Statistics for Behavioral Sciences
Midterm Exam
Course Introduction
Statistics for Behavioral Sciences introduces students to the fundamental concepts and methods of statistical analysis as applied to the study of human behavior. The course covers descriptive and inferential statistics, including measures of central tendency, variability, probability, hypothesis testing, t-tests, ANOVA, correlation, and regression. Emphasis is placed on interpreting statistical results and understanding their relevance in psychological and behavioral research. Through practical exercises and data analysis, students learn how to collect, summarize, and draw accurate inferences from behavioral data, equipping them with the quantitative skills necessary for evaluating scientific findings in the behavioral sciences.
Recommended Textbook
Statistics for Psychology 6th Edition by Arthur Aron Ph.D
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Chapter 1: Displaying the Order in a Group of Numbers
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Sample Questions
Q1) A prison psychologist recorded the number of rule infractions for 15 prison inmates over a six-month period to be 5,4,2,4,3,5,2,0,4,4,5,5,3,4,and 3.
a.Make a frequency table.
b.Make a histogram based on the frequency table.
c.Describe in words the shape of the histogram.
Answer: 11ea7a42_740f_9642_81a2_372fe50a5f5c_TB2971_00
Q2) In a histogram,the vertical axis displays __________. Answer: frequencies
Q3) If someone told you that a distribution showed a ceiling effect,you would surmise that it is
A)symmetrical.
B)positively skewed.
C)negatively skewed.
D)rectangular.
Answer: C
Q4) A listing that shows how many times each value of a variable occurs among a particular group of scores is called a(n)__________.
Answer: frequency table
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Chapter 2: Central Tendency and Variability
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Sample Questions
Q1) A concierge is interested in how long it takes to bring passengers to the airport and then return to the hotel.The round-trip travel times for six taxi drivers were 45,30,42,45,41,and 43 minutes.
a.Compute the mean,median,and mode.
b.Based on the measures of central tendency,what can you infer about the distribution?
c.Compute the variance and standard deviation.
d.Explain what the results mean to a person who has never had a course in statistics.
Answer: A)Mean = 246/6 = 41; Median = (42+43)/2 = 42.5; Mode = 45. B)The distribution is negatively skewed. C)SS = 16 + 121 + 1 + 16 + 0 + 4 = 158; SD2 = 26.33; SD = 5.13. D)No answer in Test Bank.
Q2) The symbol used in the textbook for the variance of a group of scores is
Answer: SD<sup>2</sup>
Q3) The standard deviation for the scores 1,7,and 13 is __________.
Answer: 4.90
Q4) When __________ are summed,the result will always equal zero.
Answer: deviation scores
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4
Chapter 3: Some Key Ingredients for Inferential Statistics: Z
Scores,the Normal Curve, Sample Versus Population, and Probability
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Sample Questions
Q1) If the sophomore class is 50% women,the junior class is 45% women,and the senior class is 55% women,the probability of drawing a woman who is a junior is
A)45%
B)50%
C)55%
D)95%
Answer: A
Q2) __________ is to M as is to SD.
Answer:
Q3) Using a normal curve table,if a person has a score in the bottom 42% of all scores in a distribution,the highest Z score this person can have is A)-1.41
B)-0.94
C)-0.20
D)0)25
Answer: C
Q4) The percentage of scores between the mean and any particular Z score may be found in a(n)__________.
Answer: normal curve table
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Chapter 4: Introduction to Hypothesis Testing
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Sample Questions
Q1) In hypothesis testing,a statement about the predicted relation between populations is the __________.
Q2) The comparison distribution is based on the distribution of the voting behavior of __________.
Q3) If you set alpha to .01 and are conducting a two-tailed test,what value do you need to look up in the normal curve table to determine the cutoff Z score on the comparison distribution?
A).020
B).010
C).005
D).001
Q4) The situation in which the null hypothesis is true is represented by the __________ distribution.
Q5) For a nondirectional research hypothesis,the null hypothesis is expressed in symbols as __________.
Q6) A research hypothesis that does not predict a particular direction of difference between populations is called a(n)__________ hypothesis.
Q7) If Population 2 refers to people in general,Population 1 refers to __________.
Q8) Sometimes,a research hypothesis may be referred to as a(n)__________.
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Chapter 5: Hypothesis Tests With Means of Samples
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Sample Questions
Q1) In general,the shape of a distribution of means tends to be
A)unimodal and symmetrical.
B)bimodal and symmetrical.
C)unimodal and skewed.
D)rectangular and symmetrical.
Q2) What is the standard deviation of the comparison distribution?
A).42
B).65
C)12
D)144
Q3) What is the shape of the comparison distribution?
A)positively skewed
B)negatively skewed
C)approximately normal
D)cannot be determined from the information provided
Q4) The mean of a distribution of means is
A)the square-root of the original population mean.
B)the original population mean divided by the sample size.
C)the same as the original population mean.
D)the sample mean multiplied by the variance.
7
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Chapter 6: Making Sense of Statistical Significance:decision
Errors, Effect Size, and Statistical Power
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Sample Questions
Q1) An organizational psychologist conducted a study to see whether upgrading a company's older computer system to newly released,faster machines would cause an increase in productivity from the current average of 120 units with a standard deviation of 20.The new system will be tested in a single department with 45 employees.The company has decided that an increase of less than 10 units will not justify purchasing the new system.
a.What is the predicted effect size for an increase of 10 points?
b.Explain the logic of what has been done.
c.Advanced topic: Sketch the distributions involved.
d.Advanced topic: If the data are analyzed at the .01 significance level,what will be the power of the study?
e.Advanced topic: Explain your answer to a person who understands hypothesis testing with means of samples,but who is not familiar with power.
Q2) Setting the significance level cutoff at .10 instead of the more usual .05 increases the likelihood of
A)a Type I error.
B)a Type II error.
C)failing to reject the null hypothesis.
D)accepting the null hypothesis when,in fact,it is false.
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Chapter 7: Introduction to T Tests: Single Sample and Dependent Means
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Sample Questions
Q1) When figuring the variance of the distribution of means based on an estimated population variance,you divide the estimated population variance by __________.
Q2) The formula SS/df provides a(n)__________ estimate of the population variance.
Q3) Which of the following is an assumption for the t test for dependent means?
A)The population variance is known.
B)The population mean is greater than the sample mean.
C)The population follows a normal distribution.
D)The sample follows a normal distribution.
Q4) The sum of squared deviations from the mean for a sample is 12,and there are 4 participants.The estimated population variance is __________.(Give a number.)
Q5) To find the score in a t table at which the null hypothesis will be rejected,an experimenter must know the significance level,the degrees of freedom,and
Q6) "Student's" t test was invented by
A)Philip Guinness.
B)William Gosset.
C)Jacob Cohen.
D)Joan Guinness.
Page 9
Q7) The formula (M - )/ S<sub>M</sub> is used to figure the __________.
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Chapter 8: The T Test for Independent Means
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Sample Questions
Q1) If the standard deviation of the distribution of the difference between means is 0.76,what is the t score?
A)(15 - 23)/ 0.76 = -10.53
B)(0.76)(15 - 23)= -6.08
C)[(6.5 + 4.5)/ 2] [0.76] = 4.18
D)(55 - 51)/ 0.76 = 5.26
Q2) One of the assumptions for the t test for independent means is that A)sample means are not significantly different.
B)the mean of the distribution of differences between means is 1.
C)the variance of each of the parent populations is the same.
D)the mean of each of the parent populations vary by no more than 1 standard deviation.
Q3) An experimenter hypothesizes that biology majors score higher than literature majors on an intelligence test.If the mean score for biology majors was 18.8 and the mean score for literature majors was 21.3,and the S<sub>difference</sub> was 0.9,the t score was
A)t = (18.8 - 21.3)/ 0.9<sup>2</sup> = -3.09
B)t = (18.8 - 21.3)/ 0.9 = -2.78
C)t = (18.8 - 21.3)(0.9)= -2.25
D)t = (18.8 - 21.3)/ [(2)(0.9)] = -1.39
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Chapter 9: Introduction to the Analysis of Variance
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Sample Questions
Q1) An analysis of variance differs from a t test for independent means in that an analysis of variance
A)is usually used to compare two groups,while a t test for independent means can be used to compare two or more groups.
B)can be used to compare three or more groups,while a t test for independent means cannot be used to compare more than two groups.
C)is conducted before the experiment,while a t test for independent means is conducted after the experiment.
D)includes computation of group variances as part of the analysis,while a t test does not include these computations.
Q2)
[(S<sup>2</sup><sub>Between</sub>)(df<sub>Between</sub>)]/[(S<sup>2</sup><sub> Between</sub>)(df<sub>Between</sub>)+
(S<sup>2</sup><sub>Within</sub>)(df<sub>Within</sub>)] =
A)R<sup>2</sup>
B)F
C)f
D)t
Q3) Advanced topic: R<sup>2</sup> = __________.
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Page 11
Chapter 10: Factorial Analysis of Variance
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Sample Questions
Q1) Most psychology research
A)avoids anything more than a one-way analysis of variance.
B)concurrently examines four or five main variables.
C)is limited to two-way and occasionally three-way factorial designs.
D)concurrently examines at least 20 variables.
Q2) Advanced topic: According to the structural model of the two-way analysis of variance,each score's overall deviation from the grand mean is divided into A)2 components.
B)4 components.
C)7 components.
D)as many components as there are cells in the design.
Q3) A repeated measures analysis of variance is to an ordinary analysis of variance as a t test for dependent means is to
A)a t test for a single sample.
B)a t test for independent means.
C)a two-way analysis of variance.
D)any factorial analysis of variance.
Q4) Advanced topic: N<sub>Cells</sub> - df<sub>Columns</sub> - df<sub>Rows</sub> - 1 = __________.
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Chapter 11: Correlation
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Sample Questions
Q1) Under what conditions can the possibility that Y causes X be ruled out when two variables,X and Y,are strongly correlated?
A)if the correlation is positive
B)if the correlation is negative
C)if X occurs before Y
D)if Y occurs before X
Q2) When figuring a correlation coefficient,scores are first converted to Z scores because A)the standard deviation is the same for every variable.
B)scores can never be more than 2 standard deviations from the mean.
C)all scores are on a consistent 0 to 1 scale.
D)high scores are positive numbers,and low scores are negative numbers.
Q3) Illusory correlations are caused by
A)any mistake that occurs during the figuring of the correlation coefficient.
B)comparing correlations without converting them to proportionate reductions in error.
C)incorrect theories based on prejudices.
D)the combined effects of restriction in range and curvilinearity.
Q4) In a scatter diagram,the variable thought to be the cause or the predictor goes on the __________ axis.
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Page 13
Chapter 12: Prediction
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Q1) In making a prediction using the linear prediction rule, = 7 + (1.28)(X),the "1.28" is the __________.(Give a name,not a symbol.)
Q2) When drawing a regression line for a linear prediction rule,the minimum number of predicted points on a graph that must be located is A)1.
B)2.
C)1 if it is a positively sloped line; 2 if it is a negatively sloped line. D)2 if it is a positively sloped line; 1 if it is a negatively sloped line.
Q3) The best linear prediction rule will have the smallest sum of __________.(Give a name,not a symbol.)
Q4) Researchers recommend comparing __________ to __________ when determining a predictor's relative importance.(Give symbols.)
Q5) One assumption of multiple regression is that error scores are __________.
Q6) The regression coefficient for the best linear prediction rule is __________.(Give a number.)
Q7) To find the regression coefficient for the best linear prediction rule,divide __________ by __________.(Give numbers.)
Q8) Prediction is also called __________.
Page 14
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Chapter 13: Chi-Square Tests
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Q1) One difference between a chi-square test and an analysis of variance is that in a chi-square test,all variables are __________.
Q2) The formula for the chi-squared statistic is
A) [(O-E)<sup>2</sup>/E]
B)[ (O-E)<sup>2</sup>]/E
C)O/[ (O-E)<sup>2</sup>]
D)E/[ (O-E)<sup>2</sup>]
Q3) In a chi-square test for goodness of fit,the null hypothesis is that
A)the number of people in one category is no greater than the number of people in the other.
B)the variances of the populations of categories are the same.
C)the proportion of people over categories breaks down the same for the two populations.
D)the means of the two populations of categories are the same.
Q4) Of the total sample,the percentage of agnostics,atheists,and others was
A)(12 + 13 + 22)/100 = 47%.
B)(4 + 6 + 18)/100 = 28%.
C)(8 + 7 + 4)/34 = 56%.
D)(12 + 13 + 22)/66 = 71%.
Q5) Complete the following formula: = __________.(Use symbols.)
Page 15
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Chapter 14: Strategies When Population Distributions Are
Not Normal: Data Transformations and Rank-Order Tests
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Sample Questions
Q1) A common transformation procedure when scores are positively skewed is the A)square-root transformation.
B)squared transformation.
C)exponential transformation.
D)sign-reversal transformation.
Q2) In a square-root transformation,
A)high numbers become lower,and low numbers become higher.
B)moderate numbers remain unchanged,but low numbers become slightly higher.
C)low numbers become much lower,but high numbers remain basically unchanged.
D)moderate numbers become only slightly lower,but high numbers become much lower.
Q3) Because the distribution of rank-order scores is known exactly,rather than being estimated,rank-order tests
A)do not require estimating any population parameters.
B)are used in most actual studies.
C)are almost always preferred over square-root transformations.
D)require drawing additional samples.
Q4) One type of computer-intensive method is a(n)__________.
Page 16
Q5) The null hypothesis in a rank-order test for two groups is that the two populations have the same __________.
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Chapter 15: The General Linear Model and Making Sense of
Advanced Statistical Procedures in Research Articles
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Q1) Many of the major procedures presented in this text are mathematically equivalent because they share the same central logic,a mathematical formula statisticians call the __________.
Q2) If a psychologist is concerned that when people take a test of knowledge-like a vocabulary test-for the second time that their performance is likely to be different because of having taken the test once,the psychologist is assessing __________.
Q3) The formula = a + (b<sub>1</sub>)(X<sub>1</sub>)+ (b<sub>2</sub>)(X<sub>2</sub>)+ (b<sub>3</sub>)(X<sub>3</sub>)is the formula for A)multiple regression.
B)the analysis of variance.
C)bivariate correlation.
D)the t test.
Q4) A technique that uses a path diagram with arrows between variables,but that has some advantages over path analysis is A)partial correlation.
B)multiple regression.
C)factor analysis.
D)structural equation modeling.
Page 17
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