Quantitative Methods in Psychology
Midterm Exam
Course Introduction
Quantitative Methods in Psychology introduces students to the foundational principles and techniques used to collect, analyze, and interpret numerical data within psychological research. The course covers topics such as descriptive statistics, probability theory, hypothesis testing, correlation, regression analysis, analysis of variance (ANOVA), and basic statistical inference. Emphasis is placed on understanding how quantitative methods inform the scientific study of behavior and mental processes, the importance of data integrity, and the use of statistical software for analyzing psychological data. By the end of the course, students will be able to critically evaluate research findings, design studies using sound quantitative methods, and effectively communicate statistical results relevant to psychology.
Recommended Textbook
Essentials of Statistics for The Behavioral Sciences 9th Edition by Gravetter
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Page 2
Chapter 1: Introduction to Statistics
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Sample Questions
Q1) What scale of measurement is being used when a teacher measures the number of correct answers on a quiz for each student?
A)Nominal
B)Ordinal
C)Interval
D)Ratio
Answer: D
Q2) Calculate each value requested for the following set of scores.Scores: 3,4,2,6
a. X - 2
b. (X - 2)
c. (X - 2)²
Answer: a.13
b.7
c.21
Q3) A researcher is interested in the average income for registered voters in the United States.The entire group of registered voters is an example of a population.
A)True
B)False
Answer: True
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Page 3
Chapter 2: Frequency Distributions
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Sample Questions
Q1) A histogram is constructed so that adjacent bars touch.
A)True
B)False
Answer: True
Q2) For the following distribution,what percentage of the individuals have scores of X = 1?
\[\begin{array} { l l }
X & \mathrm { f } \\
\hline 5 & 2 \\
4 & 8 \\
3 & 5 \\
2 & 3 \\
1 & 2
\end{array}\]
A)2%
B)5%
C)10%
D)20%
Answer: C
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Page 4
Chapter 3: Central Tendency
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Q1) For a severely skewed distribution,the median often provides a better measure of central tendency than the mean.
A)True
B)False
Answer: True
Q2) For the following sample of scores,1,1,2,2,2,2,4,
a.find the mean, median, and mode.
b.if a new individual with a score of X = 2 is added to the sample, what happens to the values for the mean, the median, and the mode?
c.if the score X = 4 in the original distribution is changed to X = 11, what happens to the values for the mean, the median, and the mode?
Answer: a.The mean,median,and mode are all equal to 2.
b.Adding a score of X = 2 does not change the mean,the median,or the mode.
c.Changing X = 4 to X = 11 causes the mean to change to M = 3.The median and the mode are still equal to 2.
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Chapter 4: Variability
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Q1) In a population of N = 10 scores,the smallest score is X = 8 and the largest is X = 20.What is the range for this population?
A)8
B)10
C)12-13
D)20
Q2) For a population with µ = 70 and = 5,about 95% of the individuals will have scores between X = 65 and X = 75.
A)True
B)False
Q3) For the following scores,which of the following actions will increase the range? Scores: 3,7,10,15
A)Subtract 3 points from the score X = 3
B)Subtract 3 points from the score X = 7
C)Subtract 3 points from the score X = 10
D)Subtract 3 points from the score X = 15
Q4) The range and the standard deviation are both measures of distance.
A)True
B)False
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Chapter 5: z-Scores: Location of Scores and Standardized
Distributions
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Q1) For a population with = 34,a score of X = 31 corresponds to z = -1.00.The standard deviation for the population is = 6.
A)True
B)False
Q2) Last week Sarah had exams in math and in Spanish.On the math exam,the mean was µ = 40 with = 5,and Sarah had a score of X = 45.On the Spanish exam,the mean was µ = 60 with = 8,and Sarah had a score of X = 68.For which class should Sara expect the better grade?
A)Math
B)Spanish
C)The grades should be the same because the two exam scores are in the same location.
D)There is not enough information to determine which is the better grade.
Q3) A population of scores has µ = 80.In this population,a score of X = 86 corresponds to z = +2.00.What is the population standard deviation?
A)2
B)3
C)6
D)12
Page 7
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Chapter 6: Probability
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Q1) A normal distribution has a mean of µ = 100 with = 20.If one score is randomly selected from this distribution,what is the probability that the score will have a value between X = 90 and X = 120?
A)0.1498
B)0.4672
C)0.5328
D)0.2996
Q2) A normal distribution has = 20 and = 4.What is the probability of randomly selecting a score greater than 25 from this distribution?
A)0.3944
B)0.1056
C)0.8944
D)0.7888
Q3) What proportion of a normal distribution is located in the tail beyond z = 1.50?
A)0.9332
B)0.0668
C)0.4332
D)0.1336
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8
Chapter 7: Probability and Samples: The Distribution of Sample Means
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Q1) A sample is selected from a population with a mean of µ = 40.If the sample mean is M = 45,which of the following combinations would make the sample mean a good,representative value for the population?
A)A small sample and a small population standard deviation
B)A small sample and a large population standard deviation
C)A large sample and a small population standard deviation
D)A large sample and a large population standard deviation
Q2) A random sample of n = 6 scores is selected from a population.Which of the following distributions will definitely be normal?
A)The scores in the sample will definitely form a normal distribution.
B)The scores in the population will definitely form a normal distribution.
C)The distribution of sample means will definitely form a normal distribution.
D)None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.
Q3) A sample of n = 16 scores is selected from a population with = 70 and = 8.It is very unlikely that the sample mean will be greater than 78.
A)True
B)False
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Chapter 8: Introduction to Hypothesis Testing
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Q1) You complete a hypothesis test using = .05,and based on the evidence from the sample,your decision is to reject the null hypothesis.Which of the following is true?
A)You have made a Type I error.
B)You have made a Type II error.
C)You might have made a Type I error, but the probability is less than 5%.
D)You have made the correct decision.
Q2) A researcher administers a treatment to a sample of n = 16 selected from a population with µ = 40 and = 8.If the sample mean after treatment is M = 42,then Cohen's d = 1.00.
A)True
B)False
Q3) What is the consequence of a Type II error?
A)Concluding that a treatment has an effect when it really does
B)Concluding that a treatment has no effect when it really has no effect
C)Concluding that a treatment has no effect when it really does
D)Concluding that a treatment has an effect when it really has no effect
Q4) A researcher selects a sample of n = 25 from a normal population with µ = 40 and = 10.If the treatment is expected to increase scores by 3 points,what is the power of a two-tailed hypothesis test using = .05?
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Chapter 9: Introduction to the t Statistic
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Q1) For a one-tailed test with = .05 and a sample of n = 9,the critical value for the t statistic is t = 1.860.
A)True
B)False
Q2) Which of the following samples will have the smallest value for the estimated standard error?
A)n = 4 with s<sup>2</sup> = 16
B)n = 4 with s<sup>2</sup> = 64
C)n = 16 with s<sup>2</sup> = 16
D)n = 16 with s<sup>2</sup> = 64
Q3) When n is small (less than 30),how does the shape of the t distribution compare to the normal distribution?
A)It is almost perfectly normal.
B)It is flatter and more spread out than the normal distribution.
C)It is taller and narrower than the normal distribution.
D)There is no consistent relationship between the t distribution and the normal distribution.
Q4) A sample of n = 16 scores has a mean of M = 58 with SS = 960.Use the sample to construct the 90% confidence interval for µ.
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Chapter 10: The t Test for Two Independent Samples
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Q1) If the two samples are the same size,then the pooled variance will equal the average of the two sample variances.
A)True
B)False
Q2) Which of the following research situations would be most likely to use an independent-measures design?
A)Examine the development of vocabulary as a group of children mature from age 2 to age 3.
B)Examine the long-term effectiveness of a stop-smoking treatment by interviewing subjects 2 months and 6 months after the treatment ends.
C)Compare the mathematics skills for 9th-grade boys versus 9th-grade girls.
D)Compare the blood-pressure readings before medication and after medication for a group a patients with high blood pressure.
Q3) The results from an independent-measures t hypothesis test are reported as "t(24)= 3.85, p < .01,two tailed." The research study for this test used a total of 25 subjects.
A)True
B)False
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Chapter 11: The t Test for Two Related Samples
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Q1) In general,if the variance of the difference scores increases,what will happen to the value of the t statistic?
A)It will increase in magnitude (move farther toward the tail of the distribution).
B)It will decrease in magnitude (move toward 0 at the center of the distribution).
C)It will stay the same; the t statistic is not affected by the variance of the difference scores.
D)It may increase or may decrease; there is no consistent relationship between variance and the size of the t statistic.
Q2) For a repeated-measures study,a small variance for the difference scores indicates that the treatment effect is consistent across participants.
A)True
B)False
Q3) A repeated-measures study with a sample of n = 16 participants produces a repeated-measures t = 2.00.If effect size is measured using r²,then r² = 4/20.
A)True
B)False
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Chapter 12: Introduction to Analysis of Variance
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Q1) A researcher reports an F-ratio with df = 2,18 from an independent-measures research study.Based on the df values,how many treatments were compared in the study,and what was the total number of subjects participating in the study?
A)2 treatments and 19 subjects
B)2 treatments and 20 subjects
C)3 treatments and 21 subjects
D)3 treatments and 22 subjects
Q2) For an independent-measures ANOVA comparing four treatment conditions,df between = 3.
A)True
B)False
Q3) For an analysis of variance comparing four treatment \(M S _ { \text {between } }\) = 12.What is the value of \(S S _ { \text {between } }\) A)3
Q4) Describe the circumstances in which post hoc tests are used,and explain why these tests are necessary.
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Chapter 13: Repeated-Measures and Two-Factor Analysis of Variance
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Q1) How many separate groups of participants would be needed for an independent-measures,two-factor study with 3 levels of factor A and 4 levels of factor B?
A)3
B)4
C)7
D)12
Q2) For a repeated-measures design,the differences between treatments may be caused by a treatment effect or by sampling error (random factors),but they cannot be caused by individual differences.
A)True
B)False
Q3) A repeated-measures study has n = 8 participants and k = 3 treatments.For this study,df = 21.
A)True
B)False
Q4) Obtaining a significant interaction means that both factors A and B have significant main effects.
A)True
B)False
Page 15
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Chapter 14: Correlation and Regression
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Sample Questions
Q1) What is the value of SP for the following set of data? \[\begin{array} { l l }
\mathrm { X } & \mathrm { Y } \\
\hline 1 & 4 \\
2 & 4 \\
9 & 1
\end{array}\]
A)5
B)-5
C)15
D)-15
Q2) A set of n = 25 pairs of scores (X and Y values)has a Pearson correlation of r = 0.80.How much of the variance for the Y scores is predicted by its relationship with X?
A)0.36 or 36%
B)0.20 or 20%
C)0.80 or 80%
D)0.64 or 64%
Q3) Compute the Pearson correlation for the following data.
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16
Chapter 15: The Chi-Square Statistic: Tests for Goodness of Fit
and Independence
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Q1) A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories,and a chi-square test for independence is used to examine the distribution of individuals in a 2×3 matrix of categories.Which test has the larger value for df?
A)The test for goodness of fit
B)The test for independence
C)Both tests have the same df.
D)The df value depends on the sizes of the samples that are used.
Q2) What values are specified by the null hypothesis for a chi-square test?
A)Frequencies for a sample
B)Frequencies for a population
C)Proportions for a sample
D)Proportions for a population
Q3) A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 2,what can you conclude about the two variables?
A)One variable consists of 2 categories and the other consists of 3 categories.
B)One variable consists of 2 categories and the other consists of 4 categories.
C)Both variables consist of 2 categories.
D)Both variables consist of 3 categories.
Page 17
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