# SOCW6311 Learning Resources

Required Readings

Dudley, J. R. (2020). Social work evaluation: Enhancing what we do (3rd ed.) Oxford University Press.

Chapter

SOCW6311 Learning Resources

Required Readings

Dudley, J. R. (2020). Social work evaluation: Enhancing what we do (3rd ed.) Oxford University Press.

Chapter 9, “Is the Intervention Effective?” (pp. 226–235: Read from “Determining a Causal Relationship” to “Outcome Evaluations for Practice”)

Plummer, S.-B., Makris, S., & Brocksen S. (Eds.). (2014b). Social work case studies: Concentration year. Baltimore, MD: Laureate International Universities Publishing. [Vital Source e-reader].

Read the following section:

“Social Work Research: Chi Square” (pp. 63–65)

Document: Stocks, J. T. (2010). Statistics for social workers. In B. Thyer (Ed.), The handbook of social work research methods (2nd ed., pp. 75–118). Thousand Oaks, CA: Sage. (PDF)

Copyright 2010 by Sage Publications, Inc.

Reprinted by permission of Sage Publications, Inc. via the Copyright Clearance Center.

Trochim, W. M. K. (2006). Internal validity. Retrieved from http://www.socialresearchmethods.net/kb/intval.php

Be sure to click on all the links in the narrative.

Document:Week 4: A Short Course in Statistics Handout (PDF)

Document: Week 4: Handout: Chi-Square findings (PDF)

Discussion: Selection of a Statistical Analysis Approach

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. 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.

By Day 3

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. © 2014 Laureate Education, Inc. Page 1 of 5

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

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

© 2014 Laureate Education, Inc. Page 2 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.

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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.