Social Work 6311

Description

Statistical analysis software such as SPSS is a valuable tool that helps researchers perform complex calculations. However, to use such a tool effectively, the study must be well designed. The social worker must understand the study’s purpose and select the most appropriate design. The social worker must correctly represent the relationship being examined and the variables involved. Finally, they must enter those variables correctly into the software package.

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In this Assignment, you analyze in detail the decisions made in the Chi-Square case study and the relationship between study design and statistical analysis.

RESOURCES

Be sure to review the Learning Resources before completing this activity.
Click the weekly resources link to access the resources.

WEEKLY RESOURCES

TO PREPARE
Access the Social Work Case Studies media and navigate to the Chi-Square case study.
As you again review the case, this time focus on the purpose of the evaluation, the choice of a chi-square statistic, and the research design. Consider what the statistical results indicate about the program.
BY DAY 7

Submit a 1-page paper analyzing the relationship between study design and statistical analysis used in the case study.

Explain why you think that the agency created a plan to evaluate the program.
Explain why the social work agency chose to use a chi-square statistic to evaluate whether there is a difference between those who participated in the program and those who did not. (Hint: Think about the level of measurement of the variables.)
Describe the research design in terms of observations (O) and interventions (X) for each group.
Interpret the chi-square output data and provide support for your interpretation. (Hint: Review the value.) What do the data say about the program?

Use the Learning Resources to support your paper. Make sure to include appropriate APA citations and a reference list.

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Chi-Square
SOCW 6311
Molly, an administrator with a regional organization that advocates for alternatives to
long-term prison sentences for nonviolent offenders, asked a team of researchers to
conduct an outcome evaluation of a new vocational rehabilitation program for recently
paroled prison inmates. The primary goal of the program is to promote full-time
employment among its participants.
To evaluate the program, the evaluators decided to use a quasi-experimental research
design. The program enrolled 30 individuals to participate in the new program.
Additionally, there was a waiting list of 30 other participants who planned to enroll after
the first group completed the program. After the first group of 30 participants completed
the vocational program (the “intervention” group), the researchers compared those
participants’ levels of employment with the 30 on the waiting list (the “comparison”
group).
The research question for the study is: Is there a relationship between the independent
variable, treatment, and the dependent variable, employment level? In other words, is
there a difference in the number of participants who are not employed, employed parttime, and employed full-time in the program and the control group (i.e., waitlist group)?
Data Collection and Analysis
In order to collect data on employment levels, the probation officers for each of the 60
people in the sample (those in both the intervention and comparison groups) completed
a short survey on the status of each client in the sample. The survey contained
demographic questions that included an item that inquired about the employment level
of the client. This was measured through variables identified as none, part-time, or fulltime. A hard copy of the survey was mailed to each probation officer and a stamped,
self-addressed envelope was provided for return of the survey to the researchers.
After the surveys were returned, the researchers entered the data into an SPSS
program for statistical analysis. Because both the independent variable (participation in
the vocational rehabilitation program) and dependent variable (employment outcome)
used nominal/categorical measurement, the bivariate statistic selected to compare the
outcome of the two groups was the Pearson chi-square.
The chi-square test for independence is used to determine whether there is a
relationship between the two variables that are categorical in the level of measurement.
In this case, the variables are: employment level and treatment condition. It tests
whether there is a difference between groups.
The hypotheses are:
H0 (The null hypothesis): There is no difference in the proportions of individuals in the
three employment categories between the treatment group and the waitlist group. In
© 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014). Social
work case studies: Concentration year. Laureate International Universities Publishing.
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other words, the frequency distribution for variable 2 (employment) has the same
proportions for both categories of variable 1 (program participation).

Note: It is the null hypothesis that is actually tested by the statistic. A chi-square
statistic that is found to be statistically significant (p < .05) indicates that we can reject the null hypothesis (understanding that there is less than a 5% chance that the relationship between the variables is due to chance). H1 (The alternative hypothesis): There is a difference in the proportions of individuals in the three employment categories between the treatment group and the waitlist group. • Note: The alternative hypothesis states that there is a difference. It would allow us to say that it appears that the treatment (vocational rehab program) is effective in increasing the employment status of participants. Results After all of the information was entered into the SPSS program, the following output charts were generated: Table 1. Case Processing Summary Program Participation *Employment N 59 Valid Percent 98.3% Cases Missing N Percent 1 1.7% N 60 Total Percent 100.0% The first table, titled “Case Processing Summary,” provided the sample size (N = 59). Information for one of the 60 participants was not available, while the information was collected for all of the other 59 participants. Table 2. Program Participation *Employment Cross Tabulation 5 16.7% Employment Part-Time Full-Time 7 18 23.3% 60.0% 30 100.0% 16 55.2% 7 24.1% 6 20.7% 29 100.0% 21 35.6% 14 23.7% 24 40.7% 59 100.0% None Program Intervention Participation Group Total Count % within Program Participation Comparison Count % Group within Program Participation Count % within Total © 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014). Social work case studies: Concentration year. Laureate International Universities Publishing. 3 Program Participation The second table, “Program Participation Employment Cross Tabulation,” provided the frequency table, which showed that among participants in the intervention group, 18 or 60% were found to be employed full time, while 7 or 23% were found to be employed part time, and 5 or 17% were unemployed. The corresponding numbers for the comparison group (parolees who had not yet enrolled in the program but were on the waiting list for admission) showed that only 6 or 21% were employed full-time, while 7 or 24% were employed part time, and 16 or 55% were unemployed. Table 3. Chi-Square Tests Value df Asymp. Sig (2-sided) .003 .002 .001 Pearson Chi-Square 11.748a 2 Likelihood Ratio 12.321 2 Linear-by-Linear 11.548 1 Association N of Valid Cases 59 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.88. The third table, which provided the outcome of the Pearson chi-square test, found that the difference between the intervention and comparison groups were highly significant, with a p value of .003, which is significantly beyond the usual alpha-level of .05 that most researchers use to establish significance. Discussion These results indicate that the vocational rehabilitation intervention program may be effective at promoting full-time employment among recently paroled inmates. However, there are multiple limitations to this study, including that 1) no random assignment was used, and 2) it is possible that differences between the groups were due to preexisting differences among the participants (such as selection bias). Potential future studies could include a matched comparison group or, if possible, a control group. In addition, future studies should assess not only whether or not a recently paroled individual obtains employment but also the degree to which he or she is able to maintain employment, earn a living wage, and satisfy other conditions of probation. © 2022 Walden University, LLC. Adapted from Plummer, S.-B., Makris, S., & Brocksen, S. M. (Eds.). (2014). Social work case studies: Concentration year. Laureate International Universities Publishing. A Short Course in Statistics This information was prepared to call your attention to some basic concepts underlying statistical procedures and to illustrate what types of research questions can be addressed by different statistical tests. You may not fully understand these tests without further study. However, you are strongly encouraged to note distinctions related to the type of measurement used in gathering data and the choice of statistical tests. Feel free to post questions in the “Contact the Instructor” section of the course. Statistical Symbols µ mu (population mean) α alpha (degree of error acceptable for incorrectly rejecting the null hypothesis, probability that results are unlikely to occur by chance) ≠ (not equal) ≥ (greater than or equal to) ≤ less than or equal to) ᴦ (sample correlation) ρ rho (population correlation) t r (t score) z (standard score based on standard deviation) χ2 Chi-square (statistical test for variables that are not interval or ratio scale [i.e., nominal or ordinal]) p (probability that results are due to chance) Descriptives Descriptives are statistical tests that summarize a data set. They include calculations of measures of central tendency (mean, median, and mode) and dispersion (e.g., standard deviation and range). Note: The measures of central tendency depend on the measurement level of the variable (nominal, ordinal, interval, or ratio). If you do not recall the definitions for these levels of measurement, see https://www.questionpro.com/blog/nominal-ordinal-intervalratio/ You can only calculate a mean and standard deviation for interval or ratio scale variables. For nominal or ordinal variables, you can examine the frequency of responses. For example, you can calculate the percentage of participants who are male and female; or the percentage of survey respondents who are in favor, against, or undecided. Often nominal data is recorded with numbers, e.g., male=1, female=2. Sometimes people are tempted to calculate a mean using these coding numbers. But that would be © 2022 Walden University, LLC Page 1 of 5 meaningless. Many questionnaires (even course evaluations) use a Likert scale to represent attitudes along a continuum (e.g., Strongly like … Strongly dislike). These too are often assigned a number for data entry, e.g., 1–5. Suppose that most of the responses were in the middle of a scale (3 on a scale of 1–5). A researcher could observe that the mode is 3, but it would not be reasonable to say that the average (mean) is 3 unless there were exact differences between 1 and 2, 2 and 3, etc. The numbers on a scale such as this are ordered from low to high or high to low, but there is no way to say that there is a quantifiably equal difference between each of the choices. In other words, the responses are ordered but not necessarily equal. Strongly agree is not five times as large as strongly disagree. (See the textbook for differences between ordinal and interval scale measures.) Inferential Statistics Statistical tests for analysis of differences or relationships are inferential, allowing a researcher to infer relationships between variables. All statistical tests have what are called assumptions. These are essentially rules that indicate that the analysis is appropriate for the type of data. Two key types of assumptions relate to whether the samples are random and the measurement levels. Other assumptions have to do with whether the variables are normally distributed. The determination of statistical significance is based on the assumption of the normal distribution. A full course in statistics would be needed to explain this fully. The key point for our purposes is that some statistical procedures require a normal distribution and others do not. Understanding Statistical Significance Regardless of what statistical test you use to test hypotheses, you will be looking to see whether the results are statistically significant. The statistic p is the probability that the results of a study would occur simply by chance. Essentially, a p that is less than or equal to a predetermined (α) alpha level (commonly .05) means that we can reject a null hypothesis. A null hypothesis always states that there is no difference or no relationship between the groups or variables. When we reject the null hypothesis, we conclude (but don’t prove) that there is a difference or a relationship. This is what we generally want to know. Parametric Tests Parametric tests are tests that require variables to be measured at interval or ratio scale and for the variables to be normally distributed. © 2022 Walden University, LLC Page 2 of 5 These tests compare the means between groups, which is why they require the data to be at an interval or ratio scale. They make use of the standard deviation to determine whether the results are likely to occur or very unlikely in a normal distribution. If they are very unlikely to occur, then they are considered statistically significant. This means that the results are unlikely to occur simply by chance. The T-Test Common uses: • To compare mean from a sample group to a known mean from a population • To compare the mean between two samples o The research question for a t-test comparing the mean scores between two samples is: Is there a difference in scores between group 1 and group 2? The hypotheses tested would be: H0: µgroup1 = µgroup2 H1: µgroup1 ≠ µgroup2 • To compare pre- and post-test scores for one sample o The research question for a t-test comparing the mean scores for a sample with pre and posttests is: Is there a difference in scores between time 1 and time 2? The hypotheses tested would be : H0: µpre = µpost H1: µpre ≠ µpost Example of the form for reporting results: The results of the test were not statistically significant, t (57) = .282, p = .779, thus the null hypothesis is not rejected. There is not a difference in between pre and post scores for participants in terms of a measure of knowledge (for example). An explanation: The t is a value calculated using means and standard deviations and a relationship to a normal distribution. If you calculated the t using a formula, you would compare the obtained t to a table of t values that is based on one less than the number of participants (n-1). n-1 represents the degrees of freedom. The obtained t must be greater than a critical value of t in order to be significant. For example, if statistical analysis software calculated that p = .779, this result is much greater than .05, the usual alpha-level which most researchers use to establish significance. In order for the t-test to be significant, it would need to have a p ≤ .05. ANOVA (Analysis of Variance) Common uses: Similar to the t-test. However, it can be used when there are more than two groups. The hypotheses would be H0: µgroup1 = µgroup2 = µgroup3 = µgroup4 H1: The means are not all equal (some may be equal) © 2022 Walden University, LLC Page 3 of 5 Correlation Common use: to examine whether two variables are related, that is, they vary together. The calculation of a correlation coefficient (r or rho) is based on means and standard deviations. This requires that both (or all) variables are measured at an interval or ratio level. The coefficient can range from -1 to +1. An r of 1 is a perfect correlation. A + means that as one variable increases, so does the other. A – means that as one variable increases, the other decreases. The research question for correlation is: “Is there a relationship between variable 1 and one or more other variables?” The hypotheses for a Pearson correlation: H0: ρ = 0 (there is no correlation) H1: ρ ≠ 0 (there is a real correlation) Nonparametric Tests Nonparametric tests are tests that do not require variables to be measured at interval or ratio scale and do not require the variables to be normally distributed. Chi-Square Common uses: Chi-square tests of independence and measures of association and agreement for nominal and ordinal data. The research question for a chi-square test for independence is: Is there a relationship between the independent variable and a dependent variable? The hypotheses are: H0 (The null hypothesis) There is no difference in the proportions in each category of one variable between the groups (defined as categories of another variable). Or: The frequency distribution for variable 2 has the same proportions for both categories of variable 1. H1 (The alternative hypothesis) There is a difference in the proportions in each category of one variable between the groups (defined as categories of another variable). The calculations are based on comparing the observed frequency in each category to what would be expected if the proportions were equal. (If the proportions between observed and expected frequencies are equal, then there is no difference.) © 2022 Walden University, LLC Page 4 of 5 Other Nonparametric Tests Spearman rho: A correlation test for rank ordered (ordinal scale) variables. © 2022 Walden University, LLC Page 5 of 5 Purchase answer to see full attachment