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EXERCISE
29 t-TEST FOR INDEPENDENT GROUPS I

STATISTICAL
TECHNIQUE IN REVIEW

The t-test
is a parametric analysis technique used to determine significant differences
between the scores obtained from two groups. The t-test uses the
standard deviation to estimate the standard error of the sampling distribution
and examines the differences between the means of the two groups. Since the t-test
is considered fairly easy to calculate, researchers often use it in determining
differences between two groups. When interpreting the results of t-tests,
the larger the calculated t ratio, in absolute value, the greater the
difference between the two groups. The significance of a t ratio can be
determined by comparison with the critical values in a statistical table for
the t distribution using the degrees of freedom (df) for the
study. The formula for df for an independent t-test is:

df =
number ? of ? sobjects ? in ? sample ?1
+ number ? of ? subjects ? in ? sample ?2
– 2

The t-test
can only be used once to examine data from two study samples, otherwise the
Type 1 error rate (alpha) may be inflated. A Type I error occurs when the
researcher rejects the null hypothesis when it is in actuality true. Thus if
researchers run multiple t-tests to evaluate differences of various
aspects of a study’s data, this is considered a misuse of the t-test and
often leads to an increased risk for a Type I error or finding two groups
significantly different when they are not. To correct for the risk of a Type I
error, the researcher can perform a Bonferroni procedure. The Bonferroni
procedure is a simple calculation in which the alpha is divided by the number
of t-tests run on different aspects of the study data. The resulting
number is used as the alpha or level of significance for each of the t-tests
conducted. For example, if a study’s alpha was set at 0.05 and the researcher
planned on conducting 5 t-tests on the study data, the alpha would be
divided by the 5 t-tests (0.05 ÷ 5 = 0.01), with a resulting alpha of
0.01 to be used to determine significant differences in the study. The
Bonferroni procedure formula is:

alpha (a)
÷ number ? of ?t – tests ? performed ?
on ? study ? data = more ? stringent ?
study ?a? to ? determine ? the ? significance ?
of ? study ? results .

The t-test
for independent groups includes the following assumptions:

1.
The raw scores in the population are normally distributed.

2.
The dependent variable(s) is (are) measured at the interval or ratio levels.

3.
The two groups examined for differences have equal variance, which is best
achieved by a random sample and random assignment to groups.

4.
All observations within each group are independent.

The t-test
is robust, meaning the results are reliable even if one of the assumptions has
been violated. However, the t-test is not robust regarding
between-samples or within-samples independence assumptions, or with respect to
extreme violation of the assumption of normality. Sample groups do not need to
be of equal sizes but rather of equal variance. Groups are independent if the
two sets of data were not taken from the same subjects and if the scores are
not related. Thus, paired or matched groups are dependent, not independent; but
a randomly selected sample with random assignment to groups does produce
independent groups (Burns & Grove, 2005).

RESEARCH
ARTICLE

Source: Kristofferzon, M., Löfmark,
R., & Carlsson, M. (2005). Perceived coping, social support, and quality of
life 1 month after myocardial infarction: A comparison between Swedish women
and men. Heart & Lung, 34 (1), 39–50.

Introduction

Kristofferzon,
Löfmark, and Carlsson (2005) conducted a comparative-descriptive study to
determine if women and men differ in their perceived coping, social support,
and quality of life one month post myocardial infarction (MI). The sample of
convenience included 171 subjects, 74 women and 97 men. Each participant completed
a study-specific questionnaire (demographics and risk factors), the JCS-60
(measured use of coping strategies), the social network and social support
questionnaire (measured social participation and emotional support), the SF-36
Health Survey (measured perceived health-related quality of life), and the QLI
(measured perceived quality of life). In addition, the researchers conducted a
chart review of each participant’s medical record. In this study the results
showed that “compared with men, women used more evasive and supportive coping
and rated psychologic aspects of the heart disease as more problematic to
manage. More women perceived available support from friends and grandchildren,
and more men perceived available support from their partner. Women rated lower
levels in physical and psychologic dimensions of quality of life”
(Kristofferzon et al., 2005, p. 39).

Relevant
Study Results

“A consecutive
series of patients was selected from the medical records in 1 hospital between
August 1999 and July 2001 for women and between August 1999 and August 2000 for
men. With regard to a lower incidence rate of MI in women, a longer selection
period was needed for them…. We decided to include 100 women and 100 men to
have a comfortable margin for dropouts.

“An
introductory letter, informed consent form, and questionnaires were mailed to
eligible subjects 1 month after an acute MI. After 1 week, the first author
phoned the patients. Those interested in participating returned the signed
consent form and the completed questionnaires to the investigator within 1 to 2
weeks. The same questionnaires were mailed to the subjects on 3 occasions, 1,
4, and 12 months after MI. Data from 1 month are presented in this article”
(Kristofferzon et al., 2005, p. 41).

“Of the target
population of 338 women, 20% died before inclusion, 35% did not meet the
inclusion criteria, and 23% declined participation; of the target population of
317 men, the corresponding numbers were 17%, 27%, and 26%, respectively. … The
final sample consisted of 74 women and 97 men” (Kristofferzon et al., 2005, p.
41).

InTable VI, are the quality of life measures
reported by Kristofferzon et al. (2005) in their study of women and men
following an MI. The level of significance or alpha for this study was set at
0.05.

TABLE
VI Quality of Life Experienced by Women and Men (N = 171)

Kristofferzon,
M., Löfmark, R., & Carlsson, M. (2005). Perceived coping, social support,
and quality of life 1 month after myocardial infarction: A comparison between
Swedish women and men. Heart & Lung, 34(1), p. 47.

*
PCS = PF, RP, BP, GH.

†
MCS = VT, SF, RE, MH.

‡
df = 161.

§
df = 168. QoL = Quality of life; QLI, Quality-of-Life
Index-Cardiac Version.

?
EXERCISE 29 Questions to be Graded

1.
Were the groups in this study independent or dependent? Provide a rationale for
your answer.

2.
t = -3.15 describes the difference between women and men for what
variable in this study? Is this value significant? Provide a rationale for your
answer.

3.
Is t = -1.99 significant? Provide a rationale for your answer. Discuss
the meaning of this result in this study.

4.
Examine the t ratios inTable VI.
Which t ratio indicates the largest difference between the males and
females post MI in this study? Is this t ratio significant? Provide a
rationale for your answer.

5.
Consider t = -2.50 and t = -2.54. Which t ratio has the
smaller p value? Provide a rationale for your answer. What does this
result mean?

6.
What is a Type I error? Is there a risk of a Type I error in this study?
Provide a rationale for your answer.

7.
Should a Bonferroni procedure be conducted in this study? Provide a rationale
for your answer.

8.
If researchers conducted 9 t-tests on their study data. What alpha level
should be used to determine significant differences between the two groups in
the study? Provide your calculations.

9.
The authors reported multiple df values inTable
VI. Why were different df values reported for this study?

10.
What does the t value for the Physical Component Score tell you about
men and women post MI? If this result was consistent with previous research,
how might you use this knowledge in your practice?

(Grove 217)

Grove,
Susan K.. Statistics for Health Care Research: A Practical Workbook.
W.B. Saunders Company, 022007. .