1

IDA V. MOFFETT SCHOOL OF NURSING

SAMFORD UNIVERSTIY

NURG 702: Biostatistics

HOMEWORK D: Statistics for Independent Group Comparisons

Directions: The following questions will be input into a quiz format in Moodle. As you study the content, you can select the best answer for each statement or question and mark your answers on this document. You will be notified once the quiz is set in Moodle, then you can input your answers into the Moodle quiz for Homework D.

  1. Before performing a statistical analysis, the researcher checks the assumptions for the statistical test and finds that the assumptions have been violated. What should the researcher do?
  1. Continue with the statistical analysis
  2. Reconsider the statistical analysis
  3. No action is necessary
  4. It is impossible to determine from the information given

Scenario 1 (questions 2-6): A few years ago, a report in Lancet indicated that several people in New Mexico had succumbed to a rare disease, eosinophilia-myalgia syndrome (EMS). The only circumstance they seemed to have in common was that they had taken large quantities of an amino acid health food called tryptophan (tryptophan ingestion). Through investigation, a number of people were found throughout the country that had a diagnosis of EMS (development of EMS). The question was asked, was there a statistically significant relationship between ingesting tryptophan and developing EMS? (alpha = .05)

The data are presented in the following table:

EMS Disease
Tryptophan / Yes EMS / No EMS
Yes / Cell A
20 / Cell C
18
No / Cell B
17 / Cell D
38

The analysis of the Scenario 1 data is presented in the following tables:

Case Processing Summary
Cases
Valid / Missing / Total
N / Percent / N / Percent / N / Percent
Tryptophan * EMS / 93 / 100.0% / 0 / .0% / 93 / 100.0%
Tryptophan * EMS Crosstabulation
EMS / Total
Yes / No
Tryptophan / Yes / Count / 20 / 18 / 38
Expected Count / 15.1 / 22.9 / 38.0
% within Tryptophan / 52.6% / 47.4% / 100.0%
% within EMS / 54.1% / 32.1% / 40.9%
% of Total / 21.5% / 19.4% / 40.9%
Std. Residual / 1.3 / -1.0
No / Count / 17 / 38 / 55
Expected Count / 21.9 / 33.1 / 55.0
% within Tryptophan / 30.9% / 69.1% / 100.0%
% within EMS / 45.9% / 67.9% / 59.1%
% of Total / 18.3% / 40.9% / 59.1%
Std. Residual / -1.0 / .8
Total / Count / 37 / 56 / 93
Expected Count / 37.0 / 56.0 / 93.0
% within Tryptophan / 39.8% / 60.2% / 100.0%
% within EMS / 100.0% / 100.0% / 100.0%
% of Total / 39.8% / 60.2% / 100.0%
Chi-Square Tests
Value / df / Asymp. Sig. (2-sided) / Exact Sig. (2-sided) / Exact Sig. (1-sided)
Pearson Chi-Square / 4.426a / 1 / .035
Continuity Correctionb / 3.566 / 1 / .059
Likelihood Ratio / 4.421 / 1 / .035
Fisher's Exact Test / .052 / .030
Linear-by-Linear Association / 4.379 / 1 / .036
N of Valid Cases / 93
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 15.12.
b. Computed only for a 2x2 table
  1. What is the alternative hypothesis for this chi-square test of independence?
  1. Tryptophan ingestion (yes/no) and development of EMS (yes/no) are independent (not related).
  2. Tryptophan ingestion (yes/no) and development of EMS (yes/no) are not independent (they are related).
  1. What is the level of measurement for the variable ‘tryptophan ingestion’?
  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio
  1. Is the assumption of ‘adequate sample size’ met for this analysis?
  1. Yes
  2. No
  1. What is the Pearson Chi-Square test statistic value for this analysis?
  1. 4.426
  2. 3.566
  3. 4.421
  4. 4.379
  1. Using the p value of .035 for the calculated Pearson Chi-Square, what would be the decision for this hypothesis test (alpha = .05)?
  1. Fail to reject the null hypothesis
  2. Reject the null hypothesis
  1. Which of the following assumptions for an independent t Test would be violated if the distribution for one group has a large variance and the distribution for the other group has a small variance?
  1. Independent samples
  2. Random samples
  3. Normality
  4. Homogeneity of Variance
  1. What is the nonparametric counterpart of the independent t Test?
  1. Mann-Whitney U Test
  2. Kruskal-Wallis Test
  3. Wilcoxon signed-rank Test
  4. Dependent t Test
  1. What would be the appropriate statistic to report for the magnitude of the effect in a dependent t Test analysis?
  1. Phi
  2. Point Biserial
  3. Cohen’s d
  4. Standard Error

Scenario 2 (questions 10-12): In a recent article, data were reported comparing therapeutic touch with casual touch on change in diastolic blood pressure. The means and standard deviations were reported for change in diastolic blood pressure using each type of touch. This comparison was a between-subjects design with random assignment (alpha = .05). Also, the data met the assumption for normal distribution. The data are presented in the following table:

Therapeutic Touch

/

Casual Touch

10 / 12
9 / 7
11 / 6
8 / 6
12 / 11
4 / 1
5 / 2
7 / 4
8 / 7
10 / 8
5 / 11
10 / 9
4 / 4
3 / 6
11 / 10
  1. What is the null hypothesis for this study described in Scenario 2?
  1. There is a statistically significant difference in mean change in diastolic blood pressure between patients who receive therapeutic touch and patients who receive casual touch.
  2. Patients who receive therapeutic touch have a significantly greater change in diastolic blood pressure than patients who receive casual touch.
  3. There is no statistically significant difference in mean change in diastolic blood pressure between patients who receive therapeutic touch and patients who receive casual touch.
  4. None of the above.
  1. What is the dependent variable for the study described in Scenario 2?
  1. Therapeutic touch
  2. Casual touch
  3. Touch
  4. Change in diastolic blood pressure.
  1. What is the appropriate statistical test for the study described in Scenario 2?
  1. Independent t Test
  2. Dependent t Test
  3. Mann-Whitney U Test
  4. Wilcoxon signed-rank Test
  1. Why does a one-way ANOVA require an interval or ratio (scale) level dependent variable?
  1. Two groups are compared.
  2. Several different groups are compared.
  3. A table is constructed.
  4. Means and standard deviations must be calculated.
  1. A study compares mean dosage test scores for independent groups of students who have been randomly assigned to the following teaching strategy classes: lecture, problem-based learning, and simulation. The dependent variable is mean dosage test score. Provided the assumptions for the statistical test are met, what would be the most appropriate analysis for this scenario?
  1. Independent t Test
  2. One-way Analysis of Variance (ANOVA)
  3. Kruskal-Wallis H
  4. It cannot be determined from the information provided
  1. With regard to the assumption of homogeneity of variance for the one-way ANOVA, the ANOVA tends to yield accurate results when the group sizes are approximately equal and the sample size is large, even if the population variances are not homogeneous.
  1. True
  2. False
  1. What would be the appropriate statistic to report for the strength and magnitude of the relationship in a one-way analysis of variance (ANOVA)?
  2. Phi
  3. Point Biserial
  4. Cohen’s d
  5. Eta2
  1. A researcher wants to study the effects of sleep on concentration. She selects a sample of 100 subjects and randomly assigns 25 subjects each to the following groups: 2-hours, 4-hours, 6-hours, and 8-hours of sleep, respectively, the night before reporting to the lab at 8:00 a.m. Then, she asks the subjects to do a set of 10 simple problems and records their score (that yields scale data). What test would she use to analyze the data?
  1. Kruskal-Wallis H
  2. Repeated Measures ANOVA
  3. One-Way ANOVA
  4. None of the above
  1. In the sleep concentration study (see #17), if the assumptions for a parametric one-way ANOVA are not met, an appropriate alternative statistical test would be the:
  1. Mann-Whitney U
  2. Kruskal-Wallis H
  3. Wilcoxon Signed Ranks
  4. Friedman’s
  1. The one-way ANOVA for the sleep concentration study (see #17) resulted in a rejection of the null hypothesis, a statistically significant result. What would be the next appropriate step in order to complete the analysis?
  1. A post hoc power analysis.
  2. A post hoc multiple comparison procedure.
  3. A test of the assumptions.
  4. No additional action is needed.

Scenario 3 (questions 20-26): Nurses were concerned that forcing blood transfusions through small gauge needles could result in damaged red blood cells. The nurses conducted a study to investigate their concern. Mean plasma hemoglobin levels were used as an indicator of red blood cell damage (higher values indicated more blood cell damage). Three different needle gauges (16, 18, and 21) were used in the study.

  1. What is the alternative hypothesis for the study described in Scenario 3?
  2. There is no statistically significant difference in mean plasma hemoglobin levels among blood samples from a 16 gauge needle, an 18 gauge needle, and a 21 gauge needle.
  3. There is a statistically significant difference in mean plasma hemoglobin levels among blood samples from a 16 gauge needle, an 18 gauge needle, and a 21 gauge needle.
  4. None of the above.
  1. What is the dependent variable for the study described in Scenario 3?
  2. Mean plasma hemoglobin levels
  3. Blood transfusions
  4. Needle gauge
  5. Nurses

The SPSS analysis (output) results for the Scenario 3 data are presented in the following tables:

Oneway

Descriptives
PlasmaHGB
N / Mean / Std. Deviation / Std. Error / 95% Confidence Interval for Mean / Minimum / Maximum
Lower Bound / Upper Bound
16 Gauge / 20 / 4.9000 / 2.17401 / .48612 / 3.8825 / 5.9175 / 1.00 / 8.00
18 Gauge / 20 / 6.8500 / 2.43386 / .54423 / 5.7109 / 7.9891 / 2.00 / 10.00
21 Gauge / 20 / 11.0500 / 3.25212 / .72720 / 9.5280 / 12.5720 / 5.00 / 16.00
Total / 60 / 7.6000 / 3.67861 / .47491 / 6.6497 / 8.5503 / 1.00 / 16.00
Test of Homogeneity of Variances
PlasmaHGB
Levene Statistic / df1 / df2 / Sig.
2.097 / 2 / 57 / .132
ANOVA
PlasmaHGB
Sum of Squares / df / Mean Square / F / Sig.
Between Groups / 395.100 / 2 / 197.550 / 27.921 / .000
Within Groups / 403.300 / 57 / 7.075
Total / 798.400 / 59

Post Hoc Tests

Multiple Comparisons
PlasmaHGB
Tukey HSD
(I) Needle Guage Size Group / (J) Needle Guage Size Group / Mean Difference (I-J) / Std. Error / Sig. / 95% Confidence Interval
Lower Bound / Upper Bound
16 Gauge / 18 Gauge / -1.95000 / .84116 / .061 / -3.9742 / .0742
21 Gauge / -6.15000* / .84116 / .000 / -8.1742 / -4.1258
18 Gauge / 16 Gauge / 1.95000 / .84116 / .061 / -.0742 / 3.9742
21 Gauge / -4.20000* / .84116 / .000 / -6.2242 / -2.1758
21 Gauge / 16 Gauge / 6.15000* / .84116 / .000 / 4.1258 / 8.1742
18 Gauge / 4.20000* / .84116 / .000 / 2.1758 / 6.2242

*. The mean difference is significant at the 0.05 level.

  1. Is the ‘homogeneity of variance assumption’ met for the statistical test calculated for
Scenario 3 data?
  1. Yes
  2. No
  1. Using the p value (Sig.) that corresponds to the calculated test statistic (F) for the Scenario 3 data analysis, what is the decision regarding the null hypothesis (alpha = .05)?
  1. Fail to reject the null hypothesis
  2. Reject the null hypothesis
  1. Would it be necessary to report a post hoc multiple comparison procedure for the Scenario 3 data analysis results?
  1. Yes
  2. No
  1. What needle gauge group had the highest mean plasma hemoglobin value?
  1. 16 gauge
  2. 18 gauge
  3. 21 gauge
  1. Does the evidence generated from the Scenario 3 data analysis support the use of a 21 gauge needle for blood transfusions?
  1. Yes
  2. No

  1. Which of the following statements describes the design of a two-way ANOVA?
  2. two or more independent variables and their interaction(s)
  3. two or more dependent variables and their interaction(s)
  4. one independent variable, one interaction of independent and dependent variables
  5. None of these describes the design of a two-way ANOVA.
  1. How can you speculate whether there is an interaction in a two-way ANOVA?
  2. Inspect the marginal and cell standard deviations.
  3. Graph the p values.
  4. Graph the cell means.
  5. Evaluate the main effect F against its critical value.
  1. Samples of men and women in a nursing school were asked to rate, on a 7-point scale, their interest in three of their school subjects. A factorial ANOVA (gender by subject) analyzed these data. Inspect this graph. Is there evidence of an interaction?

  1. Yes
  2. No
  3. Need more information

SCENARIO 4 (Questions 30 - 33): Two-Way ANOVA: The table below presents means for the number of hours worked (SPSS variable name = hrs1) for individuals by general happiness (SPSS variable name = happy) and job satisfaction (SPSS variable name = satjob).

JOB SATISFACTION

GENERAL HAPPINESS / Very Satisfied with Job / Moderately Satisfied with Job / A Little Dissatisfied with Job / Very Dissatisfied with Job
Very Happy / 43 / 40 / 47 / 33
Pretty Happy / 42 / 42 / 45 / 35
Not too Happy / 38 / 41 / 32 / 51
  1. What are the independent variables in Scenario 4?
  2. Job Satisfaction and General Happiness
  3. Hours Worked and Job Satisfaction
  4. Hours Worked and General Happiness
  5. None of the above
  1. What is the dependent variable in Scenario 4?
  2. Job Satisfaction
  3. General Happiness
  4. Hours Worked
  5. Job Satisfaction and General Happiness
  1. Which of the following statements represents the null hypothesis for the main effect of general happiness in Scenario 4?
  2. There is a statistically significant difference in the number of hours worked among the categories of general happiness.
  3. There is no statisticallysignificant difference in the number of hours worked among the categories of general happiness.
  4. There is no statistically significant difference in the interaction between general happiness and number of hours worked.
  5. None of the above.
  1. Which of the following is a correct statement for the alternative interaction hypothesis for the variables in Scenario 4?
  2. There is a statistically significant interaction between general happiness and job satisfaction.
  3. There is no statistically significant interaction between general happiness and job satisfaction.
  4. There is no statistically significant interaction between general happiness and number of hours worked.
  5. There is a statistically significant difference in the number of hours worked as a result of the interaction between categories of general happiness and categories of job satisfaction.

SCENARIO 4 Data Analysis:SPSS output for the assumption of homogeneity of variance for the data presented in Scenario One is providedin the tablebelow. Use this table to answer question 34.

Levene's Test of Equality of Error Variances(a)

Dependent Variable: Number of Hours Worked Last Week

F / df1 / df2 / Sig.
1.367 / 11 / 885 / .183

Tests the null hypothesis that the error variance of the dependent variable is equal across groups.

a Design: Intercept+satjob+happy+satjob * happy

  1. Based on the following information provided in the ‘Levene’s Test of Equality of Error (Variances(a)', is the homogeneity of variance assumption met for this analysis?
  2. Yes
  3. No

SCENARIO 4 Data Analysis:SPSS output of the analysis of the data presented in Scenario 4 is provided in the table below. Use this table to answer questions35 through 39.

Tests of Between-Subjects Effects

Dependent Variable: Number of Hours Worked Last Week

Source / Type III Sum of Squares / df / Mean Square / F / Sig. / Partial Eta Squared / Noncent. Parameter / Observed Power(a)
Corrected Model / 5187.921(b) / 11 / 471.629 / 2.244 / .011 / .027 / 24.689 / .943
Intercept / 329693.388 / 1 / 329693.388 / 1569.005 / .000 / .639 / 1569.005 / 1.000
satjob / 44.774 / 3 / 14.925 / .071 / .975 / .000 / .213 / .063
happy / 41.412 / 2 / 20.706 / .099 / .906 / .000 / .197 / .065
satjob * happy / 4050.265 / 6 / 675.044 / 3.213 / .004 / .021 / 19.275 / .929
Error / 185964.094 / 885 / 210.129
Total / 1757791.000 / 897
Corrected Total / 191152.016 / 896

a Computed using alpha = .05

b R Squared = .027 (Adjusted R Squared = .015)

  1. Based on the SPSS “Tests of Between-Subjects Effects” table presented above, is factor interaction statistically significant?
  2. Yes
  3. No
  1. Based on the SPSS “Test of Between-Subjects Effects” table presented above, are the main effects (general happiness and job satisfaction) statistically significant?
  2. Yes
  3. No
  1. Based on the SPSS “Test of Between-Subjects Effects” table presented above, would it be appropriate to report a Partial Eta Squared for the interaction effect?
  2. Yes
  3. No
  1. Based on the SPSS “Test of Between-Subjects Effects” table presented above, would it be appropriate to conduct a post hoc analysis for the main effects of general happiness and job satisfaction?
  2. Yes
  3. No
  1. Based on the SPSS “Test of Between-Subjects Effects” table presented above, was there sufficient power for the interaction effect analysis?
  2. Yes
  3. No
  1. I gave this assignment my best effort. (Worth 22 points.)
  2. Yes
  3. No