). With no treatment your probability of superiority is _____ percent, with treatment it increases to _____ percent, which is an increase of _____ percent.50, 75, 25What is the value of the d-statistic depicted in this figure? (32).8Type a single word to fill in the blank. (33) This is a _____ effect.In each blank, type a 2-digit number (and nothing else). With no treatment your probability of superiority is _____ percent, with treatment it increases to _____ percent, which is an increase of _____ percent.50, 70, 20What is the value of the d-statistic depicted in this figure? (34).6Type a single word to fill in the blank. (35) This is a _____ effect.In each blank, type a 2-digit number (and nothing else). With no treatment your probability of superiority is _____ percent, with treatment it increases to _____ percent, which is an increase of _____ percent.50, 65, 15What is the value of the d-statistic depicted in this figure? (36).4Type a single word to fill in the blank. (37) This is a _____ effect.In each blank, type a 2-digit number (and nothing else). With no treatment your probability of superiority is _____ percent, with treatment it increases to _____ percent, which is an increase of _____ percent.small, 50, 60, 10What is the value of the d-statistic depicted in this figure? (38).2Type a single word to fill in the blank. (39) This is a _____ effect.In each blank, type a 2-digit number (and nothing else). With no treatment your probability of superiority is _____ percent, with treatment it increases to _____ percent, which is an increase of _____ percent.small, 50, 55, 5What is the formula for variance?sum(x-xbar)^2/(n-1)What is the formula for covariance?sum((x-xbar)(y-ybar))/(n-1)Think about the formulas for variance and covariance. Which of the following is NOT part of the formula for a covariance? A. squaring values B. multiplying x values times y values C. centering scores on x D. dividing by n-1 E. summing valuesAA correlation is equal to _____ divided by _____ . A. A difference between means B. A centered score C. A covariance D. The highest possible value a covariance could take E. The highest possible value a standard deviation could take F. The cross product of two centered scoresC, DUse "cov_xy" as the symbol for the covariance between x and y and write the formula for a correlation.cov_xy/((sd_x)(sd_y))Write a linear equation that includes an "e" where the average deviation of |e| is the standard deviation.x_is=xbar_s+e_isFill in each blank by typing correctly spelled words that match the words used in the googly-eyed sheep table (the one titled, "Types of distributions"). A standard deviation pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .cases, sample, sample mean[Equation 1] y_is= (prediction_s based on x_is) + e_is [Equation 2] x_is = x_s + e_is The standard deviation_____. a. is e_is from equation 1 b. is the averaged (absolute) size of e_is from equation 1 c. is e_is from equation 2 d. is the averaged (absolute) size of e_is from equation 2D[Equation 1] y_is= (prediction_s based on x_is) + e_is [Equation 2] x_is = x_s + e_is The standard error of estimate_____. a. is e_is from equation 1 b. is the averaged (absolute) size of e_is from equation 1 c. is e_is from equation 2 d. is the averaged (absolute) size of e_is from equation 2BUse the letter "w" to indicate the term: (prediction_s based on x_is) Write a linear equation that includes an "e" where the average deviation of |e| is the standard error of estimate.y_is=w+e_isCorrectly spell the terms that need to be placed in the blanks to produce a linear equation where the average deviation of |e| is the standard error of estimate. In typing your answer, use an underscore to indicate subscripts as you do when typing formulas. y_is = (______ based on _____ ) + e_isprediction_s, x_isA standard error of estimate pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .cases, sample, predicted valueWhat is a linear equation that includes an "e" where the average deviation of |e| is the standard error of measure?x_ai=true_i+e_aiA standard error of measure pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .assessments, case, true scoreIn the equation, x= true + e, the "e" needs a subscript to indicate it belongs to: A. sample "s" B. individual "i" from sample "s" C. assessment occasion "a" for individual "i" D. assessment occasion "a" from sample "s"CIf Cronbach's alpha is .6, it indicates that A. people typically deviate from their true scores by 60%. B. the standard error of measure is .6 C. 60% of the variance is measurement error D. 60% of the variance is true varianceDWrite the linear equation that includes an "e" where the average deviation of |e| is the standard error of a mean.xbar_sp=mu_p+e_spA standard error of a mean pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .samples, population, population parameterWrite the linear equation that includes an "e" where the average deviation of |e| is the standard error of a difference between means?(ybar-ybar)_sp=(mu-mu)_p+e_spA standard error of a difference between means pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .samples, population, population parameterWrite the linear equation that includes an "e" where the average deviation of |e| is the standard error of a beta.b_sp=beta_p+e_spA standard error of a beta pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .samples, population, population parameterWrite the linear equation that includes an "e" where the average deviation of |e| is the standard error of a correlation?r_sp=rho_p+e_spA standard error of a correlation pertains to: •Observations of different _____ from a single _____ . •Deviations around a _____ .samples, population, population parameterWhen writing linear equations (for the standard deviation, standard error of estimate, standard error of measure, and standard error of a statistic), you need to use the subscripts, "i," "s," "a," and "p." "i" stands for _______ . "s" stands for _______ . "a" stands for _______ . "p" stands for _______ .individual, sample, assessment, populationThe smaller the sample. . . A. The more the standard error will have a normal distribution. B. The smaller the size of esp. C. The smaller the standard error of a statistic. D. The larger the standard error of a statistic.DThe standard error of a correlation indicates how far correlations from different studies typically deviate from ___ . A. the population parameter B. the sample mean C. the predicted values D. the true scores.AThe size of the standard error of a statistic is primarily influenced by the size of the _______ .sampleStandard error of a statistic will be almost perfectly _______ in shape.normalUsing the words "parameter" and "statistic," write the formula for a t-value.(statistic-parameter)/sd_statistic"If we knew the population parameter for this, the distribution would be a z and not a t." To which part of the t-value formula does this statement apply? A. statistic - parameter B. statistic C. parameter D. sd_statisticDIf the p value is .08, it means that A. there is a 8% probability that the null hypothesis is true. B. we can be 92% confident that the research hypothesis is true. C. if the null hypothesis were true, we would get an effect this large only 8% of the time. D. the results are significant.CWhat is the probability of committing a type I error if the null hypothesis is true?alphaThe probability of committing a type I error if the null hypothesis is false.zeroA word that means: "if the null hypothesis is true, then the results from the sample are extremely unusual."significantThe probability of making a correct decision if the null hypothesis is false.powerThe probability of committing a type II error if the null hypothesis is false.betaA person's average score on a test if he or she were assessed an infinite number of times.true scoreThe assumption that the population parameter for a statistic is equal to zero.null hypothesisA distribution of sampling error that is almost normal in shape.tTwo distributions of sampling error that are skewed in shape.f and chi^2An effect size that is typically used when one variable is dichotomous.dAn effect size that is typically used with two numerically scales variables.rThis is estimated by a correlation between two alternate forms.sd_true^2/sd^2This statistic describes a distribution that becomes almost perfectly normal in shape as the sample size increases beyond 30.sd_xbarThis is equal to true variance.Sd^2 - sd^2_measureThis is estimated by a test retest correlation.sd_true^2/sd^2This will become smaller as the sample size increases.sd_xbarThis is the standard error of measure.sd*sqrt(1-reliability)This value will become smaller as the effect size increases.sd_estThis is estimated by Cronbach's alpha.sd_true^2/sd^2How do you find pooled standard deviation?sqrt((ss_1+ss_2)/(df_1+df_2))What percent of total variance is true variance?the given Cronbach alphaWhat percent of the total variance is measurement error variance?1 - Cronbach alphaIf an individual was assessed on repeated occasions, how much would each of her observed scores typically deviate from the true score?square root (1 - cronbach alpha) * standard deviationIn the t-statistic formula, what is the assumed value for the population parameter?zeroFor a single sample estimate of a single mean write the linear equation for variance in a sample.x_is=xbar_s+e_isFor a single sample estimate of a single mean write the linear equation for sampling error variance in a population.xbar_sp=mu_p+e_spThe equation x_is = xbar_s +e_is includes two types of components. First, a _____ is a value that can vary between people in sample. Second, a _____ is a value that can vary between studies in a population.variable, parameter estimateWhich of the following are variables? Select ALL the correct answers. A. x_is B. mu_P C. xbar_is D. e_sp E. e_isA, EWhich of the following are parameter estimates? Select ALL the correct answers. A. x_is B. mu_P C. xbar_s D. e_sp E. e_isCWhich of the following answers the descriptive question and would provide the primary result we want to know when conducting a study? A. x_is B. mu_P C. xbar_s D. e_sp E. e_isCWhich of the following is the primary component that we need to use to answer the inferential question? A. x_is B. mu_P C. xbar_is D. e_sp E. e_isDA. The average deviation of Ie_isI Match each definition above with the appropriate term below standard error of measure standard deviation standard error of estimate standard error of a statistic z-score t-valuestandard deviationB. The average deviation of Ie_spI Match each definition above with the appropriate term below standard error of measure standard deviation standard error of estimate standard error of a statistic z-score t-valuestandard error of a statisticAssume you want to know the standardized e_sp for a particular study assuming the null hypothesis is true. This can be answered with: A. a descriptive statistic B. the standard error of the mean C. a t-value D. the standard error of estimatea t-valueThe standard of the error of the mean will be the largest when the standard deviation is __________ and the sample size is __________ . A. large, large B. large, small C. small, large D. small, smallBWhich of the following will produce the largest standard error of the mean? A. sd = 2, and the sample size is small B. sd = 2, and the sample size is big C. sd = 8, and the sample size is small D. sd = 8, and the sample size is bigCIf H0 is true, how many standard error units did this study deviate from the null population parameter? (82)10.53What is the average deviation of |e_is| ? (82)2.12What is the average deviation of |e_sp| ? (82).95If H0 is true, what is the standardized e_sp for this particular study? (82)10.53Which numerical value answers the descriptive question and provides the primary result the researcher wanted to know when conducting this study? (82)10To look up the probability of these results assuming the null hypothesis is true, you need to use two numerical values. One of these values is equal to 4. What is the other numerical value you need to use? (82)10.53Assume you do a paired samples study and get this dataset with 4 people. To calculate sd_diff, you would calculate the standard deviation using which set scores? (87) A. 9, 8, 6, 5 B. 7, 4, 4, 1 C. 9, 8, 6, 5, 7, 4, 4, 1 D. 2, 4, 2, 4 E. 7, 7, 3EAssume you do a paired samples study and get this dataset with 4 people. What is xbar_diff? x1= 9,8,6,5 x2= 5,5,3,33If H0 is true, how many standard error units did this study deviate from the null population parameter? (89)4.47What is the average deviation of |e_diffis| ? (89)1What is the average deviation of |e_diffsp| ? (89)4.47If H0 is true, what is the standardized e_diffsp for this particular study? (89)4.47Which numerical value answers the descriptive question and provides the primary result the researcher wanted to know when conducting this study? (89)2To look up the probability of these results assuming the null hypothesis is true, you need to use two numerical values. One of these values is equal to 4. What is the other numerical value you need to use? (89)4.47For a two-samples study investigating a difference between two means, write the linear equation for variance in a sample.y_is=ybar_0s+(ybar_1s-ybar_0s)x_is+e_isWrite this linear equation for sampling error variance in a population that includes the term "e_1-0sp." To write the most important of these two equations, you would need to include the term "e_1-0sp."(ybar_1sp-ybar_0sp)=(mu_1p-mu_0p)+e_1-0spWrite this linear equation for sampling error variance in a population that includes the term "e_0sp." To write the least important of these two equations, you would need to include the term "e_0sp."ybar_0sp=mu_0p+e_0spUse numerical values (and NOT letters or subscripts) and write the linear equation for variance in a sample using values for Person 1. (97)8 = 3 + 4(1) + 1Use numerical values (and NOT letters or subscripts) and write the most important linear equation for sampling error variance in a population assuming Ho is true.(97)4 = 0 + 4Use numerical values (and NOT letters or subscripts) and write the least important linear equation for sampling error variance in a population assuming Ho is true.(97)3 = 0 + 3Which of the following are variables? Select ALL the correct answers. y_is ybar_0s (ybar_1s-ybar_0s) x_is e_is mu_0p (mu_1p-mu_0p) e_1-0spy_is x_is e_isWhich of the following are parameter estimates? Select ALL the correct answers. y_is ybar_0s (ybar_1s-ybar_0s) x_is e_is mu_0p (mu_1p-mu_0p) e_1-0spybar_0s ybar_1s-ybar_0sWhich of the following answers the descriptive question and would provide the primary result we want to know when conducting a study?(ybar_1s-ybar_0s)If H0 is true, how many standard error units did this study deviate from the null population parameter? (103)-8.62What is the average deviation of |e_1-0sp| ? (103).58Which numerical value answers the descriptive question and provides the primary result the researcher wanted to know when conducting this study? (103)-5If you do a study investigating the difference in means between two groups, you have a few options for reporting the effects size. Which option can be interpreted most easily (and is the default option for use in this class)? A. p-value B. (ybar_1-ybar_0)/sd_pooled C. statistic/sd_statistic D. sqrt(t^2/(t^2+df))BWhen using a t-value to test for a difference between means, two assumptions need to be true for the test to be valid. One pertains to heterogeneity of variance. Which of the following is true of this this assumption? a. this assumption is more important than the assumption regarding independence of observations b. a study needs to have heterogeneity of variance to produce a valid t-test result c. this assumption would be violated if the same person participated in a study multiple times d. a significant result from a Levene's test indicates that this assumption has been violatedDIf the critical value is 1.98, this means that _____ percent of values in a t-distribution will be more extreme (in either a positive or negative direction) than 1.98.5The mean for group one is 75 and the mean for group zero is 50 (therefore the difference between means is 25). The standard error of difference is 5 and the critical value (for p= .05) is 2. What is the lower bound of the 95% confidence interval for the difference between means?15 (25-10)Fill in the blanks with correctly spelled terms.Class lecture included a description of how you can provide "five pieces of information" to answer research questions. First, you provide the name and the value of a(an) _______ statistic, and this indicates the size of the effect. Then, you provide the name and the value of a(an) ______ statistic along with a _______ value.descriptive, inferential, probabilityHow do you calculate point biserial correlation?sqrt((t^2)/(t^2+df))How do you calculate t-value?the value (mean) divided by standard error of statistic (standard error of mean)If this study were repeated over and over, how much would you typically expect the size of difference between the two groups to deviate from the true difference in the population?standard error of differenceWhat are the cutoff's for d-statistic?less than .2 is trivial, less than .5 is small, less than .8 is medium, above .8 is largeHow do you calculate standard error of mean?SD/sqrt(n)How do you calculate lower end of 95% CI?mean difference - (1.984)(standard error of mean difference)How do you calculate upper end of 95% CI?mean difference + (1.984)(standard error of mean difference)What can you find from significant result for Levene's test?difference between standard deviations, violated assumptions,What are two assumptions of an independent samples t-test?equality of variance and independence of observationsWhat are two different and unrelated types of effects that can be tested in a paired samples analysis?difference between means, correlation between pairsIf a correlation is .5, what is the percent of variance explained?.25Consider the following example: Zara's score on x= 5 Zara's score on y= 23 b0= 10 b1= 2 What is yhat for Zara?10 + 2(5) = 20Consider the following example:Zara's score on x= 5Zara's score on y= 23 b0= 10 b1= 2 What is e for Zara?3In the regression equation, what is b_0? A. The expected increase in y given a one unit increase in x B. The expected value for y when x equals zero C. A person's predicted score on the outcome variable D. Observed y minus predicted yBIn the regression equation, what is b_1? A. The expected increase in y given a one unit increase in x B. The expected value for y when x equals zero C. A person's predicted score on the outcome variable D. Observed y minus predicted yAIn the regression equation, what is e? A. The expected increase in y given a one unit increase in x B. The expected value for y when x equals zero C. A person's predicted score on the outcome variable D. Observed y minus predicted yDIn least squares regression, we calculate an intercept and a slope to minimize something. Write the formula for the thing that gets minimized.sum(y-yhat)^2Use "cov_xy" as the symbol for the covariance between x and y and write the formula for a slope.cov_xy/sd_x^2In simple regression when x and y are standardized a beta will always equal: A. y-yhat B. The covariance minus (y-yhat) C. zero. D. the correlation E. the mean of yDIn simple regression when x and y are standardized an intercept will always equal: A. y-yhat B. The covariance minus (y-yhat) C. zero. D. the correlation E. the mean of yCFor a simple regression with one predictor variable. Write the full linear regression equation for variance in a sample.y_is=b_0s+(b_1s)(x_is)+e_isFor a simple regression with one predictor variable, there are two equations for sampling error variance in a population. To write the most important of these two equations, you would need to include the term "e_1sp."b_1sp=beta_1p+e_1spFor a simple regression with one predictor variable, there are two equations for sampling error variance in a population. To write the least important of these two equations, you would need to include the term "e_0sp."b_0sp=beta_0p+e_0spAs _______ gets steeper, Σ(y-yhat) gets ______ . A. b0 , larger B. b0 , smaller C. b1 , larger D. b1 , smallerDUse "ss_est" as the symbol for the sum of squared error and write the formula for the standard error of estimate.sqrt(ss_est/(n-2))y_is=b_0s+b_1s(x_is)+e_is In the above equation, what is the average deviation of |eis|? A. The standard deviation B. The standard error of estimate C. The standard error of beta D. Observed y minus predicted yDy_is=b_0s+b_1s(x_is)+e_isIn the above equation, how is e_is calculated?A. cov_xy/sd_x^2 B. ybar-b_1(xbar) C. y-ybar D. y-yhatDΣ (y-yhat)^2 is the sum of squares _________.errorΣ (y-ybar)^2 is the sum of squares _________.totalΣ (yhat-ybar)^2 is the sum of squares _________.explainedIn simple regression, if r = 0, then the intercept is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedBIn simple regression, if r = 0, then the sum of squares error is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedCIn simple regression, if r = 0, then the sum of squares explained is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedAIn simple regression, if r = 0, then the sum of squares total is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedDImagine that you do a study and find that the total sum of squares is 12 and the error sum of squares is 9. What is the explained variance sum of squares?3Imagine that you do a study and find that the total sum of squares is 12 and the error sum of squares is 9. What is the r^2?.25 (3/12)In simple regression, if r = 1, then the sum of squares error is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedAIn simple regression, if r = 1, then the sum of squares explained is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedCIn simple regression, if r = 1, then the sum of squares total is equal to _____. A. zero B. mean of y C. sum of squares total D. Sum of squares error E. Sum of squares explainedEIf this study were repeated over and over, how much will the beta typically deviate from the true population parameter? (129).25Calculate the value that indicates the standardized e_1sp for this study assuming Ho is true. (129)6 (1.50/.25)Calculate the t-value for the correlation. (129)6Given the output above, calculate r^2. (130).25 (30/120)Calculate the value that indicates the average distance that people's predicted scores deviated from their observed scores. (130)3 (sqrt(9))Which cell is equal to Σ(y-ybar)^2? (131)HWhich cell is equal to Σ(yhat-ybar)^2? (131)AWhich cell is equal to Σ(y-yhat)^2? (131)DWhich cell is equal to p(number of predictors)?BWhich cell is equal to n - p -1?EWhich cell is equal to n-1 ?IYou define "fish time" as the number of hours a person spends with pet fish in one week. You do a study using fish time to predict ratings of life well-being, and get these results: b0 = 8 and b1 = 3. Lou was a participant in the study, and Lou's fish time was 4 hours. What is Lou's predicted life wellbeing?20 (8+3(4))You define "fish time" as the number of hours a person spends with pet fish in one week. You do a study using fish time to predict ratings of life well-being, and get these results: b0 = 8 and b1 = 3. Lou was a participant in the study, and Lou's fish time was 4 hours. If Lou's actual life wellbeing score was 25, what is Lou's life wellbeing with fish time extracted out of it?5 (25-20)You have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If the correlation between x and y is zero, then. . . the correlation between x and e is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barAYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If the correlation between x and y is zero, then. . . y-yhat is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barCYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If the correlation between x and y is zero, then. . . ebar is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barAYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If the correlation between x and y is zero, then. . . sd_e is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barEYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If there is a perfect correlation between x and y, then. . . the correlation between x and e is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barBYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If there is a perfect correlation between x and y, then. . . y-yhat is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barAYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If there is a perfect correlation between x and y, then. . . ebar is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barAYou have scores on variable x and variable y for a sample of people. You extract x out of y to create variable e. If there is a perfect correlation between x and y, then. . . sd_e is equal to _____ A. Zero B. One C. y-ybar D. sd_x E. sd_y F. y-barAUsing the letters from the Venn diagram above, type the formula that would be equal to R^2. (135)b+c+d/(a+b+c+d)Using the letters from the Venn diagram above, type the formula that would be equal to r^2 for the association between x_1 and y. (135)b+c/(a+b+c+d)If you want to know the effect of x_1 ignoring the other x variables: In the Venn diagram, this pertains to ____ . (136)area b + cIf you want to know the effect of x_1 ignoring the other x variables: The effect size is given by _____ . (136)a correlationIf you want to know the effect of x_1 ignoring the other x variables: The significance of the effect is tested with _____ . (136)a t-testIf you want to know the effect of all the x variables taken together: In the Venn diagram, this pertains to ____ . (137)area b + c + dIf you want to know the effect of all the x variables taken together: The effect size is given by _____ . (137)R^2If you want to know the effect of all the x variables taken together: The significance of the effect is tested with _____ . (137)F-testFor which of the following statistics is the expected value the same as the population parameter? A. R B. R^2 C. r D. r^2CHow many predictor variables were used in the regression equation? (139)3Based on this output, what is a value for an inferential statistic that could be used to test the significance of the effect of one x variable ignoring the other x variables? (139)2 (.28/.14)Based on this output, what is a value for an inferential statistic that could be used to test the significance of the effect of all the x variables taken together? (139)4.09 (F-stat)Based on this output, what is a value for a descriptive statistic that could be used to give an unbiased effect size for the effect of one x variable ignoring the other x variables? (139).28 (r)Based on this output, what is a value for a descriptive statistic that could be used to give the effect size for the percent of variance explained by all the x variables taken together. (139).40 (8/20)Based on this output, what is the correlation between observed y and predicted y? (139)sqrt(ss_explained/ss_total)Fill in each blank with a numerical value or with a correctly spelled component from the equation (with its subscript, if relevant).y=b_0+b_1(x_1)+b_2(x_2)+e In the regression equation above, b_1 is equal to the predicted increase in _____ for a _____ unit increase in _____ when _____ is equal to _____.y, 1, x, x_2, 0y=b_0+b_1(x_1)+b_2(x_2)+e Class lecture described a method that could be used for calculating b1 from the equation above. One of the steps in this method involved calculating a residual score for y. Write the regression equation, with subscripts, that would be used to calculate the needed residual score for y.y=b_0+b_2(x_2)+e_y.x2y=b_0+b_1(x_1)+b_2(x_2)+e Class lecture described a method that could be used for calculating b1 from the equation above. One of the steps in this method involved calculating a residual score for x1. Write the regression equation, with subscripts, that would be used to calculate the needed residual score for x1 (that is, the residual score for x_1).x_1=b_0+b_2(x_2)+e_x1.x2y=b_0+b_1(x_1)+b_2(x_2)+e Class lecture described a method that could be used for calculating b1 from the equation above. The final step in this method involved estimating a regression equation that included two residual scores and that produced a value for b1 that equaled b1 from the equation above.Write this regression equation, with subscripts, that includes two residual scores and produces the value for b1 in the equation above.e_y.x2=b_0+b_1(e_x1.x2)+eFill in the bank with a correctly spelled component from the equation (with its subscript, if relevant). Eq 1: y=b_0+(b_1)(x_1)+(b_2)(x_2)+e Eq 2: e_y.x1 =b_0+(b_2)(e_x2.x1)+e b_2 from Equation 1 is exactly equal to _____ from Equation 2.b_2y=5+4x_1+6x_2+e According to the equation above, y is expected to increase by 4 units when x1 increases by 1 units and x2 __________ . A. is 6. B. is 0. C. is 5. D. increases by 6 unitsBIf you want to know the effect of x1 after controlling for x2In the Venn diagram, this pertains to ____ . (151)area bIf you want to know the effect of x1 after controlling for x2The effect size is given by _____ . (151)a standardized betaIf you want to know the effect of x1 after controlling for x2The significance of the effect is tested with _____ . (151)a t-testUsing the letters from the Venn diagram above, type the formula that would be equal to a squared partial correlation between x1 and y. (152)b/(a+b)y=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the unstandardized beta weight for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [A]? (153)the residual for x_1y=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the unstandardized beta weight for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [B]? (153)the residual for yy=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the standardized beta weight for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [A]? (154)the residual of the z-score for x_1y=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the standardized beta weight for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [B]? (154)the residual of the z-score for yy=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the partial correlation for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [A]? (155)the z-score of the residual for x_1y=b_0+b_1(x_1)+b_2(x_2)+b_3(x_3)+e You could calculate the partial correlation for x1 above by using a simple regression equation in which [A] is used to predict [B]. What belongs in space [B]? (155)the z-score of the residual for yYou calculate a statistic and get a value of .2 for x_1 and a value of .8 for x_2. The effect for x_1 might be larger than the effect for x_2 if the value you calculated is a A. beta B. standardized beta C. partial correlation D. none of the aboveBWhich of the following is true about a standardized beta? A. It cannot be greater than 1 and cannot be less than -1. B. Residuals are extracted from x and y and then the residuals are standardized. C. Both x and y are standardized prior to extracting residuals. D. It will have a t-value that is smaller than the t-value for an unstandardized beta.CWhich of the following is equal to area B divided by area A + B? (157) A. t-value for beta B. squared beta C. squared standardized beta D. squared partial correlationDWhat descriptive statistic would you calculate if you want to know the size of the standardized association between x1 and y after controlling for other variables? (157) A. t-value B. standardized beta C. r D. R^2BThing 1: b/sd_beta Thing 2: the t-value for partial correlation Thing 3: the t-value for b(sd_x/sd_y) Which of these three things are equal to each other? A. None of them are equal B. Thing 1 and Thing 2 C. Thing 1 and Thing 3 D. Thing 2 and Thing 3 E. All three things are equalEsqrt(t^2/(t^2+df)) What does this formula do? A. Turns a t-value into a correlation effect size B. Turns a t-value into an inferential statistic. C. Turns a t-value into a standardized beta. D. Turns a t-value into b/(sd_beta) E. Turns a t-value into a value that could be larger than one.AThe key difference between a partial correlation and a semipartial correlation has to do with: A. how the residuals for the x variables are defined. B. whether variables are standardized before or after extracting residuals. C. how the variance for y is defined. D. Whether it is possible to compare relative unique contributions of each x variable.CUsing the letters from the Venn diagram above, type the formula that would be equal to a squared semi-partial correlation between x1 and y. (161)b/(a+b+c+d)deltaR^2 is equal to R^2 full minus R^2 _______.constrainedIn the first step of an analysis, income and education were used to predict happiness. Which of the following are potential second steps that would allow the computation of deltaR^2? Select all examples that are potential second steps. A. Income and education are used to predict anger. B. Income, education, and trust are used to predict happiness. C. Trust and agreeableness are used to predict happiness. D. Income, education, trust and agreeableness are used to predict happiness.B, DThe table below displays correlations between four variables from a sample of 100 people. If you used all three x variables to predict y, which variables are likely to have significant beta weights? (164) A. None of them B. x2 C. x1 and x3 D. All of themBGiven these results, what best describes how results for Equation 2 are likely to compare with results for Equation 1? (165) A. In Equation 2, R2 will increase, and b1 will be larger. B. In Equation 2, R2 will increase, and b1 will be smaller. C. In Equation 2, R2 will increase, but only a trivial amount and, and b1 will become non-significant. D. In Equation 2, R2 will decrease, and b1 will be larger.E. In Equation 2, R2 will decrease, and b1 will be smaller.BGiven these results, what best describes how results for Equation 2 are likely to compare with results for Equation 1? (166) A. In Equation 2, R2 will increase more than a trivial amount, and b1 will be smaller. B. In Equation 2, R2 will increase, but only a trivial amount and, and b1 will become non-significant. C. In Equation 2, R2 will decrease, and b1 will be larger. D. In Equation 2, R2 will decrease, and b1 will become non-significant.BPick the answer that would make this an example of a suppressor effect.The correlation between x1 and y was .24 and significant. After controlling for x2, the partial correlation between x1 and y was ________ A. Larger B. About the same C. Smaller but still significant D. Not significant E. Different from the standardized betaAybar_1-ybar_0=?The equation depicted above provides an example of ________ . (Select all the correct answers.) A. a contrast B. a focused question C. an omnibus questionA, BThe values below include a grand mean and three groups means from a study contrasting three groups. Ollie Otter is in group 1. What is Ollie Otter's predicted value on the outcome variable y? (169)9When using ANOVA to test for differences between groups. . .the sum of squares explained is typically called the sum of squares ______ groupsbetweenWhen using ANOVA to test for differences between groups. . .and the sum of squared error is typically called the sum of squares _______ groups.withinWhen using ANOVA to test for differences between groups the formula for the sum of squares for explained variance can be written as: SS_treatment=sum(_________)(ybar_group-ybar_grand)^2(n_group)When using ANOVA to test for differences between groups the formula for the sum of squares for error variance can be written as: SS_error=sum(_____________)(y-ybar_group)^2When using ANOVA to test for differences between groups the formula for the sum of squares for total variance can be written as: SS_total=sum(_______________)(y-ybar_grand)^2Assume you are using ANOVA to test for differences between groups. If you have 5 groups, how many contrasts are free to vary?4What is standard deviation for y? (175)sqrt(SS_total/df_total) = sqrt(120/10)What is the pooled within-group standard deviation for y? (175)sqrt(MS_error) = sqrt(9)What is eta^2? (175)SS_explained/SS_total = 30/120How many groups were used in the analysis? (175)3sd_est is the same thing as: A. eta^2 B. omega^2 C. the pooled within group sd D. the total, grand sdCeta^2 will be ______ R^2 and eta^2 will be _______ omega^2 A. larger than B. the same as C. smaller thanB, AThe process of creating predictor variables with values that are determined by group membership is called _________ .codingWhat is ybar_1-ybar_0? (179)3 (slope)What is ybar_0? (179)12 (intercept)What is the standardized beta? (179).42What is cov_xy/((sd_x)(sd_y))? (179).42What is eta^2? (179).18 (.42^2)What is R^2? (179).18 (.42^2)What is the mean for the treatment group? (180)15 (12+3(1))What is the predicted value for someone in the control group? (180)12 (12+3(0))What is the difference between means divided by the standard error of the difference between means? (181)5 (t-value)What is the F value? (181)25 (t-value^2)If a researcher wants to create orthogonal contrasts for a study comparing 5 groups, how many contrasts does the researcher need to create?4If the contrasts depicted in the code assignment chart above are entered into a regression equation, the equation for someone in Group 3 would be: Write the remaining part of the formula (just the part of the formula that appears after the "=" sign) and use numerical values instead of the letter "x." (183)b_0+b_1(.33)+b_2(.5)Orthogonal contrasts are being used to create contrasts for an analysis with three groups. The code assignment chart depicted above has four missing values (labeled E, F, G, H). Following procedures discussed in class lecture, figure out what the missing values need to be and then write the complete code assignment chart with all the correct values.(184).66, .33, .5, 0Assume you are creating two orthogonal contrasts. In the table below, list values you could use for the first contrast so that people in group 3 are given a negative value, and so that the contrast compares people in group 3 with people in groups 1 and 2.(185).33, .33, -.66Assume you are creating two orthogonal contrasts. In the table below, list values you could use for the first contrast so that people in group 3 are given a negative value, and so that the contrast compares people in group 3 with people in group 1 (and group 2 is not included in the comparison). (186).5, 0, -.5Given the results listed above: What is b0?(187)(ybar_1+ybar_2+ybar_3)/3Given the results listed above: What is b1?(187)((ybar_2+ybar_3)/2))-ybar_1Given the results listed above: What is b2?(187)ybar_3-ybar_2Orthogonal contrasts are being used to create contrasts for an analysis with three groups. What is the name of the descriptive statistic that provides an effect size for the difference between Group 2 and Group 3? A. F B. eta^2 C. t D. dBOrthogonal contrasts are being used to create contrasts for an analysis with three groups. What is the name of the inferential statistic that tests the significance of the difference between Group 2 and Group 3? A. F B. eta^2 C. t D. dAWhat is the d-statistic for the contrast between Group 1 and the other two groups?(190)b_1/sqrt(MS_error) 2.4/sqrt(9)What is the d-statistic for the contrast between Group 2 and Group 3?(190)b_2/sqrt(MS_error) 1.5/sqrt(9)If you wanted to do a t-test for a contrast between just Group 1 and Group 2, you would need the formula below. However, because there are more than 2 groups in this study, you would need to replace sd_pooled^2 with a value that can be calculated using the results above. What is this value? (192)16 (MS_error)If you wanted to do a t-test for a contrast between just Group 1 and Group 2, what are the appropriate degrees of freedom to use for this t-test? (193)19 (df_error)A researcher conducted 20 different t-tests, and in every case the null hypothesis was true. What is the best guess for how many of those t-tests were significant?1If Dug the dog tested only a set of planned comparisons following standard procedures for orthogonal contrasts, what is the p value for this contrast after a Bonferroni correction? (195).02(3) = .06Post hoc analysis is used to test all the possible paired group contrasts. What is the name of the inferential statistic that can be used to determine if the difference between Group 2 and Group 3 is significant? A. eta^2 B. F C. q D. dCKeeping in mind the fact that the most stringent procedures for protecting against family-wise error will produce the largest p-values, fill in the blanks to reflect the most likely outcome. A researcher used three different methods to protect against family-wise error and got p-values of .07, .04, and .02. It is most likely that: _____ produced a p-value of .07 _____ produced a p-value of .04_ ____ produced a p-value of .02 A. Fisher's Least Significant Difference procedure B. A Bonferroni correction C. A Tukey Honestly Significant Difference test.07 = B, .04 = C, .02 = A