Answer

                                Assignment (Part 1): Testing Hypotheses for Means

Scenario one

As an international development researcher, you would like to know African Citizen’s perceptions about current levels of democracy. Your working hypothesis is that a series of reforms have increased African views of the level of democracy today. You do not have a good research design to compare attitudes before and after the reforms, but know that leaders and development experts would like to see a value of 6, on the scale of 1–10. Using the data from the 2015 Afrobarometer, determine whether perceptions about current levels of democracy statistically differ from a value of 6. Please provide: a 1–2 APA style paragraph statement that furnishes an answer to this question, note the relevant statistics, comment on meaningfulness and include your relevant SPSS output.

Response

The research question:

Is the mean of perceptions about current levels of democracy of the population represented by the people in this study significantly different than 6?

Hypotheses:

There is no difference in the mean of perceptions about current levels of democracy in the population represented by the people in this study and the expected population value of 6.

To test the hypotheses, a one sample t test is used because we want to determine whether the sample in this study came from a population whose perceptions about level of democracy would be a 6, on a 1-10 scale.

Level of confidence: 95%

GET

  FILE=’C:\Users\ADMIN\Desktop\online work\spss\568903\Afrobarometer (student 8210) (2).sav’.

DATASET NAME DataSet2 WINDOW=FRONT.

DATASET CLOSE DataSet1.

T-TEST

  /TESTVAL=6

  /MISSING=ANALYSIS

  /VARIABLES=Q46A

  /CRITERIA=CI(.95).

=___5.52___            sd =_2.883______   n =_46940______   t =__-35.924_____   p =____less than 0.05___          

From the one sample t test results shown in the tables above, the mean of perceptions about current levels of democracy was 5.52(2.88), a value lower than the expected value of 6. The mean difference of -0.478 (95% CI -0.5 to -0.45) was statistically significant; t(46939) = -35.92, p < 0.05. The null hypothesis is thus rejected and the conclusion is that the mean difference is not due to chance. This finding underpins the need for more vigilant efforts towards instituting social reforms that enhance democracy.

Scenario two

As an international development researcher, you have already tested whether perceptions about the current levels of democracy differ from a value of 6. Given recent social change movements in North Africa, you now want to determine whether there is a statistical difference in these perceptions between North Africa and Southern Africa. Using the data from the 2015 Afrobarometer, please provide: a 1–2 APA style paragraph statement that furnishes an answer to this question, note the relevant statistics, comment on meaningfulness, and include your relevant SPSS output.

Response

Research question

Is there a difference in perceptions about current levels of democracy between North Africa and Southern Africa?

Hypothesis

There is no difference in perceptions about current levels of democracy between North Africa and Southern Africa

Confidence level: 95%

Dependent variable is perceptions about level of democracy today and the independent variable is country of origin

This involves two separate groups. The appropriate test to use is the independent samples t test.

T-TEST GROUPS=COUNTRY.BY.REGION(3 4)

  /MISSING=ANALYSIS

  /VARIABLES=Q46A

  /CRITERIA=CI(.95).

The answer to the research question is yes, there is a difference in perceptions about current levels of democracy between North Africa and Southern Africa. There is a statistically significant difference in the mean level of democracy today between Southern Africa and North. At 95% confidence level, alpha is found to be less than 0.05.

Evidence: The analysis has shown that Southern Africa had statistically significant higher perceptions about current level of democracy 5.78 (2.795) than North Africa 4.90 (3.092), t(21395) = 19.453, p<0.05, with a difference of 0.879 (95% CI 0.790 to .967). The conclusion is that perceptions about current level of democracy have a causal link with country of origin and it may underline the importance of creating reforms that enhance democracy in regions with low perceptions about democracy.

Scenario three

As an educational researcher, would like to know whether high school student’s perceptions about mathematical utility changed between their freshman and senior year. Each respondent is asked the same series of questions about the utility of mathematics in their future during their freshman and senior year. These questions are combined to form one variable of mathematical utility; higher values indicate higher levels of mathematical utility. Using the High School Longitudinal Survey, please provide: a 1–2 APA style paragraph statement that furnishes an answer to this question, note the relevant statistics, comment on meaningfulness, and include your relevant SPSS output.

Response:

Research question:

Is there a difference in students perceptions about future utility of mathematics between their freshman year and senior year?

Hypothesis:

There is no difference in students’ perceptions about future utility of mathematics between their freshman year and senior year

Since the question involves comparing the same group of people at two different occasions on their perceptions about future mathematics utility, the appropriate t test is the paired samples t test. In this case the dependent variable is students’ mathematics utility.

T-TEST PAIRS=X1MTHUTI WITH X2MTHUTI (PAIRED)

  /CRITERIA=CI(.9500)

  /MISSING=ANALYSIS.

The mean perception about mathematics utility for the students at freshman year was -.0096 (.99040) while at senior year the mean was 0.0059(1.00682). The paired samples t –test shows that although perceptions about mathematics utility was higher at senior year, the change was not statistically significant t (16020) = -1.649, p = 0.099.  The mean of the difference was -.01556 (1.19384); (95% CI -.03404 to 0.00293). Given these results, we fail to reject the null hypotheses that there is no difference in students’ perceptions about mathematics utility in freshman year and in the senior year. It can be concluded that perceptions about mathematics utility has no causal link with year of study.

Assignment (Part 2): t Tests in Practice

Critical evaluation of a scholarly article

Names of author (s): Ruth L Oreinstein

Title of article: Measuring Executive Coaching Efficacy? The Answer Was Right Here All the Time

Title of journal, volume number, date, month and page numbers: Consulting Psychology Journal: Practice and Research, Vol. 58, No. 2, 106–116

Issue discussed: measurement of executive coaching

The author’s purpose, approach or methods, hypothesis, and major conclusions: the paper demonstrates the executive coaching efficacy can be measured empirically by applying the Empathic Organic Questionnaire to executive coaching. It summarizes a case in which an empathic organic questionnaire was used to measure coaching efficiency at a certain organization. The hypotheses were that the coaching client would be rated as changing most, the behaviors directly related to stated coaching objectives; then the behaviors indirectly related to coaching objectives and finally the behaviors not addressed in coaching.

Critique

The title of the article is not as informative as it should be, from reading it, the reader cannot immediately tell what the paper is about. The abstract has addressed the issues discussed in the paper to a large extent. It covers a brief background on how executive coaching can be measured empirically. The methods used and analytical tools are explained clearly. The purpose of the article has been explained clearly in the introduction, with valid references in literature. The discussion of the issues is relevant in this study. Some of the references however are repeated and should be deleted. While the author has tried to explain the issue under discussion she seems biased on support of the tool she sets out to test.

Methods      

The sampling techniques are not clear, and one cannot be sure about representativeness of the sample of 20 participants who completed the survey at evaluation stage. Additionally, the sample of participants at assessment stage was less that that at evaluation (15 vs 20). This could have undermined the validity of the findings.  The participant selection process may have suffered selection bias because they were all selected by the coaching client which could have also let to a possible information bias, altogether undermining internal validity. The methods used in this case study have been clearly outlined, which provides a roadmap for any other researchers interested in replicating it. The study design selected, which is a before and after experimental study design is appropriate for this research, because it allows for comparison of measurements taken before client coaching and after the coaching.

Why did the authors use this t test?

A paired sample t test allows for comparison of measurements taken from the same subjects at different points in time. In this case, paired sample t test was applicable because the investigators wanted to measure the efficacy of an intervention ‘coaching efficacy’ by comparing data taken on various aspects of management before the intervention and after.

Do you think it’s the most appropriate choice? Why or why not?

Yes, t test would be the most appropriate test given that the research involved comparison of measurements taken from the same group of people, before an intervention and after.

Did the authors display the data?

Yes, data was displayed in three different tables: Table 1 showed those items directly related to the coaching objectives table two showed the items indirectly related to the coaching objectives while table three comprised of control items, considered unrelated to the coaching objectives. In each of the tables, the significant items have been identified.

Do the results stand alone? Why or why not?

Yes, the tables show results for individual items of the assessment tool.