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 RachelVannatta 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. One-way multivariate analysis of variance (MANOVA) is utilized to simultaneously study two or more related IVs, while controlling for the correlations among the IVs. T F*
  2. One-way multivariate analysis of covariance (MANCOVA) investigates group differences among several IVs, while also controlling for covariates that may influence the DVs. T F*
  3. Factorial multivariate analysis of variance (factorial MANOVA) extends MANOVA to research scenarios with two or more DVs that are categorical. T F*
  4. Factorial multivariate analysis of covariance (MANCOVA) extends factorial MANCOVA to research scenarios that require the adjustment of one or more covariates on the IV. T F*
  5. The primary purpose of predicting group membership is to identify specific IVs that best predict group membership as defined by the IVs. T F*
  6. Discriminant analysis and logistic regression are appropriate statistical techniques when the DV is categorical. T* F
  7. Discriminant analysis seeks to identify which combination of quantitative IVs best predicts group membership by a single DV that has two or more categories. T* F
  8. In binary logistic regression, the DV is a dichotomous variable. T* F
  9. Factor analysis and principal components analysis are different techniques, but they are very similar. T* F
  10. Factor analysis allows the researcher to explore the underlying structures of an instrument or data set and is often used to develop and test a theory. T* F
  11. Principal components analysis is generally used to reduce the number of IVs, which is advantageous when conducting multivariate techniques in which the IVs are not correlated. T F*

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

Chapter 3: Pre-Analysis Data Screening Test Items: True-False Format Instructions: Mark the statements “T” for true, “F” for false, or “?” for don’t know.

  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. A fourth purpose of screening data is to assess the adequacy of fit between the data and to make assumptions of a specific procedure. T F*
  2. Pre-analysis data screening is an analysis after the analysis. 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.
  3. Many researchers tend to assume that any missing data that occur within their dataset: a. Are random in nature.* b. Are caused by research participants not giving honest answers. c. Reflect responses to a taboo topic where participants were ashamed to answer the question(s). d. None of the above is correct.
  4. There are three fundamental causes for outliers: a. Data-entry errors were made by the researcher. b. The participant is not a member of the population for which the sample is intended. c. The participant is simply different from the remainder of the sample. d. All three are correct.*
  5. There are three general assumptions involved in multivariate statistical testing: a. Normality. b. Linearity. c. Homoscedasticity. d. All three are correct.*
  6. If the researcher determines that the data have deviated from normal, she or he can consider transforming the data by: a. A square root transformation. b. A log transformation. c. An inverse transformation. d. All three are correct.*
  7. Linearity presupposes that: a. There is a straight-line relationship between two variables.* b. The variability in scores for one continuous variable is roughly the same at all values. of another continuous variable. c. Both (a) and (b) are correct. d. Neither (a) nor (b) is correct.

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. Eta squared is viewed as a descriptive statistic and is interpreted as a measure of effect size. 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.
  2. What level of measurement is required for the independent variable (factor) and dependent variable in univariate analysis of variance (ANOVA)? a. The factor has to be at the nominal level of measurement. b. The dependent variable has to be at the interval/ratio level of measurement. c. Both of the above.* d. Neither of the above.
  3. When the value of the F ratio in ANOVA is near 1.00, this indicates that: a. The differences between groups in the factor are roughly the same as would be expected due to chance. b. There is evidence of a treatment effect. c. There is no evidence of a treatment effect. d. Both (a) and (c) are correct.*
  4. In two-way analysis of variance: a. There are two independent variables and one dependent variable. b. There are two dependent variables and one independent variable. c. The two independent variables must be at the interval/ratio level of measurement. d. Both (b) and (c) are incorrect.*
  5. Main effects in the two-way ANOVA: a. Must be reported when there are interaction effects between the independent variables. b. Need not be reported when the interaction effect between the independent variables is statistically significant. c. Indicate the differences produced by either Factor A or Factor B , independent of the other. d. Both (b) and (c) are correct.*
  6. Interaction between factors in the two-way ANOVA: a. Occurs when the effect of one factor depends on the different levels of the other factor. b. Occurs when the effect of one factor does not depend on the different level of the other factor. c. Should be reported in addition to the main effects for Factor A and Factor B. d. Both (a) and (c) are correct.*

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*
  1. ANCOVA adjusts group means as if participants scored equally on the covariates. T* F
  2. F ratios and p values for each covariate indicate the degree to which the covariate significantly influences the DV. T* F
  3. When the covariate adjustment is made, a portion of the treatment effect will be removed. 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.
  4. The first step in interpreting the results of ANCOVA is to: a. Determine if factor interaction is present by examining the F ratio and p value for interaction.* b. Obtain a measure of effect size. c. Test the various combinations of levels for Factor A and Factor B. d. Only (a) and (b) are correct.
  5. Eta squared in ANCOVA is interpreted as: a. The proportion of variance in the DV explained by the IV(s) in the sample. b. The proportion of variance in the covariate explained by the IV(s) in the sample. c. The proportion of variance in the IV(s) in the sample after partialing out the effects of the covariate(s). d. None of the above.*
  6. A two-way ANCOVA tests the following three separate hypotheses simultaneously in one analysis: a. Two of the hypotheses test the significance of the levels of the two IVs separately, after removing the effects of the covariate. b. The third tests the significance of the interaction of the levels of the two IVs, also after removing the effects of the covariate. c. The third tests the significance of the interaction of the levels of the IVs and DV after removing the effects of the covariate. d. (a) and (b) are correct.*
  7. Ideally, if quantitative variables are being used as covariates in ANCOVA, one should choose those variables that: a. Are significantly correlated with the DV. b. Have low correlations among themselves. c. Have high correlations among themselves. d. (a) and (b) are correct.*
  8. If there exists a weak correlation between two covariates, they will remove relatively unique portions of the error variance from the DV, which is: a. Advantageous.* b. Disadvantageous.

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

  1. MANOVA incorporates the interconnections of DVs into the analysis. T* F
  2. The results of MANOVA are sometimes ambiguous with respect to the effects of the IVs on individual DVs. T* F
  3. The calculations for MANOVA are based on scalar algebra. T F*
  4. The most commonly used test statistic for MANOVA is Roy’s Largest Root. T F*
  5. Wilks’ Lambda ( Ʌ ) is an inverse criterion, which means that the smaller the value of Ʌ , the less evidence for treatment effects or group differences. T F*
  6. In conducting a MANOVA, one first tests the overall multivariate hypothesis. T* F
  7. If the null hypothesis is retained, it is common practice to stop the interpretation of the analysis at this point and conclude that the treatments or conditions have no effect on the DVs. T* F
  8. One of the assumptions of MANOVA is that the observations within each sample must be randomly sampled and must be dependent on each other. T F*
  9. A second MANOVA assumption is that the observations on at least one DV must follow a multivariate normal distribution in the group. T F*
  10. A third MANOVA assumption is that the relationships among all pairs of DVs for each cell in the data matrix must be normal. T F*
  11. Multivariate Analysis of Covariance (MANCOVA) is essentially a combination of MANOVA and ANCOVA. T* F
  12. MANCOVA asks if there are statistically significant mean differences among groups after adjusting the newly created DV for differences on one or more covariates. T* F
  1. In MANCOVA, the effects of the covariates are added to the analysis, leaving the researcher with a clearer picture of the true effects of the IVs on the multiple DVs. T F*
  2. The null hypothesis being tested in MANCOVA is that the adjusted population mean vectors are not equal. T F*
  3. An assumption in MANCOVA is that linear relationships need not exist between all pairs of DVs, all pairs of covariates, and all DV-covariates in each cell. 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.
  4. Initial assessments of normality with MANCOVA is done through the inspection of: a. Histograms. b. Boxplots. c. Normal Q-Q plots. d. All of the above.*
  5. A violation of the assumption of homogeneity of regression slopes (as well as regression planes and hyperplanes) in MANCOVA is an indication that: a. There is a covariate by treatment (IV) interaction.* b. There is a covariate by DV interaction. c. Neither (a) nor (b) is correct. d. Both (a) and (b) are correct.
  6. Examining group means (before and after covariate adjustment) for each DV in MANCOVA can assist in determining how groups differed for each DV because: a. MANCOVA provides post hoc analyses. b. MANCOVA does not provide post hoc analyses.* c. MANCOVA provides post hoc analyses when there is only one covariate. d. MANCOVA provides post hoc analyses when there is only one factor.
  7. In summary, the first step in interpreting the MANCOVA results is to evaluate the preliminary MANCOVA results that include: a. Box’s test. b. Test for homogeneity of regression slopes. c. Box’s test and the test for homogeneity of regression slopes.* d. F ratio.
  8. If Box’s test is not significant when interpreting MANCOVA, which of the following test statistics should be used when interpreting the homogeneity of regression slopes and the subsequent multivariate tests? a. Wilks’ Lambda.* b. Pillai’s Trace. c. Hotelling’s Trace.