Advanced and Multivariate Statistical Methods, Exams of Nursing

Advanced and Multivariate Statistical Methods

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Advanced and Multivariate Statistical Methods,
Sixth Edition, Craig A. Mertler and Rachel Vannatta Reinhart, Routledge.
Chapter 1: Introduction to Multivariate Statistics
Test Items: True-False Format
Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.
1. The use of multivariate statistical techniques has become more commonplace largely
due to the increasingly complex nature of research designs and related research
questions. T*
F
2. A study appropriate for multivariate statistical analysis is typically defined as one
with several dependent variables (DVs).
T*
F
3. The basic distinction between experimental and nonexperimental research designs
is whether the levels of the independent variable(s) have been manipulated by the
researcher.
T*
F
4. In nonexperimental research (e.g., descriptive, correlational, survey, or causal-
comparative designs), the researcher has no control over the levels of the
independent variables (IVs).
T*
F
5. In an experimental research study, if the researcher finds a statistically significant
difference between two or more of the groups representing different treatment
conditions, she or he can have some confidence in attributing causality to the IV.
T*
F
6. Nonexperimental research studies also enable a researcher to conclude that the IV
and DV are related and infer causality.
T
F*
7. In experimental studies, IVs may also be referred to as criterion or outcome variables.
T
F*
8. In experimental studies, DVs are sometimes referred to as the predictor or
causal variables.
T
F*
9. Univariate statistics refers to analyses where there is only one IV and one DV.
T
F*
10. Bivariate statistics refers to analyses that involve two variables where one is identified
as an IV and the other is identified as a DV.
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Advanced and Multivariate Statistical Methods ,

Sixth Edition , Craig A. Mertler and Rachel Vannatta Reinhart, Routledge. Chapter 1: Introduction to Multivariate Statistics Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  1. The use of multivariate statistical techniques has become more commonplace largely due to the increasingly complex nature of research designs and related research questions. T* F
  2. A study appropriate for multivariate statistical analysis is typically defined as one with several dependent variables (DVs). T* F
  3. The basic distinction between experimental and nonexperimental research designs is whether the levels of the independent variable(s) have been manipulated by the researcher. T* F
  4. In nonexperimental research (e.g., descriptive, correlational, survey, or causal- comparative designs), the researcher has no control over the levels of the independent variables (IVs). T* F
  5. In an experimental research study, if the researcher finds a statistically significant difference between two or more of the groups representing different treatment conditions, she or he can have some confidence in attributing causality to the IV. T* F
  6. Nonexperimental research studies also enable a researcher to conclude that the IV and DV are related and infer causality. T F*
  7. In experimental studies, IVs may also be referred to as criterion or outcome variables. T F*
  8. In experimental studies, DVs are sometimes referred to as the predictor or causal variables. T F*
  9. Univariate statistics refers to analyses where there is only one IV and one DV. T F*
  10. Bivariate statistics refers to analyses that involve two variables where one is identified as an IV and the other is identified as a DV.

T

F*

  1. Quantitative variables are also referred to as continuous or interval variables. T* F
  2. Categorical variables consist of separate, indivisible categories. T* F
  3. Categorical variables may also be referred to as nominal, ordinal, discrete, or qualitative. T* F
  4. A dichotomous variable is one that has only two possible levels or categories. T* F
  5. Age is a quantitative variable, but one could recode the values so that it would be transformed into a dichotomous variable. T* F
  6. When conducting a multivariate analysis, the best recommendation is to obtain the solution with the largest number of variables. T F*
  7. The mathematical calculations involved in multivariate statistical analyses are performed only on a correlation matrix. T F*
  8. Orthogonality is perfect association between variables. T F*
  9. Orthogonality is not a desirable quality for multivariate statistical analyses. T F*
  10. Having a data set with orthogonal variables is not the ideal situation. T F*
  11. When variables are correlated, they have overlapping, or shared, variance. T* F
  12. Using a standard analysis approach, the overlapping portion of variance is included in the overall summary statistics of the relationship of the set of IVS to the DV, but that portion is not assigned to either of the IVs as part of their individual contribution. T* F
  13. The sequential analysis requires the researcher to prioritize the entry of IVs into the equation or solution. T*

Chapter 2: A Guide to Multivariate Techniques Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  1. The primary factor that determines the statistical test students should use is the number of independent and dependent variables. T F*
  2. When investigating the relationship between two or more quantitative variables, chi-square is the appropriate test. T F*
  3. The Pearson correlation coefficient measures the association between two quantitative variables, distinguishing between the independent and dependent variables. T F*
  4. Multiple regression is used when there are several dependent variables and one independent quantitative variable. T F*
  5. When testing for the significance of group differences, the number of IVs, the number of DVs, and the number of categories in the DV determine the appropriate test. T F*
  6. The most basic statistical test that measures group difference is the T - test. T* F
  7. One-way analysis of variance (ANOVA) only determines the significance of group differences and does not identify which groups are significantly different. T* F
  8. One-way analysis of covariance (ANCOVA) is similar to ANOVA but additionally controls for a variable that may influence the DV. T* F
  9. Factorial analysis of variance (factorial ANOVA) extends ANOVA to research scenarios with two or more IVs that are categorical. T* F
  10. Factorial analysis of variance (factorial ANCOVA) examines group differences in a single quantitative dependent variable based upon two or more categorical independent variables, while controlling for a covariate that may influence the DV. T* F
  1. Questions that address structure usually distinguish between independent and dependent variables. T F*
  2. When investigating the relationship between two or more quantitative variables, the T - test is the appropriate test. T F*
  3. Prediction of group membership is evaluated by ANOVA, ANCOVA, MANOVA, and MANCOVA . T F*
  4. Significance of group differences is evaluated by discriminant analysis and logistic regression. T F* Test Items: Multiple-Choice Format Instructions: Circle the letter of the best answer. If you do not know the best answer, you may put a question mark to the left of the answers instead of circling a letter.
  5. The Pearson correlation coefficient: a. Measures the association between two quantitative variables without distinction between the IV and DV.* b. Utilizes the relationship between the IV and DV to predict the score of the DV from the IV. c. Both (a) and (b) are correct. d. Neither (a) nor (b) is correct.
  6. In path analysis, path coefficients are calculated: a. After the data are analyzed. b. To estimate the strength of the relationships in the hypothesized causal model.* c. At any time. d. None of the above is correct.
  7. When conducting MANOVA, if DVs are: a. Correlated, then it is appropriate to conduct several ANOVAs. b. Not correlated, then it is appropriate to conduct several ANOVAs.* c. Not correlated, then there is no relationship between the variables. d. None of the above is correct.
  8. Factorial MANCOVA requires: a. Two or more IVs that are quantitative. b. Two or more DVs that are categorical. c. Two or more DVs that are quantitative. d. Only (c) is correct.*
  9. Binary logistic regression requires: a. Two or more IVs (categorical/quantitative). b. One DV (two categories).

c. Both (a) and (b) are correct.* d. None are correct.

  1. The best thing to do when a data set includes missing data is to collect new data. T F*
  2. If a researcher decides that the missing data are important and need to be addressed, the first thing to do is to estimate the missing values and then use these values during the main analysis. T F*
  3. A third alternative for handling missing data deletes the missing values using a regression approach. T F*
  4. Cases with unusual or extremely large values at one or both ends of a sample distribution are known as outliers. T F*
  5. One of the fundamental causes for outliers is that data-entry errors were made by the research participant. T F*
  6. The problem with outliers is that they can distort the results of a statistical test. T* F
  7. Univariate outliers are cases with extreme values on one variable. T* F
  8. Multivariate outliers are cases with unusual combinations of scores on two or more variables. T* F
  9. A statistical procedure known as Mahalanobis distance can be used to identify outliers of any type. T* F
  10. Robustness refers to the relative insensitivity of a statistical test to violations of the underlying inferential assumptions. T* F
  11. Kurtosis is a quantitative measure of the degree of symmetry of a distribution about the mean. T

F*

  1. Skewness is a quantitative measure of the degree of peakedness of a distribution. T F*
  2. The Kolmogorov-Smirnov statistic tests the null hypothesis that the variables in the population are linear. T F*
  3. One of the characteristics of multivariate normality is that any linear combination of the variables must be nonnormally distributed. T F*
  4. If a distribution differs only moderately from normal, a log transformation should be obtained. T F*
  5. Linearity presupposes that there is a straight-line relationship between two variables. T* F
  6. Residuals are defined as the portion of scores not accounted for by the multivariate analysis. T* F
  7. Homoscedasticity is the assumption that the variability in scores for one continuous variable is roughly the same at all values of another continuous variable. T* F
  8. With univariate analyses, homogeneity of variances is assessed statistically with Levene’s test. T* F
  9. In multivariate situations, homoscedasticity can be assessed statistically by using Box’s M test for equality of variance-covariance matrices. T* F
  10. The main purpose for screening data prior to conducting a multivariate analysis is to deal with the accuracy of the findings. T F*
  11. Another purpose for screening data is to enter missing data and assess the effect of and ways to deal with complete data. T F*
  12. A third purpose of screening data is to assess the effects of large values on either end of the distribution. T

Chapter 4: Factorial Analysis of Variance Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  1. The univariate case of ANOVA is a hypothesis-testing procedure that simultaneously evaluates the significance of mean differences on a DV between two or more treatment conditions or groups. T* F
  2. The treatment conditions or groups are defined by the various levels of the IV, or factor in ANOVA terminology. T* F
  3. One-way ANOVA studies the effect that one factor has on one DV. T* F
  4. The null hypothesis in a one-way ANOVA states that there is no difference among the treatment conditions or groups. T* F
  5. The alternative or research hypothesis says that at least one of the group or treatment means is significantly different from the others. T* F
  6. One possible interpretation of the results of a one-way ANOVA is that there really are differences between the treatment conditions or groups. T F*
  7. Another possible interpretation of the results of a one-way ANOVA is that any expected differences between the conditions or groups represent real differences in the population. T F*
  8. The test statistic for ANOVA is partial eta squared. T F*
  9. The F ratio in ANOVA is based on mean differences as opposed to variances. T F*
  10. The numerator of the F ratio is referred to as the error variance. T F*
  11. One of the two possible causes or explanations for the differences that occur between groups or treatments in ANOVA is that the differences are due to treatment effects. T* F
  1. Another possible cause or explanation for the differences that occur between groups or treatments in ANOVA is that the differences occur simply due to chance. T* F
  2. Post hoc tests are also known as multiple comparisons. T* F
  3. Research designs that include more than one factor are called factorial designs. T* F
  4. The simplest of factorial designs is the two-way analysis of variance (ANOVA). T* F
  5. A two-way ANOVA consists of two DVs and one IV. T F*
  6. The purpose of factorial ANOVA is to test the mean differences with respect to some IV. T F*
  7. The two-way ANOVA tests two separate hypotheses simultaneously in one analysis. T F*
  8. Any dependent differences produced by either Factor A or Factor B are called main effects. T F*
  9. The null hypothesis for the main effect states that there is a difference in the scores due to the level of A. T F*
  10. Interaction between factors occurs when the effect of one factor depends on different levels of the other factors. T* F
  11. The null hypothesis for the tests of an interaction effect with a factorial ANOVA states that there is no interaction between Factor A and Factor B. T* F
  12. The validity of the results of a factorial ANOVA is dependent upon three assumptions, one of them being that the distributions of scores on the DV must have equal variances. T* F
  13. Eta squared is commonly viewed as the proportion of variance in the DV explained by the IVs in the sample. T* F

Chapter 5: Analysis of Covariance Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  1. Analysis of covariance (ANCOVA) mirrors the ordinary analysis of variance (ANOVA), but only before the effect of the covariate has been partialed out. T F*
  2. The effects of the covariate are removed by adjusting the scores on the IV in order to reflect the initial differences on the covariate. T F*
  3. The first major purpose for the use of ANCOVA is to increase the sensitivity of the F tests of main effects and interactions by reducing the error variance, primarily in experimental studies. T* F
  4. The second major purpose for the use of ANCOVA involves a statistical adjustment procedure where the means of the DVs for each group are adjusted to where they would be if all groups had scored equally on the covariate. T* F
  5. The third major purpose for the use of ANCOVA is to interpret differences in levels of the IV when several DVs are included in the analysis. T* F
  6. One of the assumptions for ANCOVA is that the observations within each sample must be randomly sampled and must be dependent on one another. T F*
  7. Another assumption is that the distribution of scores on the independent variables must have equal variances. T F*
  8. An additional assumption of ANCOVA is that a linear relationship exists between the DVs and the covariate(s). T* F
  9. ANCOVA assumptions also require that the regression slopes for a covariate are homogeneous. T* F
  10. The sixth assumption for ANCOVA is that the covariate is reliable and is measured without error. T*

F

  1. The assumption of homogeneity of variances is best tested through the use of Levine’s test. T F*
  2. The assumption of linearity is more precisely tested by obtaining and examining residual plots between the covariates and the IVs. T F*
  3. Regression is incorporated into ANCOVA in order to predict scores on the DV based on knowledge of scores on the covariate. T* F
  4. A violation of the assumption of homogeneous regression slopes is crucial with respect to the validity of the results of ANCOVA. T* F
  5. The null hypothesis being tested with the assumption of homogeneity of regression slopes is that all regression slopes are equal. T* F
  6. The logic of ANCOVA is identical to the logic behind ANOVA. T F*
  7. The initial phase of the analysis with ANCOVA involves the statistical adjustments of the DV group means in order to control for the effects of the covariate on the IVs. T F*
  8. Interpretation of ANCOVA results is similar to that of ANOVA. T* F
  9. If the F test of factor-covariate interaction is significant, then the full ANCOVA should not be conducted. T* F
  10. If factor-covariate interaction is not significant, then one can proceed with interpreting the Levene’s test as well as proceeding with the full ANCOVA. T* F
  11. If the Levene’s test is significant, then homogeneity of variance is assumed. T F*
  12. Line graphs are typically created to graphically represent any interaction between/among covariates based upon the DV. T F*

c. Of no consequence because the correlation is weak. d. None of the above is correct.

Chapter 6: Multivariate Analysis of Variance and Covariance Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  1. Multivariate analysis of variance (MANOVA) is designed to test the significance of group differences with several dependent variables. T* F
  2. At a minimum, the DVs should have some degree of linearity and share a common conceptual meaning. T* F
  3. Using more than one DV when comparing treatments or groups based on differing characteristics is good because any worthwhile treatment or substantial characteristic will always affect participants in more than one way. T F*
  4. MANOVA tests whether mean differences among k groups on a combination of DVs are unlikely to have occurred by chance. T F*
  5. The new DV formed in MANOVA is, in fact, a nonlinear combination of the original measured DVs, combined in such a way as to maximize the group differences. T F*
  6. The new DV formed in MANOVA is created by developing a linear equation where each measured DV has an associated weight and, when combined and summed, creates maximum separation of group means with respect to the new DV. T* F
  7. A factorial MANOVA is a design that involves multiple IVs as well as multiple DVs. T* F
  8. One advantage of using MANOVA, as opposed to doing a couple of ANOVAs, is the slight improvement in the chances of discovering what actually changes as a result of the differing treatments or characteristics. T F*
  9. A second advantage of using MANOVA is that it consistently reveals differences not shown in separate ANOVAs. T F*
  10. A third advantage of using MANOVA is that the overall Type I error rate is increased. T F*