Conducting statistical analysis can prove an intimidating task for some students. However, statistical analysis is the critical component of social work research that can link interventions to client outcomes. Statistical analysis software simplifies the task of the mathematical computations. It is the social worker’s responsibility to choose the proper research design and type of statistical analysis.

This week, you analyze the relationship between study design and statistical analysis in a case study. You also interpret the results of the research from the case study and a SPSS data that will be provided to you.

Though data analysis occurs after the study has completed a data collection stage, the researcher needs to have in mind what type of analysis will allow the researcher to obtain an answer to a research question. The researcher must understand the purpose of each method of analysis, the characteristics that must be present in the study for the design to be appropriate and any weaknesses of the design that might limit the usefulness of the study results. Only then can the researcher select the appropriate design. Choosing the appropriate design enables the researcher to claim the data that is potential evidence that provides information about the relationship being studied. Notice that it is not the statistical test which tells us that research is valid, rather, it is the research design. Social workers must be aware of and adjust any limitations of their chosen design that may impact the validity of the study.

To prepare for this Discussion, review the handout, A Short Course in Statistics and pages 210–220 in your course text *Social Work Evaluation: Enhancing What We Do*. If necessary, locate and review online resources concerning internal validity and threats to internal validity. Then, review the “Social Work Research: Chi Square” case study located in this week’s resources. Consider the confounding variables, that is, factors that might explain the difference between those in the program and those waiting to enter the program

Part 1- 3 paragraphs

**Post** an interpretation of the case study’s conclusion that “the vocational rehabilitation intervention program may be effective at promoting full-time employment.” Describe the factors limiting the internal validity of this study, and explain why those factors limit the ability to draw conclusions regarding cause and effect relationships.

Part 2- 1 page paper APA

Statistical analysis software is a valuable tool that helps researchers perform the complex calculations. However, to use such a tool effectively, the study must be well designed. The social worker must understand all the relationships involved in the study. He or she 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, he or she must enter those variables correctly into the software package. This assignment will allow you to analyze in detail the decisions made in the “Social Work Research: Chi Square” case study and the relationship between study design and statistical analysis. Assume that the data has been entered into SPSS and you’ve been given the output of the chi-square results. (See Week 4 Handout: Chi-Square findings).

To prepare for this Assignment, review the **Week 4 Handout: Chi-Square Findings** and follow the instructions.

**Submit** a 1-page paper of the following:

- An analysis of the relationship between study design and statistical analysis used in the case study that includes:
- An explanation of why you think that the agency created a plan to evaluate the program
- An explanation of why the social work agency in the case study 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**) - A description of the research design in terms of observations (O) and interventions (X) for each group.
**Interpret the chi-square output data. What do the data say about the program?**

Week 4 Handout: Chi-Square Findings

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 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 part-time and employed full-time in the program and the control group (i.e., waitlist group)? 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 other words, the frequency distribution for variable 2 (employment) has the same proportions for both categories of variable 1 (program participation).

** It is the null hypothesis that is actually tested by the statistic. A chi square statistic that is found to be statistically significant, (e.g. 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.

** The alternative hypothesis states that there is a difference. It would allow us to say that it appears that the treatment (voc rehab program) is effective in increasing the employment status of participants.

Assume that the data has been collected to answer the above research question. Someone has entered the data into SPSS. A chi-square test was conducted, and you were given the following SPSS output data:

,

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Week 4: A Short Course in Statistics Handout

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 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) χ

2 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 http://www.ats.ucla.edu/stat/mult_pkg/whatstat/nominal_ordinal_interval.htm 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

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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.

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These tests compare the means between groups. That 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)

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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)

Non-parametric Tests Nonparametric tests are tests that do not require variable 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.)

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See the SOCW 6311: Week 4 Working With Data Assignment Handout to explore the Crosstabs procedure for chi square analysis.

Other non-parametric tests: Spearman rho: A correlation test for rank ordered (ordinal scale) variables.

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