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Assignment: Working with Data

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:

1. An analysis of the relationship between study design and statistical analysis used in the case study that includes:

0. An explanation of why you think that the agency created a plan to evaluate the program

0. 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)

0. A description of the research design in terms of observations (O) and interventions (X) for each group.

0. Interpret the chi-square output data. What do the data say about the program?

Resources



https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-6311/artifacts/Chi_Square_CaseStudy.pdf


https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-6311/artifacts/USW1_SOCW_6311_Week04_05_statisticsForSocialWorkers.pdf


http://www.socialresearchmethods.net/kb/intval.php


https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-6311/artifacts/USW1_SOCW_6311_Week04_aShortCourseInStatisticsHandout.pdf

https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-6311/artifacts/USW1_SOCW_6311_Week4HandoutChi-SquareFindings.pdf

Assignment: Working

with

Data

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 pa

ckage. 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’v

e 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 an

alysis of the relationship between study design and statistical analysis used in the

case study that includes:

o

An explanation of why you think that the agency created a plan to evaluate the

program

o

An explanation of why the social work agency in the case s

tudy 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

)

o

A description of the research design in ter

ms of observations (O) and

interventions (X) for each group.

o

Interpret the chi

square output data. What do the data say about the

program?

Resources

https://content.waldenu.edu/content/dam/laureate/laureate

academics/wal/ms

socw/socw

6311/artifacts/Chi_Square_Case

Study.pdf

https://content.waldenu.edu/content/dam/laureate/laureate

academics/wal/

ms

socw/socw

6311/artifacts/USW1_SOCW_6311_Week04_05_statisticsForSocialWorkers.pdf

http://www.socialresearchmethods.net/kb/intval.php

https://content.waldenu.edu/content/dam/laureate/laureate

academics/wal/ms

socw/socw

6311/artifacts/USW1_SOCW_6311_Week04_aShortCours

eInStatisticsHandout.pdf

Assignment: Working with Data

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:

o An explanation of why you think that the agency created a plan to evaluate the

program

o 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)

o A description of the research design in terms of observations (O) and

interventions (X) for each group.

o Interpret the chi-square output data. What do the data say about the

program?

Resources

https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-

6311/artifacts/Chi_Square_CaseStudy.pdf

https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-

6311/artifacts/USW1_SOCW_6311_Week04_05_statisticsForSocialWorkers.pdf

http://www.socialresearchmethods.net/kb/intval.php

https://content.waldenu.edu/content/dam/laureate/laureate-academics/wal/ms-socw/socw-

6311/artifacts/USW1_SOCW_6311_Week04_aShortCourseInStatisticsHandout.pdf

RESEARCH

63

Social Work Research:
Chi Square

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 partici-
pants 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).

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 full-time. 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 rehabili-
tation 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.

SOCIAL WORK CASE STUDIES: CONCENTRATION YEAR

64

After all of the information was entered into the SPSS program,
the following output charts were generated:

TABLE 1. CASE PROCESSING SUMMARY

Cases

Valid Missing Total

N Percent N Percent N Percent

Program
Participation
*Employment

59 98.3% 1 1.7% 60 100.0%

TABLE 2. PROGRAM PARTICIPATION
*EMPLOYMENT CROSS TABULATION

Employment

TotalNone
Part-
Time

Full-
Time

Program
Participation

Intervention
Group

Count
% within
Program
Participation

5
16.7%

7
23.3%

18
60.0%

30
100.0%

Comparison
Group

Count
% within
Program
Participation

16
55.2%

7
24.1%

6
20.7%

29
100.0%

Total Count
% within
Program
Participation

21
35.6%

14
23.7%

24
40.7%

59
100.0%

TABLE 3. CHI-SQUARE TESTS

Value df Asymp. Sig. (2-sided)

Pearson Chi-Square 11.748a 2 .003

Likelihood Ratio 12.321 2 .002

Linear-by-Linear
Association

11.548 1 .001

N of Valid Cases 59
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.88.

RESEARCH

65

The first table, titled Case Processing Summary, provided the
sample size (N 5 59). Information for one of the 60 participants
was not available, while the information was collected for all of the
other 59 participants.

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 corre-
sponding 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.

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.

These results indicate that the vocational rehabilitation inter-
vention program may be effective at promoting full-time employ-
ment 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.

© 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)
a 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)
? (sample correlation)
? rho (population correlation)
t r (t score)
z (standard score based on standard deviation)
?

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

© 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 (a) 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.

© 2014 Laureate Education, Inc. Page 3 of 5

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)

© 2014 Laureate Education, Inc. Page 4 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: ? = 0 (there is no correlation)
H1: ? ? 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.)

© 2014 Laureate Education, Inc. Page 5 of 5

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.

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:

Statistics for Social
Workers

J. Timothy Stocks

tatrstrrsrefers to a branch ot mathematics dealing ‘”‘th the direct de<erip-
tion of sample or population characteristics and the an.ll)’5i• of popula·
lion characteri>tics b)’ inference from samples. It co•·ers J wide range of
content, including th~ collection, organization, and interpretJtion of
data. It is divided into two broad categoric>: de;cnptive >lathrics and
inferential >lJt ost ics.

Descriptive statistics involves the CQnlputation of statistics or pnr.1meters to describe a
sample’ or a popu lation _~ All t he data arc available and used in <.omputntlon o f t hese
aggregate characteristics. T his may involve reports of central tendency or v.~r i al>il i ty of
single variables (univariate statistics). ll also may involve enumeration of the I’Ciation-
sh ips between or among two or moo·e variables’ (bivariate or multivariJte stot istics}.
Descriptiw statistics arc used 10 provide information about a large m.b> of data in a form
that ma)’ be easily understood. The defining characteristic of descriptive ;tJtistks b that
the product is a report, not .on inference.

Inferential statisti<> imolvc’ the construction of a probable description of the charac·
teristics of a population b•sed on s.unple data. We compute statistics from .1 pJrtial;et of
the population data (a samplt) to estimate the population parameters. Thrse t<timates
are not exact, but \·e can mo~k..: reawnable judgments as w hoV preruc our c~lim:ues are.
Included within inferential statiwcs i;, hypothesis testing, a procedure for U>ing mathe-
m:uics tO provide evidence for the exi<tence of relationships between o r among variable;.
T bis testing is a form of inferential •”l~umem.

Descriptive Statistics

Measures of Central Tendency
Measures of central tenden’)’ are individual numbers that typify the tot.tl set of ~cores.
The three most frequently used mca>urcs of centraltendenq are the arithmetic mean, the
mode, and the median.

Arir!Jmeric .1ea11. The arithmetic mean usually is simply called the mca11. It also is called
the m-erage. It is computed b)’ adding up all of a set of scores and dwidmg by the number
of scores in the set. The algebraic representation of this is

75

76 PA11 f I • OuANTifAllVi AffkOAGHU: fouHo~;noM Of Ot.r”‘ CO ltf(TIO’J

~, =l:: X ,
11

where 11 represents the popu I at ion mean, X represems an individual score, and rr is t he
number of scores being adde(l.

The formula for the sample mean is the same except t hat the mean is represented by
the variable lener with a bar above it:

– l:;X X= –.
II

Following are t he numbers of class periods skipped by 20 seventh-graders d uring
I week: {1, 6,2,6, 15,2(),3,20, 17, 11, 15, 18,8,3, 17, 16, 14, 17,0, 101. Wecomputethe
mean by adding up the class periods missed and dh•iding by 20:

l:;X 219 •
J.l = — = – = 10.9o.

II 20

Mode. The mode is the most frequently appearing score. It really is not so much a measure
of centrality as it is a measure of typicalness. It is found by o rganizing scores int o a fre-

quency distribution and determining which score has t he greatest fre-

TABLE 6 . 1 Truancy Scores
quency. Table 6. 1 displays the truancy scores arranged in a frequency
distribution.

Score

20
19

18
17

16
IS
14
13
12
II

10
9
8
7

6
5
4

3

2
1
0

frequ ency

2
0
1

3
1

2
I

0
0
l

I
0
1

0
2
0
0
2

0

Because 17 is the most frequently appearing number, the mode (or
modal number) of class periods skipped is 17.

Unlike the mean or median, a distribution o f scores can have more
than one mode.

,llfedinrr. lf we take all the scores in a set of scores, place t hem in o rder
from least to greatest, and count in to the middle, then the score in the
middle is the median. This is easy enough if there is an odd number of
scores. However, if there is an even number of scores, then there is no
single score in the middle. In this case, t he two middle scores are
selected, and their average is the median.

There a.re 20 scores in the previous example. The median would be
the a”erage of the lOth and lith scores. We usc t he frequency table to
find these scores, which are 14 and J 5. T hus, the median is 14.5.

Measures of Variabi li ty
Whereas measures of central tendency are used to estimate a typical
score in a dimibution, measures of variability may be thought of ns a
way in which to measure departu re from typic<~lness. They pro”ide
information on how “spread out” scores in a d istribution are.

J<auge. The range is the easiest measure of variability to calculate. It is
simply the distance from the minimum ( lowest) score in a distribution

If
10

R

:.aJ
13

de

c .. …nu 6 • STAnsnu t<~~ Soc&AL Wouta~ 77

to the maximum ( highest) score. h is obtained by subtracting the 111ini murn score flom
lhe maximum ~cor~.

Let us compute th.- rang.- for the following dJt.l ~ct:

/1, 6, 10, 14, 18,22/.

‘T’he n1inimum i!) 2, and tht.” tnJximum is 22:

Range = 22 – 2 20.

Sum ofSquaus. The sum of squares is a measure of the total amount of variability in” set
of scores. Jts na me tells how to wmpute it. Smu ofsqunres is short (or sum ofsqumed dc1ti
til ion scores. It is represented by the S)’lnbol SS.

The formulas for sample and population sums ot squares are the same except for sam-
ple and populat•on mean symbob:

SS = I(X ~tl’

Using the dJtJ set fo r t11e range, the sum of squnres would be computed as in
‘ldble6.2.

V.~rinuce. Another name for variance i~ mean square. This is short for mean of squared
devintron score<. 1l1is is obtained by dividi ng the sum of squares by the number of scores
(11). It is a me,tsure of the average amount of variabilit y associated with each score in a set
of scores. The population variance fOI’mu la is

ss
a2= -.

n

whc1e cr2 is the syn>bol for populn tion variance, SS is the symbol fo r sum of squares, and
11 st,uJds for th e number of scores in the population.

The variance for the example we used to compute
sum of squares would be

TAOLE 6.2 Computing the Sum of Squares

X X m

2 tO

6 6

10 ]

l<t 12

18 >6
<