Statistical Methods for the Behavioral Sciences
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Course Introduction
This course provides an in-depth introduction to the statistical techniques commonly used in behavioral science research, including psychology, sociology, and related fields. Students will explore fundamental concepts such as descriptive statistics, probability, hypothesis testing, correlation, regression, and analysis of variance (ANOVA). Emphasis is placed on applying statistical reasoning to real behavioral data, interpreting results, and understanding the assumptions underlying each technique. Through lectures, hands-on exercises, and data analysis projects, students will develop the skills needed to critically evaluate research findings and conduct their own statistical analyses using statistical software.
Recommended Textbook
Social Statistics for a Diverse Society 8th Edition by Chava Frankfort Nachmias
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Chapter 1: The What and the Why of Statistics
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Q1) A(n)______ is a property of people or objects that can take two or more values.
A)unit of analysis
B)variable
C)level of measurement
D)theory
Answer: B
Q2) Imagine you are a researcher who is interested in knowing whether or not a person was married in their twenties.What would be the level of measurement for this variable?
Answer: Nominal
Q3) Identify the independent variable,the dependent variable,and the unit of analysis in the following hypothesis: Documented immigrants in the United States are less likely than undocumented immigrants to use social welfare programs.
Answer: Independent variable = migration type (legal/illegal);dependent variable = use of social services;and unit of analysis = individuals
Q4) Statistical procedure can be divided into two major categories: ______ statistics and ______ statistics.
Answer: descriptive;inferential
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3
Chapter 2: The Organization and Graphic Presentation of Data
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Q1) Which graphic device would be most appropriate to display information about "The sex ratio at birth - that is,the ratio to the number of males to the number of females - is 1.05 in the United States"?
Answer: A bar graph or pie chart
Q2) Imagine one of your colleagues is constructing a pie chart to graph results of the survey question "Which state do you live in?" What should be your first response upon reviewing their work?
A)To note whether the "slices" of the pie sum to 100%
B)To suggest that he or she has in fact used an inappropriate graphic device
C)To ensure that the frequencies at each time point sum to N
D)To check whether the bars representing the categories are contiguous as they should be
Answer: A
Q3) What is the formula for a percentage?
A)p = f/N
B)p = N/f
C)p = (f/N)100
D)p = (N/f)100
Answer: C
Page 4
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Chapter 3: Measures of Central Tendency
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Q1) Which of the following statements are true with respect to the data: 71,73,71,65,70?
A)The mode,median,and mean are the same.
B)The median and mean are both 70.
C)The mode and mean are both 71.
D)The mode is 71.
Answer: B,D
Q2) Numbers that describe what is average or typical of a distribution are referred to as A)frequencies.
B)bar charts.
C)measures of central tendency.
D)measures of variability.
Answer: C
Q3) When the mean is lower than the median (or positioned to the left of the median),the distribution is positively skewed.
A)True
B)False
Answer: False
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Chapter 4: Measures of Variability
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Q1) Calculate the value of the standard deviation for the following sub-sample: 24,27,35,31,21,22,28,18,25,24,36,20.
Q2) Calculate the range for the following sub-sample: 24,27,35,31,21,22,28,18,25,24,36,20.
Q3) Consider the following hypothetical scores: 21,25,37,38,39,42,44,45.Which value is closest to the variance?
A)9
B)19
C)24
D)77
Q4) The sum of the deviations of scores from the mean is always positive.
A)True
B)False
Q5) In a distribution where all the scores are identical,
A)the standard deviation is zero.
B)distribution is skewed.
C)the variance is zero.
D)the mean,median,and mode are all the same.
Q6) What is the most basic consideration in choosing a measure of variability?
Q7) Calculate the range for the following sub-sample: 2,7,4,4,1,2,2,3,1,2,4,5.
Page 6
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Chapter 5: The Normal Distribution
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Q1) What percentage of the area under the normal curve falls between ±1 standard deviations?
A)99.72
B)95.46
C)68.26
D)20.00
Q2) The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Suppose that a person experienced their first marriage at age 23.If the area beyond the Z-score associated with age 23 is 0.24,what proportion of respondents experienced their first marriage after age 23?
Q3) The annual salaries of employees in a large company are normally distributed with a mean of $50,000 and a standard deviation of $20,000.What percent of people earn between $45,000 and $65,000?
Q4) For a Z score of zero,what is the proportion of area between the mean and the Z score?
A)0.0
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Chapter 6: Sampling and Sampling Distributions
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Q1) If the mean and standard deviation of a population are 436 and 103 respectively,what is the standard error of the mean for a sample of size 8?
Q2) Probability
A)can be expressed as a proportion.
B)can be expressed as a percentage.
C)can take a maximum value of 1.
D)can take a minimum value of 1.
Q3) A group that includes all the cases in which a researcher is interested is referred to as a
A)sample.
B)population.
C)case.
D)dataset.
Q4) A theoretical probability distribution of all possible sample values for the statistics in which we are interested in is referred to as a A)sample.
B)sampling distribution.
C)population.
D)sampling frequency.
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Chapter 7: Estimation
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Q1) Margin of error
A)refers to confidence intervals.
B)is equal to standard error of the mean.
C)is equal to standard error of the proportion.
D)is the radius of confidence intervals.
Q2) Which of the following is true about the relationship between the population mean and the mean of the sampling distribution?
A)population mean = mean of the sampling distribution
B)population mean mean of the sampling distribution
C)population mean < mean of the sampling distribution
D)population mean > mean of the sampling distribution
Q3) A sample of 150 U.S.adults is composed of 100 women and 50 men.Estimate the standard error of the proportions for the male population.
Q4) A sample of 150 U.S.adults is composed of 100 women and 50 men.Estimate the confidence interval for the male population with 99% confidence.
Q5) In a survey sample of 1000 respondents,the mean annual salary is $32,245,with a standard deviation of 4021.54.Calculate a 99% confidence interval for these data.
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Chapter 8: Testing Hypotheses
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Q1) The 40-hour work week is generally considered as a standard in American society today.Using data from the 2010 General Social Survey,you wish to determine whether the mean number of hours worked per week by men in the sample differs from the 40-hour standard.State the null and research hypotheses for this single-sample t test.
Q2) Which of the following is the null hypothesis for a two sample t test?
A)µ µ
B)µ < µ
C)µ > µ
D)µ = µ
Q3) In a simple random sample of 120 women and 150 men from a population of 150,000,25% of the women and 37% of the men are smokers.Suppose you are interested in comparing the proportion of smokers by sex,compute the Z statistic.
Q4) The probability associated with rejecting the null hypothesis when it is true is called
A)Type I error.
B)Type II error.
C)alpha.
D)lambda.
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Chapter 9: Bivariate Tables
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Q1) An additional variable considered in a bivariate relationship,usually with the aim of controlling for the effects of this variable,is referred to as a(n)______ variable.
A)independent
B)dependent
C)control
D)elaboration
Q2) For which pair of variables is it impossible to determine the direction of the relationship?
A)Educational level and attendance of religious services
B)Sex and religious preference
C)Socio-economic status and calorie consumption
D)Occupational prestige and grocery budget
Q3) What are the limitations of elaborations?
Q4) A conditional relationship is a relationship in which the control variable's effect on the independent variable is conditional on its interaction with the dependent variable.
A)True
B)False
Q5) Define an intervening relationship.
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Chapter 10: The Chi-Square Test and Measures of Association
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Q1) The sampling distribution of chi-square sampling can be best described as A)a square.
B)negatively skewed.
C)flat.
D)a family of distributions.
Q2) In order to determine the statistical significance of the chi-square statistic,you need to know the number of cells in the table for which the expected frequencies are free to vary given that the marginal totals are already set.What is the statistical name for this quantity and how is it calculated?
Q3) Suppose you obtain a chi-square statistic of 67.81.Are your results statistically significant if the critical value obtained from the distribution of chi-square is 3.84 with an alpha level of .05?
Q4) The number of degrees of freedom for a chi-square test is calculated as A)n-1.
B)n+1.
C)(rows-1)(columns+1).
D)(rows-1)(columns-1).
Q5) Why is it sometimes important to condition one's result by another variable?
Q6) What interpretation do we get if Kendall's Tau-b reaches a value of 1?
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Chapter 11: Analysis of Variance
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Q1) The correlation ratio or eta square
A)allows the researcher to make a statement about the strength of the relationship. B)represents the proportions of variance that is explained by the independent variables.
C)is the ratio of SST to SSB.
D)ranges from 0.0 to ±1.
Q2) The F statistic is the ratio of between-group variance to within-group variance.
A)True B)False
Q3) What does the within-group sum of squares measure?
A)The sum of the squared deviations between each group mean and every other group mean
B)The sum of the squared deviations between each group mean and the mean across all groups
C)The sum of the squared deviations between each individual observation and its group mean
D)The sum of the squared deviations between each individual observation and the mean across all groups
Q4) What can you say about the relationship if eta square is 0.85?
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Chapter 12: Regression and Correlation
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Q1) The residual is the difference between the predicted \( \hat{Y} \) and the observed Y,i.e. \( e=\hat{Y}-Y \) .
A)True
B)False
Q2) A scatter diagram is a visual method used to display a relationship between two ______ variables.
A)nominal
B)unrelated
C)interval-ratio
D)ordinal
Q3) A bivariate regression assumes that the variables have a linear or straight-line relationship.
A)True
B)False
Q4) Which type of relationship occurs when all observations fall along a straight line?
A)Deterministic linear relationship
B)Scatter plot relationship
C)Vertical relationship
D)Linear relationship
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