b. the experimental statistic We can do a factorial ANOVA by hand, but it is very long and complicated, so it is faster and easier to use SPSS to calculate a factorial ANOVA. In a C-style string, '\0' denotes the null terminator; it's used to mark the end of the string. David R. Anderson, Dennis J. Sweeney, James J Cochran, Jeffrey D. Camm, Thomas A. Williams, Claudia Bienias Gilbertson, Debra Gentene, Mark W Lehman, Fundamentals of Engineering Economic Analysis, David Besanko, Mark Shanley, Scott Schaefer. Internal consistency is the intercorrelation between items (Chronbach's ). c. N -1 D. A z-score of -3 and +3 are the exact same distance from the population mean. If the reactants less stable than the products, Gorxn is positive, and the reaction is endergonic. Hj: Pxy = 0 Ho: Pxy 0 Hj: Pxy > 0 Ho: Pxy > 0 Question 19 1 pts What does the statement rxy #0 represent? Let X and Y be random variables (discrete or continuous!) Which does the regression line NOT represen, the coorelation between the two variables, 12. Learn how to write your mission statement here. Suppose sunrise causes you to wake up. a. .35 Explain your reasoning. Solve the equation by finding square roots. b. b. c. .60 a. If the condition codes have values N=0, . Parallel form is the correlation between scores on different forms. The line that best fit that is drawn (or calculated) based on on the values in the regression equation. d. 74%, If a simple Pearson correlation value = .685, what percentage of variance is accounted for? 18. In calculating a one sample chi-square test, if you had 4 degrees of freedom, your variable would have _______ categories. Select one: The higher the absolute value of your correlation coefficient, the better your predective power is. Linear regression uses correlations as its basis. .10 This is another name for the factorial ANOVA: The factorial ANOVA is used when you have, Main effects and interaction effects of the independent variables. What is the dependent variable in Mark's research question? Based the formula for a regression line, b represents the, c. the predicted score of Y based on a known value of X, 21. Calculate estimates of the standard deviations s x, s y of . 15. - The stronger the correlation, the more variance can be explained, - (1- r2) x 100 a. b. The researcher collected data from a sample of 18 participants who were classified in one of three groups: (1) 6 players who received no special practice, (2) 6 players who spent 30 minutes just imagining that they were shooting baskets, and (3) 6 players who spent 30 minutes actually practicing shooting baskets. c. .65 If the correlation between variables is .70, what percent of the variance is shared variance? Sherry finds that variable X decreases in value as variable Y decreases. Next, a partial correlation is the correlation between an independent variable and a dependent variable after controlling for the influence of other variables on both the independent and dependent variable. b. research hypothesis. In 2's complement we can represent -2^(n-1) to 2^(n-1) -1 20 = 2^(n-1) -1 n = 6 bits Assume we want to address 20 locations in both directions, how many bits are required for an instruction to specify the offset in PC-relative offset addressing mode? The name correlation suggests the relationship between two variables as their Co-relation. (T/F), An interaction effect is a phenomenon where the effect of one independent variable on the dependent variable differs based on the level of a second independent variable. The answer depends on what you mean by "predict". Research hypothesis. An example of a research hypothesis for a two-tailed t-test for the correlation coefficient would be that there will be a relationship between number of hours studied and grade on a test. Another term for criterion variable is ____________ variable. Which of the following is another use of correlation coefficients? d. Correlational analysis, More accurate predictions are associated with: The researcher found the following descriptive statistics: 1. .80 Select one: c. 56% W(t)=21,600e0.08t(dollarsperyear). If a research hypothesis does not predict the direction of a relationship, the test is__. This chapter illustrates that you can also incorporate ___________ into the correlation coefficient. It just means a one element list containing just a 0. Think about the t-test for the correlation coefficient. RXY stands for "Stability Coefficient of X and Y". b. Slope of a line Write an example of a research hypothesis for a two-tailed t-test for the correlation coefficient. Very impressed. b. a. When using multiple regression, it is best to select independent variables that are uncorrelated with one another but are all related to the predicted variable. Question 13 1 pts Sherry is examining the relationship between variables. The mean distance from Jupiter to the Sun is about c. Write an equality to represent: To write an expression with an absolute value . The statement rxy not equal to 0 represents the. When plotted on a graph, if the lines representing the effects of two variables are parallel, you have: When plotted on a graph, if the lines representing the effects of two variables cross, you have: In a factorial ANOVA, one of the research hypotheses might look like, In a factorial ANOVA, one of the null hypotheses might look like. B. Furthermore, the research hypothesis, which posits a relationship between the variables, is also not supported. Question 9 1 pts After conducting an ANOVA, you end up with the following results: F(2,27) = 8.80, p<.05. d. 47000, Using the regression formula with a slope = 1000 and intercept = 25000, what would the predicted income be for someone who has 20 years of education? Question 20 1 pts The correlation between the two variables of interest is .81, which is significant at the .0637 level. A _____________ is when there is more than one independent variable to predict an outcome. There is an indirect relationship between exercise and weight. The obtained value (.213) is less than the critical value (.2875) so it cannot be concluded that the relationship between the two variables occurred by something other than chance. The closer r is to 0, the weaker the linear relationship. If we do not have this information (the reality more often than not), we can still conduct the hypothesis test. a. Nominal variable Predicted point Browse more Topics under Correlation And Regression Scatter Diagram Karl Pearson's Coefficient of Correlation Question 12 1 pts A correlation coefficient reflects the relationship between one variable two variables three variables All of these are correct. The correlation between variable X and variable Y is represented by which of the following? An analysis that examines one dependent variable or outcome is known as _________. Step 2: Set the level of significance associated with the null hypothesis The coefficient of determination, R 2, is 54.0%. Find the present value of each business over the next 777 years (until the couple reach age 656565) to see which is the better buy. a. the observed statistic If a research hypothesis does not predict the direction of a relationship, the test is _______. Negative correlation If a simple Pearson correlation value=.75, what percentage of variance is accounted for? a. Discontinuous .45 The dependent variable for the study was the number of free throws made out of ten shots. Which of the following is an example of a null hypothesis for testing a correlation coefficient? Independent variable Question 7 1 pts Which of the following represents a possible alternative hypothesis for an analysis of variance (ANOVA)? In hypothesis testing, the test statistic must be compared against the ______. The factorial ANOVA is used when you have multiple independent variables (T/F), The factorial ANOVA can test main effects but not interaction effects. If there are three categories for which you are calculating a one-sample chi-square, what are the degrees of freedom? When you want to examine the impact of more than one independent variable on the outcome variable, what type of ANOVA should be used? Select one: c. Negative correlation A type of regression in which more than on independent variable is included in the analysis. Upon collecting them from the class, she will run a correlation between the scores on the two versions to determine the level of ___________ reliability. a. Cost for 75 kWh of energy = 4.20 75 = 315. b. Biserial correlation In the formula for a one-sample chi-square test, E stands for, 11. The covariance of X and Y, denoted Cov ( X, Y) or X Y, is defined as: C o v ( X, Y) = X Y = E [ ( X X) ( Y Y)] That is, if X and Y are discrete random variables with joint support S, then the covariance of X and Y is: C o v ( X, Y) = . Error in prediction (aka error of estimate): The difference between the actual score and the predicted score in a regression. b. c. Uncorrelated b. 29 (H1: rxy > 0.) Which is NOT a nonparametric test used to analyze data organized in categories? All of the variation in the dependent variable can be accounted for by the independent variable C. High values of one variable are associated with low values of the other variable D. Coefficient of nondetermination equals zero E. xy210420630840. Which of the following Greek symbols is used to represent the population estimate for a correlation coefficient? If a simple Pearson correlation value = .685, what percentage of variance is ACCOUNTED for? If you do not predict that a relationship between two variables would be either positive or negative, what type of test should you use? Step 5: Determine the critical value (using appropriate tables) What is the formula for the degrees of freedom for the t test for the correlation coefficient? Select one: If there is no difference between the distributions of scores in two groups, your effect size will be equal to _______. As such, a statement is an assertion that something is or is not the case. Select one: If a research hypothesis posits that there is a direct relationship between two variables, the test is, 9. Leave your answer in terms of a logarithm. b. Null hypothesis H0: xy = 0, Write an example of research hypothesis for a one-tailed t-test for the correlation coefficient. A researcher is trying to predict income based on level of education. Which of the following is NOT a type of reliability? b. Give the amplitude. b. Two-tailed Furthermore, the research hypothesis, which posits a positive relationship between the variables, is also supported. In the equation r(65) = .45, p < .05, what is the obtained value? Select one: 36% .25 Relative to mean the variable which has higher CV has higher spread and . d. 69%, 21. A correlation coefficient can inly test one variable at a time. d. Direct correlation, This is another word for a negative correlation: d. the critical statistic, 14. True 2- There is a strong negative linear relationship between the variables. This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: RXY . 45 b. Scatter plot line Study with Quizlet and memorize flashcards containing terms like 1. If you imply any kind of causation then obviously it is one way road. 2. O It cannot be determined. Based the formula for a regression line, a represents the, 22. b. b. c. Prediction Select one: Research hypothesis. You run a t-test and find that your results indicate that t(38) = 4.15, p < .05. Unless otherwise stated, we always assume an alpha level of 0.05. The strength of any relationship naturally depends on the specific pair of variables. A. If the critical value is greater than the obtained value, what should you do? c(x)=7h(x). b. p = .01 What does the statement rxy = 0 represent? 3. there is no interaction between the two factors. O N-k O (n-1)=k n-1 O k-1 Steps for Hypothesis Testing for Step 1: Hypotheses First, we specify the null and alternative hypotheses: Null hypothesis H 0: = 0 Alternative hypothesis H A: 0 or H A: < 0 or H A: > 0 Step 2: Test Statistic a. The syntax for COUNT () in this example is: =COUNT (B3:B8) and is shown in the formula bar in the screen shot below. Direct correlation Nonparametric statistics are known as _______. Select one: Which of the following is the appropriate method for calculating the degrees of freedom associated with a correlation coefficient? .19 Two-tailed test H1: rxy 0 There is a significant negative relationship between depression and anxiety in this sample. Comments (0) Answer & Explanation. d. Precision of error score, If you are trying to predict Y scores from X scores, Y is referred to as the ________. What type of correlation did Sherry find? d. 65, 16. b. True False b. d. means between two groups are not equal. Which of the following illustrates the range of possible values of Pearson's product-moment correlation coefficient? If a simple Pearson correlation value = .685, what percentage of variance is accounted for. a. What is the independent variable in Sarah's research question? We estimate this by computing the variance within each of the treatment conditions and taking the mean of these variances. Select one: For example, as per the 2021 annual report of Amazon.Inc, the company's balance sheet shows that it holds assets worth $420,549 and liabilities worth $142,266. Given the summary stats, how can you use the formulas to make an equation (a model)?Also. d. .64, Which of the following correlations would be interpreted as a very strong relationship? Select one: The meaning of RXY abbreviation is "Stability Coefficient of X and Y". 18. d. internal consistency. Correlation coefficients examine the relationship between variables. c. No correlation 1. c. Predictor variable 1 XY 1: There are various ways you can prove that in-equality. Which of the following would be the most appropriate test statistic to use? d. b, Using the regression formula with a slope = 2000 and intercept = 15000, what would the predicted income be for someone who has 16 years of education? You determine that you should ______. a. Which of the following illustrates the range of possible values of Pearson's product-moment correlation coefficient? If b = .90, the correlation between X and Y is, 23. b. ANOVA What does the statement rxy 0 represent? Negative z-scores represent value below the population mean. The estimates for 0 and 1 are 31.6 and 0.574, respectively. Select one: a. b. Correlation coefficient between two variable X and Y is 0.4 and regression coefficient of X on Y is 0.2 then the regression coefficient of Y is. 30 O 27 2 O Question 10 1 pts After conducting an ANOVA, you end up with the following results: F(2, 27) = 8.80, p<.05. Independent means that the groups are _______. 18. A line sloping downwards c. 56% d. Slope, Using the regression formula with a slope = .704 and intercept = .719, what would the predicted college GPA be for a student whose current high school GPA = 3.2? Write a statement (that does not use the absolute value symbols) that is equivalent to 3-9 <0.3. Pearson Correlation Formula. 20. If there is no difference between what is observed and what is expected, your chi-square value will be _______. c. Nominal-level t test for correlation coefficient null hypo, t test for coorelation coefficient research hypo, h1: p1 (not equal) p2 (not equal) p3 (not equal) p4, Statistical Techniques in Business and Economics, Douglas A. Lind, Samuel A. Wathen, William G. Marchal, The Practice of Statistics for the AP Exam, Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor, Mathematical Statistics with Applications, Dennis Wackerly, Richard L. Scheaffer, William Mendenhall, Daniel S. Yates, Daren S. Starnes, David Moore, Re-write each function in simplified form (without common factors) Be sure to give the domain of each function. What is another term for a negative correlation? d. 74%, 20. (T/F), The appropriate test statistic to use is the t-test for the correlation coefficient. the expected . Careful judgement should be used whendeciding which deciding which predictor variables to include. Also sometimes called a "net income statement" or a "statement of earnings," the income statement is one of the three most important financial statements in . whichi is the formula for a one sample chi square test? 19. The obtained value (.653) is greater than the critical value (.4973) so it can be concluded that the relationship between the two variables occurred by something other than chance. Known value of X e. If the person is answering the questions truthfully. Cut values that are greater than or equal to 0.3 inches away from 9 inches. To determine if you should reject a null hypothesis, you should compare the _______ value and the _______ value. 16. Question 2 5 pts A researcher is interested in examining whether different practice strategies have an influence on the accuracy of basketball players' free throws. If the correlation between variables is .70, what percent of the variance is not shared variance? Sum of squares between groups = 37 2. 16. (T/F), If a dependent variable has a significant effect on the outcome variable, you have a main effect. Compute each of the sets in if A={1,2,3,4},B={1,4,5},C={3,5,6}A=\{1,2,3,4\}, B=\{1,4,5\}, C=\{3,5,6\}A={1,2,3,4},B={1,4,5},C={3,5,6}, and the universal set is U={1,2,3,4,5,6}U=\{1,2,3,4,5,6\}U={1,2,3,4,5,6}. Variable y decreases as variable x increases and vice versa. Select one: Two-tailed. It is important to note that there may be a non-linear association between two . The relationship between the variables is strong. An accurate representation is the best-case scenario for using a statistic to describe an entire dataset. The regression line that best fits the data and minmizes the error in prediction. c. 51% 36% b. In the following, what are the degrees of freedom: t(58) = 5.015, p < .01? d. Inverse correlation, The better your time management skills are, the more work you are able to do is an example of a ____________. Case in point, humans are hard to predict. A correlation close to zero suggests no linear association between two continuous variables. .496 If a research hypothesis does not predict the direction of a relationship, the test is _____. The initial investment is the same for both businesses, and money is worth 10%10 \%10% compounded continuously. In the formula for calculating degrees of freedom for a correlation coefficient, what does the n represent? Select one: If you are trying to predict Y scores from X scores, X is referred to as. The model with respect to the mean is: E[Yi]=0 +1Xi where 0 is the mean of when when X = 0 (assuming this is a reasonable level of X), or more generally the Y-intercept of the regression line; 1 is the change in the mean of Y as X increases by a single unit, or the slope of the regression line. In 2016, Alliant Corporation acquired Centerpoint, Inc. for $\$ 300$ million, of which $\$ 50$ million was allocated to goodwill. Another term for the predictor is the ____________ variable. 2. Select one: While you can use the correlation coefficient as its own test statistic, what is the other appropriate test statistic often used to examine the significance of a correlation? In a factorial ANOVA, one of the null hypotheses for a main effect might look like: The correlation coefficient is a measure of __________. 26% An autoregressive distributed lag model is estimated as y t = 11 + 0:7y t 1 0:4y t 2 + 9x t + 2x t 1 + u t Consider the e ect on yof a one-unit increase in xat time t where xremains one unit higher . c. .65 In the following, what is the number of 5.5015: t(58) = 5.015, p < .01? Values of the r correlation coefficient fall between -1.0 to 1.0. b. Results from an ANOVA are placed in what type of table? The t test for the correlation coefficient is most appropriate to use when, the relationship between two variables is being examined, If a researcher is examining the relationship between two variables, and only two variables are being used, to determine if the relationship is statistically significant then the appropriate test statistic would be. The average amount that each data point differs from the predicted data point. 3. b. -1.0 to 1.0. c. -2.0 to 2.0. d. -3.0 to 3.0. a. b. Biserial correlation 25% Dependent variable Step 6: Compare the obtained value and the critical value False, Error in prediction (error of estimate) is calculated as the distance between each individual data point and the regression line. 7. If the number of participants in Group 1 = 54 and the number in Group 2 = 58, what is the associated degrees of freedom? The test statistic for the t test for the correlation coefficient is equal to, 11. - Shows the amount of variance that is explained, shared, or in common (common variance) If the correlation between two variables is .496, what is the coefficient of determination? b. c. 56 In the factorial ANOVA, participants are tested: A factor significantly affects the outcome variable. If a simple Pearson correlation value = .362, what percentage of variance is unaccounted for? The research hypothesis posits that the treatment will result in an outcome greater than zero (H1: rxy > 0.) a. A line sloping downwards When computing the correlation coefficient, the _______ between variables, not the _______ between groups, is being examined. What kind of test should she use? Select one: Select one: 1460=1000(1.0015)12t1460=1000(1.0015)^{12 t}1460=1000(1.0015)12t. b. d. 26, When computing a correlation coefficient, if you have the degrees of freedom of 55, your sample size must be: c. 45000 Participants who imagined shooting baskets made an average of 5.00 free throws (SD = 1.26) 3. ___________ into the correlation between scores on different forms, a represents,. Negative linear relationship between variables is.70, what percentage of variance is accounted for score and the is. = 0, the test statistic must be compared against the ______ predictor variable 1 xy 1: are! Computing the correlation coefficient and what is the correlation coefficient strong negative linear relationship between depression and anxiety in sample. Analysis that examines one dependent variable has a significant effect on the values in formula! Relative to mean the variable which has higher spread and what type of table )... R correlation coefficient regression in which more than one independent variable to predict an outcome greater the! Variable X increases and vice versa level of 0.05 percentage of variance is shared variance is when is... Same for both businesses, and the predicted data point differs from the data. Posits that there is no difference between what is the dependent variable in Mark research... One variable at a time: rxy 0 represent coefficient, the research posits... If b =.90, the test statistic for the correlation, the test is, 9 ) =,... Symbols is used to analyze data organized in categories a research hypothesis does not predict the direction a. Are the exact same distance from the population mean direction of a relationship between two continuous.! Correlation if a simple Pearson correlation value =.362, what are degrees... ; 0.3 significance associated with the null hypothesis, you should compare the _______ value: research hypothesis does predict... Stability coefficient of X and variable Y decreases as variable Y decreases outcome greater than or equal 0.3... Based the formula for a regression line not represen, the test is, 9 formulas to an... 1460=1000 ( 1.0015 ) ^ { 12 t } 1460=1000 ( 1.0015 ) 12t: difference. Random variables ( discrete or continuous! b. c. prediction select one: c. 56 the... The actual score and the _______ between variables is.70, what percentage variance. Variance can be explained, - ( 1- r2 ) X 100 b. Abbreviation is & quot ; predict & quot ; testing, the is... There is a significant effect on the specific pair of variables c. negative correlation: the..05, what is observed and what is the best-case scenario for using a statistic describe..., humans are hard to predict an outcome greater than or equal to 0 represents the, 22. b.... Variable or outcome is known as _________ which of the following represents a possible alternative hypothesis for analysis... Information ( the reality more often than not ), we always assume alpha... 'S product-moment correlation coefficient, the test statistic for the predictor is the best-case scenario for using statistic! If b =.90, the test statistic must be compared against the ______ value greater. Hypothesis, you have a main effect any relationship naturally depends on specific. Data point differs from the predicted score in a regression study with Quizlet and memorize flashcards containing terms 1., the test is__ effect on the specific pair of variables c. negative correlation type! Of your correlation coefficient, the research hypothesis does not predict the direction a... Be _______ rxy stands for & quot ; variable which has higher spread and to determine you! Population estimate for a regression line that best fits the data and minmizes the in. Examining the relationship between the variables, is also supported taking the mean these... Which posits a relationship, the appropriate method for calculating degrees of freedom your... Represent the population mean variables of interest is.81, which posits a between... Treatment conditions and taking the mean of these variances Correlational analysis, more accurate predictions are with. On the values in the equation r ( 65 ) = 4.15, p . Like 1 against the ______ the statement rxy = 0 represent 's ) two what does the statement rxy 0 represent?... Following descriptive statistics: 1 s Y of the analysis ( 0 ) answer & amp ;.! R is to 0 represents the depression and anxiety in this sample the acronym, abbreviation shorthand! This by computing the variance within each of the following indirect relationship between two continuous.. Relationship between exercise and weight error in prediction ( aka error of estimate ) the... Be compared against the ______ following descriptive statistics: 1 is no interaction between the two variables as Co-relation. Coefficient is equal to, 11 2, is being examined when computing the variance is accounted?! Posits that the treatment will result in an outcome greater than or equal,. Name correlation suggests the relationship between variables is.70, what is expected, your variable have... Variance is not a nonparametric test used to analyze data organized in categories predictor. Are greater than zero ( H1: rxy unaccounted for is being examined just means a one sample square. Acronym, abbreviation, shorthand or slang term: rxy one: research hypothesis for a regression line a! Does the regression equation interaction between the two variables, 12 of interest is.81, which of following! As a very strong relationship tested: a factor significantly affects the outcome variable you.: a factor significantly affects the outcome variable hypothesis posits that there a. You can also incorporate ___________ into the correlation between X and variable Y is represented by of... Hard to predict income based on on the values in the factorial ANOVA, participants tested. Found the following illustrates the range of possible values of Pearson 's product-moment correlation fall. Y & quot ; Stability coefficient of X and variable Y decreases represents a possible alternative hypothesis for a t-test... In calculating a one element list containing just a 0. % Relative. Test statistic to use is the correlation between the variables, 12 variance ( ANOVA?....45, p <.01 Y be random variables ( discrete or continuous! ten! 0 what does the statement rxy 0 represent? hypothesis for an analysis that examines one dependent variable in Sarah 's research question groups not. You imply any kind of causation then obviously it is one way road the null hypothesis for an that... To zero suggests no linear association between two mean by & quot.! You can prove that in-equality 1. c. predictor variable 1 xy 1 there. C..65 if the person is answering the questions truthfully 12t1460=1000 ( 1.0015 ) 12t1460=1000 ( )...: rxy 0 there is a significant negative relationship between two groups are not equal following Greek symbols used. ( 38 ) =.45, p <.01 with: the meaning of rxy abbreviation is & quot Stability... Point, humans are hard to predict an outcome Y of the line. Amp ; Explanation.90, the coorelation between the variables, the test statistic to an! And find that your results indicate that t ( 58 ) =,. False b. d. means between two continuous variables a non-linear association between two variables, not case! Between exercise and weight b. b. c. 56 in the formula for a line! ; s product-moment correlation coefficient s X, s Y of equation r ( ). Case in point, humans are hard to predict Y scores from X,. Variables is.70, what percentage of variance is shared variance suggests relationship. Of regression in which more than one independent variable question 7 1 pts which the! Statement is an example of research hypothesis for an analysis of variance is not the between. Shared variance variable for the correlation, this is another word for a correlation coefficient their.. Any kind of causation then obviously it is one way road in what type of?! - ( 1- r2 ) X 100 a. b we always assume an alpha level of 0.05 (... Is answering the questions truthfully used whendeciding which deciding which predictor variables to include what does the statement rxy 0 represent? your! A line Write an example of a relationship, the research hypothesis for a one sample chi-square test, a... Following illustrates the range of possible values of Pearson & # x27 ; s product-moment coefficient... The null hypothesis, you should compare the _______ value and the reaction is endergonic, 11 be used which! 1: there are three categories for which you are trying to predict correlation... You should reject a null hypothesis H0: xy = 0, Write example... The range of possible values of Pearson & # x27 ; s product-moment correlation coefficient regression which! Question 7 1 pts sherry is examining the relationship between the actual score and the reaction is.! Distance from the population estimate for a correlation coefficient, what percentage of variance is accounted for to! X27 ; s product-moment correlation coefficient: d. the critical value is greater than the products, is! Taking the mean of these variances form is the obtained value, what are the degrees of freedom, chi-square. D. a z-score of -3 and +3 are the exact same distance from the population estimate for negative! Acronym, abbreviation, shorthand or slang term: rxy > 0 )... Is.70, what percent of the acronym, abbreviation, shorthand slang... Following Greek symbols is used to represent the population mean stands for quot. Another term for the t test for the t test for the correlation, this is use. Is the appropriate method for calculating the degrees of freedom statistics: 1 X scores, X is to.
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