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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

Four groups have the following means on the covariate: 35, 42, 28, 65.What is the grand mean?(a) 43.5(b) 42.5(c) 56.7 (d) None of the above
You can perform ANCOVA on:(a) Two groups(b) Three groups(c) Four groups(d) All of the above
When carrying out a pretest–posttest study, researchers often wish to:(a) Partial out the effect of the dependent variable(b) Partial out the effect of the pretest(c) Reduce the correlation between
Which is the covariate?(a) Scores on the memory test(b) The amounts of alcohol(c) IQ(d) None of the above
His analysis would show:(a) Differences between groups on the memory test, partialling out the effects of IQ(b) Differences on IQ, partialling out the effects of IQ(c) Differences on IQ, partialling
The independent variable is:(a) Reaction time(b) Group(c) Age(d) None of the above
The covariate is:(a) Reaction time(b) Group(c) Age(d) None of the above
The dependent variable is:(a) Reaction time(b) Group(c) Age(d) None of the above
Using difference scores in a pretest–posttest design does not partial out the effect of the pretest for the following reason:(a) The pretest scores are not normally correlated with the posttest
The highest level of verbal ability is shown by:(a) Group 1(b) Group 2(c) Group 3(d) They are all identical
Which is the most appropriate statement? The differences between the groups are:(a) Likely to have arisen by sampling error alone F(1,65) = 150.46, p < 0.001(b) Likely to have arisen by sampling
The effect size for the differences between the groups is approximately:(a) 2%(b) 12%(c) 21%(d) 70%
The strongest difference between the groups is between:(a) 1 + 2 versus 3(b) 2 + 3 versus 1(c) 1 + 3 versus 2(d) They are all identical
The group with the widest confidence interval around the mean level of verbal ability is:(a) Group 1(b) Group 2(c) Group 3(d) They are all identical
In order to name factors that have been extracted, researchers look at:(a) The rotated factor loadings(b) The unrotated factor loadings(c) The table of eigenvalues(d) None of the above
The differences between factor analysis and principal components analysis are relatively unimportant when the data set is:(a) Large and the participant numbers are high(b) Large and the participant
A factor is thought of as an underlying latent variable:(a) That is influenced by observed variables(b) That is unexplained by unobserved variables(c) Along which individuals differ(d) Along which
Look at the following diagram.Theses variables are:(a) Perfectly related to each other (b) Totally unrelated to each other (c) Share a moderate correlation with each other (d) None of the above
A vector is:(a) A curved line with an indefinite length(b) A straight line with an indefinite length(c) A straight line with a definite length(d) A curved line with a definite length
Factor analysis deals with:(a) Patterns of correlations (c) Frequency counts(b) Patterns of mean values (d) None of the above
Factor analysis requires that variables:(a) Are not related to each other(b) Are related to each other(c) Have only a weak relationship with each other(d) Are measured in the same units
Using the correlational matrix to perform factor analysis rather than the variance–covariance matrix ensures that the data:(a) Will be statistically significant (c) Are unstandardised(b) Are
The decision on how many factors to keep is decided on:(a) Statistical criteria (c) Both (a) and (b)(b) Theoretical criteria (d) Neither (a) nor (b)
The original unrotated matrix is usually rotated so that:(a) The factors are more significant (c) Interpretation is easier(b) The mathematical calculations are easier (d) All of these
A scree plot is a number of:(a) Variables plotted against variance accounted for(b) Variables plotted against factor loadings(c) Factors plotted against correlation coefficients(d) None of the above
It is possible to extract:(a) As many factors as variables(b) More factors than variables(c) More variables than factors(d) None of the above
How many components have an eigenvalue above 1?(a) 3(b) 4(c) 5(d) 6
If a three-factor solution is retained, approximately how much variance has been accounted for?(a) 43%(b) 35%(c) 24%(d) 10%
How many variables were in this analysis?(a) 3(b) 10(c) 22(d) Impossible to tell
What is the minimum number of participants recommended for a factor analysis?(a) 50(b) 70(c) 100(d) 500
Which factor represents ‘risk seeking’?(a) Factor 1 (c) Factor 3(b) Factor 2 (d) Factor 4
Which factor represents ‘non-verbal orientation’?(a) Factor 1 (c) Factor 3(b) Factor 2 (d) Factor 4
On Factor 2, only one of the items is positive. This is because:(a) The authors have made a mistake(b) The positive item is coded in the opposite way to the other two items(c) The three items are
Only the most ‘significant’ loadings are shown in this table. This is because it is customary to blank out loadings below:(a) 0.4(b) 0.5(c) 0.6(d) 0.7
What is the value of Box’s M?(a) 8.49(b) 58320(c) 0.058(d) 3
What is the value of Wilks’ lambda?(a) 9(b) 0.574(c) 0.742(d) None of the above
What is the most appropriate conclusion to be drawn from the above printout?(a) There is a multivariate difference, not attributable to sampling error, between males and females(b) Writing skills but
Which of the following is true of MANOVA?(a) It analyses multiple IVs only(b) It analyses multiple DVs with one or more IVs(c) It can be used only with categorical data(d) All of the above
Which of the following are multivariate methods of calculating F?(a) Wilks’ lambda(b) Pillai’s trace(c) Hotelling’s trace(d) All of the above
Box’s M test:(a) Is a test of the homogeneity of variance assumption underlying ANOVA(b) Should be ignored at all times(c) Is a test of the homogeneity of variance–covariance matrices(d) Is
If you have correlated DVs in a MANOVA with a two-group IV you should:(a) Cry(b) Conduct t-test analyses of the single DVs(c) Conduct χ2 analyses of the DVs followed by t-tests(d) None of the above
For uncorrelated DVs how do we examine the relative contributions of the individual DVs to the combined DVs when our IV has only two conditions?(a) Conduct separate t-tests and adjust α to keep down
If we had three DVs and found a multivariate difference, what level of α would we set for each t-test to keep the overall α at 5%?(a) 5%(b) 1%(c) 1.67%(d) 3.33%
Which of the following are true of MANOVA?(a) It forms a linear combination of the IVs(b) It forms a linear combination of the DVs(c) It is an extension of χ2(d) It correlates the IVs with all of
The assumption of multivariate normality means that:(a) Only the DVs should be normally distributed(b) All DVs and all IVs should be normally distributed(c) All DVs and all possible linear
Which of the following are linear combinations?(a) A + B + C + D(b) b1x1 + b2x2 + b3x3 . . . + a(c) The Lottery numbers(d) Both (a) and (b) above
Which of the following are assumptions underlying the use of multivariate statistics?(a) Homogeneity of variance–covariance matrices(b) That we have equal sample sizes(c) That we have nominal-level
Which part of the MANOVA printout gives us information about differences between the conditions of the IVs in terms of the linear combination of the DVs?(a) The Box’s M tests(b) The univariate
If you have correlated DVs, which of the following are applicable?(a) You should use t-tests to examine the contribution of the individual DVs to the linear combination of the DVs(b) You should not
What are the DVs in this study?(a) Condition and intercept (c) Greenhouse and Geisser(b) Anxiety and depression (d) None of the above
How many conditions are there in the IV?(a) 1 (b) 2 (c) 3 (d) 4
Is there a multivariate difference between the conditions of the IV?(a) Yes(b) No(c) Can’t tell from the above printout(d) Yes but none of the DVs individually contribute significantly to the
Which of the following would you report in a write-up?(a) Pillai’s trace = 0.497(b) Wilks’ lambda = 0.503(c) Hotelling’s trace = 0.989(d) Roy’s largest root = 0.989
Are there any univariate differences present?(a) Yes, for anxiety only(b) Yes, for depression only(c) Yes, for anxiety and depression(d) There are no univariate differences present
The Wilcoxon matched pairs signed-ranks test (the Wilcoxon) is appropriate for:(a) Within-participants designs(b) Between-participants designs(c) Matched-participants designs(d) Both (a) and (c) above
To assess the difference in scores from two conditions of a between-participants design, with ranked data, you would use:(a) The independent t-test(b) The Wilcoxon(c) Related t-test(d) Mann–Whitney
Look at the following partial printout of a Mann–Whitney U analysis from SPSSFW:The above information suggests that:(a) There will be a statistically significant difference between conditions (b)
The Wilcoxon matched-pairs signed ranks test can be used when:(a) There are two conditions(b) The same participants take part in both conditions(c) There is at least ordinal level data(d) All of the
The Mann–Whitney U involves:(a) The difference in the means for each condition(b) The sum of the ranks for each condition(c) Finding the difference in scores across conditions, then ranking these
A Mann–Whitney test gives the following result:U = 9, p = 0.1726 (2-tailed probability)The researcher, however, made a prediction of the direction of the difference, and therefore needs to know the
If, in a repeated-measures design with two conditions, you have a small number of participants, with skewed, ordinal data, the most appropriate inferential test is:(a) Unrelated t-test(b) Related
If a Wilcoxon test shows that t = 3 with an associated probability of 0.02, this means:(a) Assuming the null hypothesis to be true, a t-value of 3 would occur 2% of the time through sampling
A t-value of 3 has been converted into a z-score of −3.2. This means:(a) The calculations are incorrect(b) There is not likely to be a statistically significant difference between conditions(c)
Which is the most sensible conclusion?(a) There are no significant differences between the three groups, p > 0.05(b) There are significant differences between the groups, p = 0.003(c) There are no
Which group had the highest scores?(a) Group 1(b) Group 2(c) Group 3(d) Cannot tell
How many participants were in the study?(a) 5(b) 10(c) 15(d) 20
Which is the most sensible conclusion?(a) There are differences between the groups, but these stand a 21% chance of being due to sampling error(b) There are differences between the groups, and these
How many participants were in the study?(a) 7(b) 14(c) 21(d) Cannot tell
The participants were measured:(a) At two timepoints(b) At three timepoints(c) At four timepoints(d) Cannot tell
Which is the most appropriate statement? In general terms, the affective measures and pain show a:(a) Weak relationship(b) Moderate relationship(c) Strong relationship(d) Perfect relationship
The strongest relationship is between pain and:(a) Tension(b) Autonomic(c) Fear(d) Punishment
Look at the following text, taken from Daley et al. (2003). They were making comparisons between mothers of children with and without behavioural problems.Mann–Whitney U tests were used . . .
Look at the output below.Which is the most appropriate statement? The relationship between the two ratings is (a) Strong (rho = 0.7, p (b) Strong (rho = 0.6, p (c) Moderate (r = 0.7, p (d) Moderate
Look at the following table. Professor Green predicted that strength would relate positively to motivation. Unfortunately the Professor meant to obtain one-tailed p-values. Professor Green wants you
Statistical Literacy The value zc is a value from the standard normal distribution such that P zc x zc 5 c.
Statistical Literacy The point estimate for the population mean m of an x distribution is x, computed from a random sample of the x distribution.
Statistical Literacy Consider a random sample of size n from an x distribution.For such a sample, the margin of error for estimating m is the magnitude of the difference between x and m.
Statistical Literacy Every random sample of the same size from a given population will produce exactly the same confi dence interval for m.
Statistical Literacy A larger sample size produces a longer confi dence interval for m.
Statistical Literacy If the original x distribution has a relatively small standard deviation, the confi dence interval for m will be relatively short.
Statistical Literacy If the sample mean x of a random sample from an x distribution is relatively small, then the confi dence interval for m will be relatively short.
Statistical Literacy For the same random sample, when the confi dence level c is reduced, the confi dence interval for m becomes shorter.
Critical Thinking Sam computed a 95% confi dence interval for m from a specifi c random sample. His confi dence interval was 10.1 m 12.2. He claims that the probability that m is in this interval is
Critical Thinking Sam computed a 90% confi dence interval for m from a specifi c random sample of size n. He claims that at the 90% confi dence level, his confi dence interval contains m. Is his
Basic Computation: Confi dence Interval Suppose x has a normal distribution with s 5 6.A random sample of size 16 has sample mean 50.(a) Check Requirements Is it appropriate to use a normal
Basic Computation: Confi dence Interval Suppose x has a mound-shaped distribution with s 5 9.A random sample of size 36 has sample mean 20.(a) Check Requirements Is it appropriate to use a normal
Basic Computation: Sample Size Suppose x has a mound-shaped distribution with s 5 3.(a) Find the minimal sample size required so that for a 95% confi dence interval, the maximal margin of error is E
Basic Computation: Sample Size Suppose x has a normal distribution with s 5 1.2.(a) Find the minimal sample size required so that for a 90% confi dence interval, the maximal margin of error is E 5
Profi ts: Retail Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profi ts per employee. The following data give annual profi ts per employee (in
Statistical Literacy Student’s t distributions are symmetric about a value of t.What is that t value?
Statistical Literacy As the degrees of freedom increase, what distribution does the Student’s t distribution become more like?
Critical Thinking Consider a 90% confi dence interval for m. Assume s is not known. For which sample size, n 5 10 or n 5 20, is the critical value tc larger?
Critical Thinking Consider a 90% confi dence interval for m. Assume s is not known. For which sample size, n 5 10 or n 5 20, is the confi dence interval longer?
Critical Thinking Lorraine computed a confi dence interval for m based on a sample of size 41.Since she did not know s, she used s in her calculations.Lorraine used the normal distribution for the
Critical Thinking Lorraine was in a hurry when she computed a confi dence interval for m. Because s was not known, she used a Student’s t distribution.However, she accidentally used degrees of
Basic Computation: Confi dence Interval Suppose x has a mound-shaped distribution. A random sample of size 16 has sample mean 10 and sample standard deviation 2.(a) Check Requirements Is it
Basic Computation: Confi dence Interval A random sample of size 81 has sample mean 20 and sample standard deviation 3.(a) Check Requirements Is it appropriate to use a Student’s t distribution to
Archaeology: Tree Rings At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years a.d. for an archaeological excavation site(Bandelier Archaeological Excavation Project: Summer
Camping: Cost of a Sleeping Bag How much does a sleeping bag cost? Let’s say you want a sleeping bag that should keep you warm in temperatures from 20F to 45F. A random sample of prices ($) for
Diagnostic Tests: Total Calcium Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level

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