Introduction to Statistics for the Social Sciences SBS
Introduction to Statistics for the Social Sciences SBS 200 - Lecture Section 001, Fall 2019 Social Sciences Room 100 10: 00 - 10: 50 Mondays, Wednesdays & Fridays. December 6
No more labs
Before next exam: December 9 th Study Guide for Exam 4 is available on class website Review worksheet is available on class website 285 animated clicker questions are available on class website Animated solutions to the review worksheet are available on website
Today we will review this worksheet from lab and complete some practice clicker questions
Just one quick favor… Please use your phone or laptop Please take just a minute to complete Course Evaluations online…. . Check your email for a link or go to… tceonline. oia. arizona. edu
narrower go down As variability goes down, it is easier to reject the null ANOVA 99. 18%
z= 52 -40 z = 2. 4 5 Go to table Add area Lower half . 4918 +. 5000 =. 9918 also fine: 99. 18%. 9918. 5000 . 4918 40 4 2. z =
narrower go down As variability goes down, it is easier to reject the null ANOVA 99. 18% 0 Interval True experiment
Education Income has the largest correlation coefficient of 0. 85 Yes No IQ Age No 0. 91 Income x Education is a significant correlation, p < 0. 05 None r 2
Standard error of the estimate because it is a measure of the amount of error in the regression line (average of residuals) 81% because. 92 =. 81 19% The correlation between the heights of mothers and their daughters is moderate, positive and statistically significant, r(28) = 0. 60; p< 0. 05 36% is explained because. 62 =. 36 64% because if 36% is explained then 64% is not explained - 100 – 36 = 64 75% because. 52 =. 25, so 25% is explained so 75% is not explained
r = 0. 92 r 2 = 0. 8464 b = 6. 0857 84. 64% 15. 36% b = 6. 0857 55. 286 b = 6. 0857 residual r r 2 b a
-1. 0 +1. 0 anything +1. 0 anything 0 any positive number
They are both difference from expected value Residual is difference from score to predicted score (y – y’) Deviation score is difference from score to mean (x - µ) Over-performing The standard error of the estimate is the average of the residuals just like standard deviation is the average of the deviation scores zero That there is no significant difference between these groups
1 3 427. 19 -4. 58 -14. 83 6. 10 Y’ = 427. 19 - 4. 58 (temp) - 14. 83 (insulation) + 6. 10 (age) Y’ = 427. 19 - 4. 58 x 1 - 14. 83 x 2 + 6. 10 x 3
1 3 Yes Decrease variability (by increasing sample size or minimize variability due to error) Decrease level of confidence from 99% to 95% Easier Narrower Easier Common and rare scores Drop from 5% to 1%
Type of cartoon Two-tail 48 Level of aggression True No difference in level of aggression based on type of cartoon watched Type of cartoon did make difference in level of aggression did make a difference didn’t make a difference Mean approaches true population Shape approaches normality Variability goes down it didn’t it did
58 3. 5 100 3 12 25 4. 0 3. 49 3 100 12 25 4. 0 3. 49 84 percentile
Just for fun In multiple regression what is the range of values for a coefficient of regression? a. 0 to +1. 0 b. 0 to -1. 0 c. -1. 0 to +1. 0 d. -∞ to +∞ Correct Y’ = a + b 1 X 1 + b 2 X 2 + b 3 X 3
Just for fun Correct If r = 1. 00, which inference cannot be made? a. The dependent variable can be perfectly predicted by the independent variable b. This provides evidence that the dependent variable is caused by the independent variable c. All of the variation in the dependent variable can be accounted for by the independent variable d. Coefficient of determination is 100%.
Just for fun Winnie found an observed correlation coefficient of 0, what should she conclude? a. Reject the null hypothesis b. Do not reject the null hypothesis c. Not enough info is given Correct
Just for fun In a regression analysis what do we call the variable used to predict the value of another variable? a. Independent b. Dependent c. Correlation d. Determination Correct
Just for fun What can we conclude if the coefficient of determination is 0. 94? a. r 2 = 0. 94 b. direction of relationship is positive c. 94% of total variation of one variable is explained by variation in the other variable. d. Both A and C e. All of the above are correct Correct
Just for fun What is the range of values for a coefficient of determination? a. 0 to +1. 0 b. 0 to -1. 0 c. -1. 0 to +1. 0 d. -∞ to +∞ Correct
Just for fun Which of the following statements regarding the coefficient of correlation is true? a. It ranges from -1. 0 to +1. 0 b. It measures the strength of the relationship between two variables c. A value of 0. 00 indicates two variables are not related d. All of these Correct
Just for fun What does a coefficient of correlation of 0. 70 infer? (r = +0. 70) a. Almost no correlation because 0. 70 is close to 1. 0 b. 70% of the variation in one variable is explained by the other c. Coefficient of determination is 0. 49 d. Coefficient of nondetermination is 0. 30 Correct
Just for fun The Pearson product-moment correlation coefficient, r, requires that variables are measured with: a. an interval scale b. a ratio scale c. an ordinal scale d. a nominal scale e. either A or B. Correct
Just for fun If r = 0. 65, what does the coefficient of determination equal? a. 0. 194 b. 0. 423 c. 0. 577 d. 0. 806 Correct
Just for fun What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be? a. Regression equation b. Slope of the line c. Standard error of estimate d. Least squares principle Correct
Just for fun Agnes compared the heights of the women’s gymnastics team and the scores they got. If she doubled the number of players measured, but ended up with the same correlation (r) what effect would that have on the results? a. the r is the same, so the conclusion would be the same b. the r is the same, but with more people, degrees of freedom (df) would go up and it would be harder to reject the null hypothesis. c. the r is the same, but with more people, degrees of freedom (df) would go up and it would be easier to reject the null hypothesis. Correct
Just for fun Which of the following is true about the standard error of estimate? a. It is a measure of the accuracy of the prediction b. It is based on squared vertical deviations between Y and Y’ c. It cannot be negative d. All of these Correct Standard error of the estimate: • a measure of the average amount of predictive error • the average amount that Y’ scores differ from Y scores • a mean of the lengths of the green lines
Just for fun If all the plots on a scatter diagram lie on a straight line, (perfect correlation) what is the standard error of estimate? a. - 1 b. +1 c. 0 d. Infinity Correct Standard error of the estimate: • a measure of the average amount of predictive error • the average amount that Y’ scores differ from Y scores • a mean of the lengths of the green lines
Just for fun Scatterplot A Scatterplot B Scatterplot C Which of these correlations would be most likely to have the highest positive value for r? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given Correct
Just for fun Scatterplot A Scatterplot B Scatterplot C Which of these scatterplots will have the smallest “y intercept”? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given Correct
Just for fun Scatterplot A Scatterplot B Scatterplot C Which of these correlations would be most likely to represent the correlation between salary and expenses? a. Scatterplot A b. Scatterplot B c. Scatterplot C d. Can not be determined from the information given Correct
Just for fun Which of the following correlations would allow you the most accurate predictions? a. r = + 0. 01 b. r = - 0. 10 c. r = + 0. 40 d. r = - 0. 65 Correct
Just for fun After duplicate correlations have been discarded and trivial correlations have been ignored, there remain a. two correlations b. three correlations c. six correlations d. nine correlations Correct
Just for fun Which of the following conclusions can not be made from the data in the matrix? a. There is a significant correlation between Science and Reading b. There is a significant correlation between Math and Reading c. There is a significant correlation between Math and Science Correct
Just for fun What is the null hypothesis of a correlation coefficient? a. It is zero (nothing going on) b. It is less than zero c. It is more than zero d. It equals the computed sample correlation Correct
Just for fun In the regression equation, what does the letter "a" represent? a. Y intercept b. Slope of the line c. Any value of the independent variable that is selected d. None of these Correct Y’ = a + bx 1 + bx 2 + bx 3 + bx 4
Just for fun Assume the least squares equation is Y’ = 10 + 20 X. What does the value of 10 in the equation indicate? a. Y intercept b. For each unit increased in Y, X increases by 10 c. For each unit increased in X, Y increases by 10 d. None of these Correct
Just for fun In the least squares equation, Y’ = 10 + 20 X the value of 20 indicates a. the Y intercept. b for each unit increase in X, Y increases by 20. c. for each unit increase in Y, X increases by 20. d. none of these. Correct
Just for fun In the equation Y’ = a + b. X, what is Y’ ? a. Slope of the line b. Y intercept c. Predicted value of Y, given a specific X value d. Value of Y when X = 0 Correct
Just for fun If there are four independent variables in a multiple regression equation, there also four a. Y-intercepts (a). b. regression coefficients (slopes or bs). c. dependent variables. d. constant terms (k). Correct Y’ = a + bx 1 + bx 2 + bx 3 + bx 4
Just for fun If the coefficient of determination (r 2) is 0. 80, what percent of variation is explained? a. 20% b. 90% c. 64% d. 80% Correct What percent of variation is not explained? a. 20% b. 90% c. 64% d. 80% Correct
Just for fun Which of the following represents a significant finding: a. p < 0. 05 b. t(3) = 0. 23; n. s. c. the observed t statistic is nearly zero d. we do not reject the null hypothesis Correct
Thank you for a wonderful semester! and good luck with your studies See you at thefinal exam.
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