SUMMER 2011 RE-EXAM PSYF11STAT - STATISTIK

Transcription

1 SUMMER 011 RE-EXAM PSYF11STAT - STATISTIK Full Name: Årskortnummer: Date: This exam is made up of three parts: Part 1 includes 30 multiple choice questions; Part includes 10 matching questions; and Part 3 includes 3 written/calculation questions. You have three hours to complete the exam. Please clearly mark your answer for each question in the spaces provided using either pen or pencil. In Part 3, you may provide your written answers in either Danish or English. You will find a formula sheet and critical value tables for t and χ at the end of this exam booklet. GOOD LUCK! 1

2 PART 1. MULTIPLE CHOICE QUESTIONS (30 POINTS) Please circle the best answer for each of the questions below. 1. In experimental studies, we typically aim to: a. Eliminate systematic and unsystematic variation b. Balance systematic and unsystematic variation c. Maximize systematic variation and limit unsystematic variation d. Maximize unsystematic variation and limit systematic variation. Which of the following methods would come closest to recruiting a random sample of University students? a. Drawing 50 telephone numbers from a hat containing the phone numbers of all students b. Asking 50 people in the library on a Saturday morning to participate in your study c. Asking the first 50 names from an alphabetical list of all students to participate d. Advertising for 50 participants by putting up a poster in the canteen 3. If a researcher creates a variable that measures a person s reaction time (in milliseconds) on a cognitive task, what type of variable it is? a. Binary b. Nominal c. Ordinal d. Ratio 4. The frequency distribution below is: a. Platykurtic b. Positively skewed c. Negatively skewed d. Leptokurtic 5. Which of the following is NOT a measure of central tendency? a. The mean b. The median c. The standard deviation d. The mode 6. What is the range for the following distribution: ? a. 10 b c. 6 d. 34

3 7. If an individual has a z score of -.58, what percentage of people would be expected to have a score LOWER than this? a. 95% b. 99% c. 1% d. 5% 8. If the scores on an exam have a mean of 6 and a standard deviation of 4, what is the z-score for an exam score of 18? a. b. 11 c. d Which of the following terms best describes the sentence: It is expected that male and female participants will report equal numbers of sexual partners? a. An alternative hypothesis b. A directional hypothesis c. A null hypothesis d. A non-directional hypothesis 10. The standard error is equal to the standard deviation of. a. The distribution of the sample data b. The normal distribution c. The sampling distribution of means d. The sum of errors 11. Critical values for significance in a theoretical distribution depend on: a. Sample size b. Whether your hypothesis is directional or non-directional c. The p level you have chosen for the test d. Both b and c e. All of the above 1. If a test is NOT statistically significant, it means that: a. There is a low probability of the result occurring if the null hypothesis is true b. The result is not very important c. The null hypothesis has been proven true d. There is a high probability of the result occurring if the null hypothesis is true 13. The assumption of normality applies to which of the following test(s)? a. The z-test b. Linear Regression c. Both a and b d. None of the above 3

4 14. Which of the following indicates the strongest correlation between two variables? a. r=.63 b. r=.00 c. r= -.3 d. r= What is the co-efficient of determination for the analysis shown below? a b c..000 d. None of the above 16. Determine the predicted value of y for a regression line with an intercept of 13.6, a slope of 0.43, and an x value of 4. a b c d In a regression analysis, F measures: a. The intercept of the regression line b. The slope of the regression line c. The overall fit of the model c. The effect of individual predictors 18. What is the risk of making a Type 1 error for the t-test shown in the output below? a. 1.07% b. 10.7% c. 3.86% d. 38.6% 4

5 19. What can you conclude from the output below? Measure: MEASURE_1 Mauchly's Test of Sphericity b Within Subjects Effect factor1 Mauchly's W Approx. Chi-Square df Sig a. That the assumption of homogeneity of variance has been violated b. That the assumption of homogeneity of variance has been satisfied c. That the assumption of sphericity has been satisfied d. That the assumption of sphericity has been violated 0. One possible solution to deal with a violation of sphericity is to use: a. A Welch correction b. A log transformation c. A Brown Forsyth correction d. A Huynh-Feldt correction 1. A clinical psychologist compares the scores of 15 depressed patients with 15 phobic patients on a social avoidance test and gets the following results (higher scores = more avoidance). Based on this SPSS output, what should he report? a. Depressed patients had significantly higher scores on the avoidance test as compared to phobic patients, t(8)= -4.3, p<.001 b. Phobic patients had significantly higher scores on the avoidance test as compared to depressed patients, t(8)= -4.3, p<.001 c. The avoidance scores for phobic and depressed patients did not differ significantly, t(8)= - 4.3, p>.05 d. Phobic patients had significantly higher scores on the avoidance test as compared to depressed patients, t(18.75)= -4.3, p<.001 5

6 . A psychologist collects data on students fear of statistics before (n=0) and after (n=0) they complete a statistics course (higher scores = more fear). What is the effect size for this test? a..31 b..5 c..01 d If an ANOVA F-ratio is greater than 1, what can we conclude? a. Effect > Error b. Error > Effect c. F is significant d. F is not significant 4. If you run a one-way independent ANOVA comparing 4 groups, with 7 people in each group, what are the degrees of freedom for your test? a. 3, 4 b. 3, 8 c. 4, 4 d. 4, 8 5. If you have run an ANOVA comparing 5 groups and want to use a Bonferroni correction for your pairwise comparisons, you should: a. Divide the p value by 5 b. Divide the p value by 10 c. Divide the F value by 5 d. Divide the F value by The statistical symbol typically used to represent a Kruskall-Wallis test is: a. t b. H c. U d. X 6

7 7. If you have a repeated measures design with three conditions, a sample size of 3, and a significant K-S test, what should you do? a. Automatically use a Repeated measures ANOVA b. Automatically use a Friedman s test c. Use the central limit theorem to justify using a Repeated measures ANOVA d. Use the central limit theorem to justify using a Friedman s test 8. A researcher has conducted a Friedman s ANOVA to explore the effect of three different treatment conditions on an ordinal measure of outcome. What type of posthoc test should he conduct to identify which conditions differ from one another? a. Independent t-tests b. Dependent t-tests c. Mann-Whitney tests d. Wilcoxon Signed-rank tests 9. The critical value for p<.05 with 10 degrees of freedom is in the chi-squared distribution. If a researcher calculates that his chi-squared value is also 18.31, what should he do? a. Reject the null hypothesis b. Fail to reject the null hypothesis c. Conclude that the alternative hypothesis has been proven true d. Both a and c 30. The best effect size measure to use for a 3 x 3 Chi-square test is: a. Z b. Cramer s v c. Phi d. Odds ratio 7

8 PART. MATCHING QUESTIONS (10 POINTS) Match each question on the left to one of the possible answers on the right. Each answer can be used only once. Please write the letter that identifies your answers in the blank spaces provided. Questions 1. The experimental design best able to control for unsystematic variance is a design.. A frequency distribution (histogram) that has two peaks can be described as. 3. A significance test should be used when a researcher has stated a directional hypothesis. 4. The variable is manipulated or controlled by the researcher in an experimental study 5. The value of y when x = 0 in a regression equation is equal to the. 6. The difference between the observed value of a variable and the value predicted by a statistical model is called the. 7. A is an objective and standardized measure of an effect that can be directly compared across studies. 8. is a measure of the symmetry of a frequency distribution. 9. A measure that accurately measures what it intends to is said to be a measure. 10. The measures whether the difference between two group means is large enough to be significant. Possible Answers A. Normal B. F-ratio C. t-value D. Unreliable E. Between-subjects F. Leptokurtic G. Sampling distribution of means H. Confounding I. Within-subjects J. One-tailed K. Brown-Forsythe L. Platykurtic M. Effect size N. Significance O. Greenhouse Geisser P. Kurtosis Q. Correlational R. Independent S. Outcome T. p level U. Standard error V. Bimodal W. Valid X. Bonferroni Y. Two-tailed Z. Gradient AA. Variance BB. Skew CC. Intercept DD. Deviance EE. Reliable 8

9 PART 3. WRITTEN/CALCULATION QUESTIONS (30 POINTS) Please answer each of the questions below in as much detail as possible. Each question is worth a total of 10 points. You may choose to answer in either Danish or English. 1. A cognitive psychologist is interested in exploring the relationship between age and verbal ability. She recruits a sample of 10 adults and asks them to complete a simple verbal fluency task in which they have to name as many different animals as possible in a 60 second period. For each participant she records their age (in years) and the total number of animals they are able to name (see below). When exploring her data, the psychologist finds that both variables are normally distributed. Participant ID Age (years) Number of Animals Named a. What test should the psychologist use to analyze her data? b. Calculate the appropriate statistic by hand (show all of the steps in your calculation) c. Determine whether your test is statistically significant and give an effect size d. What should the psychologist conclude? Please provide your answers here (you may continue on the next page): 9

10 Answers (cont): 10

11 1. A work psychologist has been hired by a large clothing company to compare customers satisfaction with their shopping experience at boutiques located in four different cities (Aarhus, Odense, Copenhagen and Vejle). The psychologist recruits 3 participants (8 from each store) and asks them to complete a survey measuring their satisfaction (scored from 0-50, where higher scores = more satisfaction). When testing his assumptions, the psychologist finds that the K-S test was p>.05 for all four locations, and he gets the following output for Levene s test: Based on the description and output above, identify the type of test(s) the psychologist should use to examine whether there is a difference in customer satisfaction across cities. Provide a step-by-step decision process and include as many details as possible in your answer (you do not need to calculate the actual test). Please provide your answer here (you may continue on the next page if needed): 11

12 1. Answer (cont): 1

13 3. Many people believe that they can tell when someone is lying, often claiming that the person looks, speaks, or acts differently when lying as compared to when they are telling the truth. In order to explore this issue, a social psychologist designs an experimental study in which 3 participants are asked to listen to the same person telling two different stories. One story is true, and the other is a lie. After each story, the 3 participants are asked to rate how confident they are that the story is true on an ordinal scale (lower scores= less confidence in the truth of the story). Based on this description and the SPSS output provided below, decide what type of analysis was done and report the psychologist s findings in the proper format. Statistics Lying_condition Truth_condition N Valid 3 3 Missing 0 0 Median Ranks N Mean Rank Sum of Ranks Truth_condition - Lying_condition Negative Ranks 8 a Positive Ranks 15 b Ties 0 c Total 3 a. Truth_condition < Lying_condition b. Truth_condition > Lying_condition c. Truth_condition = Lying_condition Test Statistics Truth_condition - Lying_condition Z a Asymp. Sig. (-tailed).116 a. Based on negative ranks. 13

14 Please provide your answer here: 14

15 Regression s Descriptives PSYF11STAT- FORMULA SHEET Mean Median Mode x Mean= Mdn= N +1 Mode= most common score N Variance Standard deviation Range ( x x) = N 1 s = ( x x) N 1 Standard Error Z- scores SE= s N Correlation Pearson s r Coefficient of Determination r cov xy = = r = s x s y ( x x)( y y) ( N 1) sxsy t-statistic (for significance of r) Df for t r r = N t r 1 r z= x x s Range df = N Where N = x biggest x smallest R = r = number of participants Regression Equation Model Fit for Regression y= b0 + b1 x1 +ε t-tests Independent t-test Df for Independent t-test (equal sample size) df = N t = Dependent t-test Df for Dependent t-test (paired samples) df = N 1 t = s d d / Effect size for t-tests Mann-Whitney/Wilcoxon-signed rank tests Effect size r = x x 1 s n z 1 N s + 1 n N r = Where N = total t t + df number of R Where N Where N observations SS = SS F= = total MS MS Model Total Model Re sidual number of = number of participants (n1 + n +...) participants

16 One-Way ANOVA Independent ANOVA F-ratio Df for Independent ANOVA F= MS MS Model( Between) Re sidual( Within) df Model = k 1 Where k = number of groups df Residual = N k Where N = total number of participants (n + n +...) 1 Dependent ANOVA F-ratio Df for Dependent ANOVA (Repeated Measures) F = MS MS Model( Condition) Re sidual( Error) df df Model Residual = k 1 = df Within df Model Chi-Squared Chi-squared statistic Expected cell frequency χ ( O E) E = row total* column total E= N( total) Df for Chi-Squared df = (# rows 1)*(# columns 1) Odds Ratio for Outcome 1 OR= Odds of Outcome 1 for Predictor Variable Category 1(N with outcome' 1' Odds of Outcome 1 for Predictor Variable Category (N with outcome'1' / Odds Ratio for Outcome OR= Odds of Outcome for Predictor Variable Category 1(N with outcome' ' Odds of Outcome for Predictor Variable Category (N with outcome'' / / N with outcome'' ) N with outcome '' ) / N with outcome'1' ) N with outcome '1' ) Note: you choose which level of the outcome variable to report the odds for. E.g., the odds of outcome 1, or the odds of outcome

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