Variability That Educational Researchers Use Us Called Variance

Doctoral (PhD) Question 1


The process of education research just like other kinds of behavioral research revolves around the concept of variability. Particularly, all behavioral research attempts to answer questions about behavioral variability. One aspect of this variability that educational researchers use us called variance (he amount of observed variability) in participants’ behavior. This variance in research cab classified into three types. Below are five research designs where researchers had a special type of variance in mind and took steps to deal with that concern.

For each, identify the category, type of variance, and explain (in detail) how the researcher solved for the variance.

1. Previous research in counseling which dealt with testing anxiety reported that gender was an important factor. A researcher conducted an experimental study in which she randomly assigned college freshman into two groups. One group was treated with a direct counseling technique and the other group with an indirect counseling technique. Once the data were collected the researcher delimited her study to mail freshmen students only

2An educational researcher participated in a state wide study on enhancing the reading fluency among African-American males. Due to the large sample of African-American male students involved in the study, it was recommended that any assessment done would have to be done using standardized inventory with scantrons. To be sure that the student’s performance on the test would not be affected because they did not know how to use the scantrons, instructions will be given to students on the use of scantrons before administering the assessments.

3.A researcher wanted to investigate the impact that a new three component tutorial program would have on the mathematics performance of undergraduate education majors. To assess the effectiveness of the total program she randomly assigned students to one of three groups. The students in Group One received instructions using a computer software package, students in Group Two received instruction via video of a teacher lecturing on math concepts, and the students in Group Three received face to face instruction in the classroom on a Smart Board. At the end of the semester a post-test was given and the students’ math scores were recorded. To be sure that the students’ math results depended only upon the teaching method provided, all three groups only received their method of tutoring. Neither group of students was allowed to use, hear or see any of the other instructions.

4.An educational researcher was interested in the effect of being tutored as opposed to not being tutored on the performance of the statistics portion of the doctoral comprehensive examination. To be sure that the treatment would provide the plausible explanation for the difference in performance, the students were matched according to the relevant factors associated with their statistical ability.

5.An educational researcher tested the effects of a new statistical software package he developed on his students’ performance in his statistics classes. To be sure that the treatments in both classes were as different as possible, one class was taught statistics using the new software package and the other class was taught using the old software package.

Doctoral (PhD) Question 2

Reliability and Validity

Reliability and validity are used to test instruments for inclusion in a research study and to evaluate examinations prepared by the investigator.As a researcher, you need to:

a)      Define reliability and validity

b)      List and explain in detail four types of reliability and validity

c)       Discuss Reliability Coefficient

d)      Identify which two types of validity are criterion related and explain the term criterion related

Doctoral (PhD) Question 3

Quantitative Research

In quantitative research, the description of instrument quality typically deals with two measurements-related concepts – reliability and validity. Below you will find seven questions, regarding reliability and validity, you are to answer five of the seven questions.

A.      Discuss the two types of construct validity. In your discussion, explain how each can be established.

B.      Identify three types of interitem reliability. You are to elaborate on two of the three. Finally, in your discussion, explain how all three are stablished.

C.      As a researcher, when would you calculate the Cronbach’s alpha instead of the Kuder-Richardson procedure.

D.      Explain what face validity shows.

E.       What is the relationship between reliability and validity?

F.       A researcher developed a scale of altruism and wanted to demonstrate if the items truly reflected altruism and not another concept, such as social desirability. The researcher compared the results from her test with results from a test of social desirability and find significant differences between the results of the two tests. What type of validity have the researcher established?? (Be specific)

G.     Identify the type of reliability that is used to measure the following research situations:

1.       A researcher has participants to complete a seven-item leadership style survey and measures the extent to which responses for those seven items are consistent or the same for each participant.

2.       A researcher asks a sample of students who are obese to rank their favorite foods before eating in the school cafeteria and measures the extent to which participants’ rankings are consistent at both times.

3.       A researcher has two observers rate the same classroom and measures the extent to which the two judges agree in their assessment.

Doctoral (PhD) Question 4

Quantitative Research

In quantitative research, the nature of the sample will influence either (1) the accuracy of the inferential guess of (2) the definition of the population toward which the inferential guess is directed. In order to understand the way in which sampling can affect the inferential process as stated above, you are to answer five of the following seven questions related to this concept.

A.      What are two major advantages offered by probability sampling designs over nonprobability sampling designs.

B.      Identify three factors that can determine sample size. How does one of these factors affect the decision about sample size.

C.      As a researcher, how can you increase the probable accuracy of a simple random sample?

D.      All else equal, the bigger the probability sample the better the sample. Why!

E.       Why would a researcher combine probability and nonprobability sampling within the same sampling design?

F.       When is stratified random sampling more efficient than simple random sampling?

G.     If you read two studies, and these studies both used equally representative samples., but Study A gathered data from a sample of 50 and Study B gathered data from a sample of 200, which study would you have the most confident about the results?

Doctoral (PhD) Question 5

Research Methodology

The best type of research methodology a researcher can employ to have confident in a true cause and effect relationship is an experimental design. Below you will find seven questions related to this type of methodology. You are to answer five of the seven questions.

A.      As a researcher, why can you assume that the groups in a pretest posttest control group design are equivalent at the beginning of the experiment?

B.      What are the three requirements for demonstrating cause and effect in an experiment?

C.      Name two advantages of using a pretest in a research design.

D.      Within a true experimental design there are three types of randomization that can be taken. Identify these types of randomization and what step each one take in the process to ensure the quality of true randomness.

E.       The advantage of this design is that a researcher can compare the first two groups to determine how much gain is achieved and can also compare the last two groups to determine whether the treatment is more effective than the control conditions in the absence of a pretest. Name this design and indicate its only potential drawback.

F.       What does the “pre” in “pre-experimental design” represent?

G.     Below there are three research situations dealing with the various types of threats to internal validity. For each situation, Identify the appropriated threat to internal validity.

1.       A physical trainer wants to compare the effects of two types of exercise programs on weight loss. He divides his clients into two groups: one focused on short-interval circuit training and one focused on a cardio warm-up followed by a free-weight workout. Without his knowledge, some of his clients have decided to cut out carbohydrates in their diet with the hope of increasing their weight loss.

2.       The Bar examination (standardized test) is one of several academic standards that a Law student must pass to become a lawyer. On all portions of this examination, scorers are asked to use grading rubrics to score essay sections. Which threat to validity might grading rubrics help reduce.

3.       A group of special education children with emotional disorders is placed in a special program to improve the quality of their social interactions based on their extreme test scores. At the end of the program, the average increase in the quality of their interactions is 57%.

Doctoral (PhD) Question 6


1. A researcher investigated the relationship between demographic factors and the personality types of doctoral students in statistics. The researcher wanted to determine a students’ personality type (sociability, conventional and realistic) based on their demographic characteristics if income, age and attitudes toward statistics. To conduct this study, data from 250 doctoral students from five universities were collected. The discriminant function analysis was used to provide the results for the study.

Answer the questions on the following page using the tables below contain the results to the study.

Function Eigenvalue Percent of Variance Cumulative Percent Canonical Correction
1 .109 79.56 79.56 .314
2 .028 20.44 100.00 .167
Function Wilks Chi Squared df Sig
1 .866 53.87 24 .000
2 .962 14.63 14 .403

Standardized Canonical Discriminant Function Coefficients

  Function 1 Function 2
Income .345 .287
Age .419 .313
Attitudes .799 .422

Classification Results

  Predicted Group Membership  
Personality Types Sociability Conventional Realistic Total
Sociability 102 15 8 125
Conventional 37 10 18 65
Realistic 28 22 10 60
Sociability 81.6 12.0 6.4 100
Conventional 65.7 15.4 27.7 100
Realistic 46.7 36.7 16.7 100

45.7% of original grouped cases correctly classified

A.      How many significant discriminant function(s) was/were identified in the model?

B.      How strong is the association between the corresponding discriminate function scores and group membership?

C.      What percent of the variance in personality types is due by D1?

D.      What percent of the members of sociability group were correctly classified?

E.        What test is used to test the assumption of homogeneity or the variance/covariance matrices across groups in discriminant analysis? If this assumption is violated, name two things you can do as a researcher to overcome this violation.

F.       What discriminating variable(s) had the largest correlation with D1?

G.     What percent of the variance on D1 and D2 is associated with between groups differences?

H.      In a research study where there are 4 categories of the dependent variables and three predictors, how many discriminant functions will be calculated?

I.        What percent of the variability discriminant function can be explained by the different levels in the dependent variable?

Doctoral (PhD) Question 7


A researcher wanted to determine the casual effects of selected demographic factors (gender and ethnicity) on the persistence rate of college students attending a Historically Black University. Further, the researcher wanted to determine whether certain demographic factors have a direct effect on persistence rate, or if their relationship with persistence is due solely on their effects on ACT composition and/or number of development courses taken. The hypothesized causal relationships between the above variables and students’ persistence rate are presented in Figure I.

Answer the questions on the following page using the  model containing the results of the study.

Figure 1

      Z1 Ethnicity   Z2 Gender   ZACT Composition   Z4 Number of Developmental Courses   Z5 Persistence Rate  

A.      Is this a recursive or non-recursive model? ___________________________________________

B.      How many endogenous variables are in this model? ____________________________________

Name them. ____________________________________________________________________


C.      How many exogenous variables are in this model? _____________________________________

Name them. ____________________________________________________________________


D.      What is the indirect effect of Ethnicity on Persistence Rate within the model?

E.       What is the direct effect of ACT Composite on Persistence rate within the model?

F.       What is the indirect effect of Gender on Persistence rate within the model?

G.     What is the total effect on ACT Composite upon Persistence rate within the model?

H.      How many structural coefficients were in the casual model?

Doctoral (PhD) Question 8


A researcher conducted a study to assess the contracting of a sexually transmitted disease (yes or no) among college students as a function of ethnicity and age. Two hundred fifty African American and 125 white college students were randomly selected to participate in the study. The outcome variable that is recorded is whether the student did contract (1) or did not contract (0) a sexual transmitted disease. The predictor variable ethnicity is categorical, and it is coded 1 = African American and 0 = White American. The African American groups will be used as the reference group. A binary logistic regression model was developed and calculated to provide results for the study.

Answer the questions on the following page using the tables below

Table 1.1

College students who have contracted a Sexually Transmitted Disease by Gender and Age

  Ethnicity   Age Sexual Yes Disease No   Odds
White 20 or Below 27 45 0.600
  21 or Above 18 35 0.514
  Subtotal 45 80 0.562
African American 20 or Below 84 63 1.333
  21 or Above 31 72 0.431
  Subtotal 115 135 0.851

Table 1.2

Model Summary

  Chi Square df Sig
Method 11.251 2 .008
-2 log likelihood = 37.360     NagelKerke R Square = .255

Table 1.3

Classification Table for Sexually Transmitted Disease

      Predicted Percentage Correct
    Yes No  
Observed Yes 111 49 74.0
  No 108 107 70.4
  Overall percentage = 58.4   Cut Value is .50

Table 1.4

Variables in the Equation

Variable B S.E. Wald df Sig Exp (B)
African American 1.5883 .7000 5.1479 1 .0233 * 1.516
Age 2.1194 .7468 8.0537 1 .0045 ** .493
Constant -2.0446 .6100        

* p < .05

* p < .01

A.      The model predicts correctly ____________________ students out of ________________ that would contract a sexually transmitted disease.

B.      The odds for African American college students to have contracted a sexually transmitted disease are _________________ times higher than for white students, other things being equal.

C.      White College students regardless of age have an odd of contracting a sexually transmitted disease of

D.      Test the overall model that the predictors variables ethnicity and age were statistically reliable in predicting those college students who would contract a sexually transmitted disease and those who would not.

E.       What percent of the variance in odds of contracting a sexually transmitted disease can be explained by ethnicity and age combined?

F.       How many African American college students contracted sexually transmitted disease for each one thousand who have not?

G.     Based on the odds ratio, for 1 year increases in age the predicted odds of contracting a sexually transmitted disease is

Doctoral (PhD) Question 9


For each of the following research situations determine the appropriate statistical test to be used. (Be specific for example one-way, two-way, or three ANOVA)

A.      The Texas Department of Health and Social Services reimburses nursing homes in the state for the services provided. The department develops a set of formulas for rates for each facility, based on factors such as level of care, mean wage rate. And average wage rate in the state. Nursing homes were classified in the State of Texas basis of ownership (private party, A non-profit organization, and government). A researcher wanted to investigate the effects of ownership on costs. Four costs, computed on a per-patient-day basis and measured in hours per patient day, were selected for analysis (cost of nursing labor, cost of dietary labor, cost of plant operation and maintenance labor and cost of housekeeping and laundry labor).

B.      A researcher was concerned about the effect of family background and appearance on the amount of time donated to help a particular individual. Regarding family background, the female participants were classified into two groups (codependent, women with an alcoholic parent; non-codependent, women with non-alcoholic parents). Members of these two groups were randomly assigned to one of two conditions; they were asked to donate time to help a man who was described to them as either Mr. Wrong (exploitative, selfish, and dishonest) or Mr. Right (nurturant, helpful). The researcher predicted that women from a non-dependent/non-alcoholic family background would be more helpful to a person described as nurturant and helpful, whereas women from a codependent/alcoholic family background would be more helpful to a person described as needy, exploitative, and selfish.

C.      A researcher wanted to investigate the effect of authoritarian personality characteristics on the academic success of doctoral students in the College of Education. The students were randomly assigned to four groups (very low, low, high, and very high) regarding personality trait. A concomitant variable was used, representing the average anxiety level of the student.

D.      An athletic trainer was interested in football players (N=30) who participated in an intensive fitness program sponsored by the university. Each player was put on a program of exercise (average 2.5 an hour) and was given a dieting regimen in which the caloric intake was recorded for each meal. The weight loss for each football player was measured after 2 months on this routine. A moderate association seems to exist between weight loss (in pounds) and average daily amount of exercise (in hours). The relationship between the two above variables increased dramatically when each football player consumed the same daily average number of calories. (average calorie intake was held constant).

E.       A researcher wanted to examine the attendance rate change data for the 50 states in America. The percent change in attendance rate from the 2000 Department of Education statistics to the 2010 Department of Education, Statistics for each state was coded as 0 or 1, according to whether the change was below or above the media change for all states. The demographic variables used to see how well the states were classified (as below or above the median were (a) per capita income for each state (in million), (b) percent dropout rate; (c) percent of disciplinary referrals and (d) per pupil expenditures (in thousands). Test the relationship between demographic factors and attendance rate.

F.       A researcher conducted a study on the relationship between pollution variables and mortality (death per 100,000 population) from 50 metropolitan areas in the United States. The unique contribution of the variables annual mean precipitation (in inches), median number of school years completed (education), percentage of the population that is non-white, relative pollution potential of oxides of nitrogen (NOx) and relative pollution potential of sulfur dioxide (SO2) on morality were used as independent variables. The control variable of precipitation, education and non-white were entered in step one by the researcher. The pollution variables were entered in step two. Controlling the aforementioned variables in step one, is there evidence that mortality is associated with either of the pollution variables.

Doctoral (PhD) Question 10


Below there are three questions dealing with univariate and multivariable ANOVA.

A.      As a researcher, you compared two different teaching methods and that the covariate was IQ. The homogeneity of regression sloped was tested and rejected. (1) What does this imply. (2) Name two things you can do to correct this violation.

B.      As part of a recent-study in the Department of Mathematics, three task were employed to ascertain differences between good and poor undergraduate students on computation assignments when dealing with fundamentals of mathematics: working with decimals dealing with negative numbers and summation notation. In the following table are means and standard deviations for the percentage of correct answers on the three dependent variables. There were 15 students in each group.

Task Good Computationer    M   SD Poor Computationer      M   SD
  17.29 10.15 14.30 11.22
Observed 15.89   9.27 12.66 10.28
  18.00   6.25 15.00   9.25

The following is from the results section of the above study:

                The data were analyzed using a multivariate analysis or covariance using academic variables (grade point average, math usage SAT subtest and composite SAT) as covariates, math ability as the independent variable, and math scores (number of correct decimal problems, number of correct negative problems and number of correct summation notation problems) as the dependent variables. The overall test was significant, F (3, 23) = 7.86, p < .001. To control for experiment wise Type 1 error at .05, each of the three univariate analyses was conducted as a per comparison rate of .012. No significant difference was observed between groups on decimals, univariable F (1, 25) = 2.62, p > .05. Similarly, no significant difference was observed between groups on negative problems, univariate F (1 25) = 1.46, p > .05.

                However, students with good computation skills obtained significantly higher scores on the summation problems than students with computation skills, univariate F (1, 25) = 18.26, p < .001.

Based on the above results answer the following:

C.      (1) From the above. Result, can you as a researcher be confident that the covariates are appropriate here?

(2) The “overall” multivariate test referred to is not identified as to whether it is Wilks’ Lambda, Roy’s largest root, and so on. Would it make a difference as to which multivariate test was employed in this case?

(3) The researcher opined (stated) about controlling the experiment-wise error rate at .05 by conducting each test at the .012 level of significance. Which post hoc procedure should be employed here?

(4) Is there a sufficient number of participants for the readers of this study to have confidence in the reliability of the adjusted means?

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