Educational Statistics Study Guide Questions
Course Introduction
Educational Statistics is a foundational course that introduces students to the principles and methods of statistical analysis within educational contexts. The course covers key concepts such as descriptive statistics, probability distributions, sampling methods, hypothesis testing, correlation, and regression analysis, all geared toward the interpretation and evaluation of educational data. Emphasis is placed on understanding and applying statistical techniques to real-world educational research problems, equipping students with the skills to critically analyze data and make informed decisions in educational practice and policy. Through hands-on activities and the use of statistical software, students develop competencies in data collection, analysis, and interpretation relevant to educational settings.
Recommended Textbook
Statistics for the Behavioral Sciences 5th Edition by James Jaccard
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Chapter 1: Introduction and Mathematical Preliminaries
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Sample Questions
Q1) A sample is simply a(n):
A)aggregate of all cases
B)random population
C)subset of the population
D)statistic
Answer: C
Q2) The essential characteristic of random sampling is that every member of the population:
A)is selected for the study
B)is systematically selected
C)has an equal chance of being selected
D)is excluded on random criteria
Answer: C
Q3) Taking measurements on a sample and then,from the observations,inferring something about a population is known as _____:
A)random sampling
B)inferential statistics
C)descriptive statistics
D)inferential parametrics
Answer: B
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Chapter 2: Frequency and Probability Distributions
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Sample Questions
Q1) A frequency distribution is a table that lists _____ on a variable and shows the number of individuals who obtained each _____.
A)scores;value
B)classes;frequencies
C)frequencies;class
D)scores;frequency
Answer: A
Q2) In frequency distributions for qualitative variables,the concepts of cumulative frequencies,cumulative relative frequencies,and cumulative percentages:
A)are still applicable
B)are mathematically different
C)are functionally equivalent
D)are not applicable
Answer: D
Q3) One should always report at least 10 groups in a grouped frequency distribution.
A)True
B)False
Answer: False
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Chapter 4: Percentiles percentile Ranks standard Scores
and the Normal Distribution
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Sample Questions
Q1) The standard deviation of a set of standard scores in a distribution is _____.
A)100
B)50
C)1
D)0
Q2) A negative standard score of -1 means you____________________.
Q3) The proportion of scores occurring between standard scores of 0 and -1 is _____ the proportion of scores occurring between standard scores of 0 and +1.
A)equal to B)less than C)greater than D)less than or equal to
Q4) A set of scores that is positively skewed will become normally distributed after they have been converted to standard scores.
A)True
B)False
Q5) In what sense are percentile ranks and standard scores similar to each other?
Q6) The median is the same as the____________________.
Q7) What is a z score?
5
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Chapter 5: Pearson Correlation and Regression: Descriptive Aspects
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Sample Questions
Q1) Which of the following r values indicates the weakest relationship between two variables?
A).45
B)-.30
C).03
D)-.45
Q2) If grade point average (GPA)and number of hours partying were related according to the following linear model: GPA= 4.00 - .40 Hours,what GPA would you predict if you partied for 8 hours?
A).80
B)2.20
C)1.00
D)3.60
Q3) The slope of a line indicates the number of units variable Y is predicted to change given a one unit change in X.
A)True
B)False
Q4) The absolute magnitude of the standard error of the estimate is not meaningful. A)True B)False
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Chapter 3: Measures of Central Tendency and Variability
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Sample Questions
Q1) The more extreme a score is relative to the other scores in the distribution,the less it will change the value of the mean if it is deleted from the analysis.
A)True
B)False
Q2) In a normal distribution,the _____.
A)mean is usually higher than the mode
B)median is usually lower than the mean
C)mean,median,and mode might be equal
D)mean,median,and mode are always equal
Q3) If the variance of a distribution is 100 the SD is____________________.
Q4) The sum of squares takes into account all of the scores in a data set.
A)True
B)False
Q5) Based on the Method of Presentation section of Chapter 3,the symbol n indicates
A)the sample size in a particular group.
B)the total sample size in the study.
C)the population sample size.
D)the number of groups in the study.
Q6) Kurtosis is determined by the ____________________in the distribution.
Q7) What is the standard deviation?
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Chapter 7: Estimation and Sampling Distributions
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Sample Questions
Q1) The sample variance overestimates (is larger than)the population variance across all possible samples of a given size.
A)True
B)False
Q2) An unbiased estimate of the population variance can be obtained by dividing the sample sum of squares by N - 1.
A)True
B)False
Q3) Given: ì = 3.5,ó = 2.09.Calculate ó for sample size of 16.
A)7.656
B).131
C).5225
D).539
Q4) Irrespective of its specific computation,any sum of squares divided by its associated degrees of freedom is referred to as a mean standard deviation.
A)True
B)False
Q5) What is a sampling distribution of the mean?
Q6) What is an unbiased estimator?
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Chapter 8: Hypothesis Testing: Inferences About a Single Mean
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Sample Questions
Q1) Confidence intervals are calculated around the observed sample mean rather than ì.
A)True
B)False
Q2) Type II errors are made when you _____ H<sub>0</sub> and H<sub>0</sub> is
A)reject;false
B)fail to reject;false
C)accept;true
D)fail to reject;true
Q3) As a rough guide,investigators generally attempt to achieve statistical power in the range of .05 to .95,depending on the nature of the proposition being investigated.
A)True
B)False
Q4) When a researcher obtains a result that is consistent with the null hypothesis,he or she accepts the null hypothesis as being true.
A)True
B)False
Q5) Distinguish between directional and nondirectional tests.
Q6) What is the null hypothesis?
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Chapter 6: Probability
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Sample Questions
Q1) In a horse race,people are allowed to bet on which horses will finish a race in positions 1,2,or 3.If the field contained 7 horses,how many ways can 3 horses finish in the three positions?
A)7!
B)210
C)35
D)3
Q2) In factorial notation,the expression 0! equals 1.
A)True
B)False
Q3) The probability of drawing a red card from a deck of normal playing cards is .5 (half red,half black).A magician draws 12 cards from the deck.What is the probability that the magician draws 8 red cards?
A).0002
B).042
C).121
D).696
Q4) When two events are related,this means that one causes the other.
A)True
B)False
Page 10
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Chapter 9: Principles of Research Design and Statistical
Preliminaries for Analyzing Bivariate Relationships
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Sample Questions
Q1) Once subjects have been selected they should be ____________________to groups.
Q2) The experimenter will manipulate the_____.
A)independent variable
B)dependent variable
C)the placebo
D)Both the independent and dependent variables
Q3) Statisticians can determine the effects of violating assumptions by using _____ or performing _____.
A)mathematical logic;Monte Carlo studies
B)observational designs;experimental designs
C)Monte Carlo studies;one-sample t tests
D)violation estimates;factorial designs
Q4) Compare and contrast between- versus within-subjects variables and designs.
Q5) In a(n)_____design,an individual in one condition is paired with a different individual in another condition who has similar characteristics.
A)independent groups design
B)correlated groups design
C)matched-subjects design
D)repeated measures design
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Chapter 10: Independent Groups T -Test
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Sample Questions
Q1) The nature of the relationship is determined by_____
A)examining the sample means
B)examining the t-value
C)examining the confidence intervals
D)All of these
Q2) Many properties of a sampling distribution of the mean do not hold for a sampling distribution of the difference between two independent means.
A)True
B)False
Q3) Which of the following assumptions applies to the independent groups t test?
A)The samples have been randomly drawn from their respective populations.
B)The scores in each population are normally distributed.
C)The variances of both populations are homogeneous.
D)All of these
Q4) For a nondirectional alternative hypothesis it is written as H<sub>1</sub>: ì<sub>1</sub> ? ì<sub>2.</sub>
A)True
B)False
Q5) Unexplained error or variance may be due to_________.
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Chapter 11: Correlated Groups T-Test
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Sample Questions
Q1) Which of the following statistical tests should be used to analyze the relationship between the independent and dependent variables when the independent variable is within-subjects?
A)one-sample z test
B)independent-groups t test
C)correlated-groups t test
D)Pearson correlation
Q2) The correlated-groups t test is robust to violations of the normality assumption if
A)the data is measured on a quantitative scale
B)there are homogeneous variances in the population
C)the population of difference scores is large
D)the sample size is relatively large
Q3) The 95% confidence interval for the mean differences is reported following _____.
A)one-sample z test
B)independent-groups t test
C)correlated-groups t test
D)Pearson correlation
E)both b & c
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Chapter 13: One-Way Repeated Measures Analysis of Variance
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Sample Questions
Q1) How is the total variability in the dependent variable partitioned in a repeated measures design?
Q2) The function of the sum of squares subjects is to remove variability due to _____ from the dependent variable so that a more sensitive test of the relationship between the independent and dependent variables can be performed.
A)treatment effects
B)individual differences
C)group differences
D)none of these
Q3) Since the value of F required to reject the null hypothesis becomes more extreme as the degrees of freedom become smaller,repeated measures analysis of variance might actually be less powerful than between-subjects analysis of variance when individual differences have only a minimal influence on the dependent variable.
A)True
B)False
Q4) Compare the different sums of squares for a repeated measures design with the sums of squares for a between-subjects design.
Q5) What does the mean square subjects contribute to the F test?
Page 14
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Chapter 14: Pearson Correlation and Regression: Inferential Aspects
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Sample Questions
Q1) Which of the following is NOT one of the assumptions of the Pearson correlation?
A)The sample is independently and randomly selected from the population.
B)The variances of the Y scores are equal at every value of X in the population.
C)The variables X and Y are qualitative in nature.
D)The joint distribution (or scatterplot)of X and Y represent a bivariate normal distribution.
Q2) The mean of a sampling distribution of r is approximately equal to r.
A)True
B)False
Q3) A psychologist believes that arousal level is related to quality of performance.He obtains measures of arousal and performance on a group of 20 people,and finds a correlation coefficient of .430.If the alpha level is .05,nondirectional test,how would this result be reported in a psychological journal?
A)r(18)= .430,p > .05
B)r(19)= .430,p > .05
C)r(20)= .430,p < .05
D)r(20)= .430,p > .05
Q4) How is the nature of the relationship between two variables evaluated in a correlational analysis?
Page 15
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Chapter 15: Chi-Square Test
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Sample Questions
Q1) If the researcher suspects that the strength of the relationship between two variables in the population is .50 as indexed by Cramer's statistic,what sample size should she use in a study involving a 3 x 3 contingency table and an alpha level of .05 to achieve a power of .70?
A)7
B)19
C)22
D)28
Q2) When a sample is selected so that it consists of a specified number for one of the two variables,the marginal frequency for that variable is ____________________.
Q3) Summarize the steps involved in computing expected frequencies.
Q4) Each unique combination of _____ in a contingency table is referred to as a(n)_____.
A)variables;cell
B)cells;variable
C)rows;cell
D)cells;expected frequency
Q5) The shape of the chi-square distribution depends on how many ____________________ are associated with it.
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Chapter 16: Nonparametric Statistics
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Sample Questions
Q1) In all the nonparametric tests presented in the chapter,scores must be in the form of
Q2) The strength of the relationship for Spearman correlation is indicated by the sign of the correlation coefficient and the nature of the relationship is indicated by the magnitude of the correlation coefficient.
A)True
B)False
Q3) The nonparametric tests presented in the text are based on what type of scores?
A)rank scores
B)z scores
C)t scores
D)F scores
Q4) The Wilcoxon rank sum test is a nonparametric alternative to which parametric test?
A)independent groups t test
B)correlated groups t test
C)one-way between-subjects analysis of variance
D)one-way repeated measures analysis of variance
E)Pearson correlation
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Chapter 17: Two-Way Between-Subjects Analysis of Variance
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Sample Questions
Q1) In two-way between-subjects analysis of variance,the relevant mean squares are obtained by dividing the sum of squares for each source of between-group variability by its degrees of freedom.
A)True
B)False
Q2) In the two-way ANOVA,which of the following sources of variability is NOT a component of the sum of squares between?
A)within group variability
B)variability due to the first independent variable
C)variability due to the second independent variable
D)variability due to the interaction effect
Q3) Discuss the analysis of interaction effects in terms of the nature of the relationship in two-way analysis of variance.
Q4) When dealing with sample data,the existence of a given population main effect or interaction can be affirmed only by a:
A)visual inspection of sample means
B)visual inspection of slopes
C)significant statistical test
Page 18
Q5) Under what conditions is the two-way between-subjects analysis of variance used?
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Chapter 18: Overview and Extension: Statistical Tests for More Complex Designs
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Sample Questions
Q1) Although the joint influence of two between-subjects independent variables on a dependent variable can be studied using two-way between-subjects analysis of variance,it is not possible to study the joint influence of two within-subjects independent variables.
A)True
B)False
Q2) When both of the variables under study are qualitative and between-subjects in nature,the appropriate method of data analysis is the A)independent groups t test.
B)one-way between-subjects analysis of variance.
C)two-way between-subjects analysis of variance.
D)chi square test.
Q3) Dr.Johnson sets his alpha level at .05 and uses a directional test,his degrees of freedom is 60 what is his critical t?
A)2.00
B)2.021
C)1.671
D)1.684
E)none of these
19
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