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4Experimental
To prepare for this Assignment:
• Review Lesson 24, “Independent-Samples t test,” in the Green and
Salkind text.
• Consider how descriptive statistics inform the researcher.
• Review the media, The t Test for Independent Samples.
• Review the Assignment Exemplar document provided in this week’s
Learning Resources.
Submit a 3- to 4-page paper using the Assignment Exemplar:
Your paper must include the following elements:
• An APA Results section for Independent Samples t test. (See an example
of an APA Results section on The t Test for Independent Samples.)
• The critical elements of your SPSS output, including:
o A properly formatted research question
o A properly formatted H10 (null) and H1a (alternate) hypothesis
o A descriptive statistics narrative and properly formatted descriptive
statistics table
o A properly formatted box plot (see page 128 of the Green and Salkind
text)
o A properly formatted inferential APA Results Section (see page 128
of the Green and Salkind text)
o An appendix including the SPSS output generated for descriptive and
inferential statistics (see SPSS output on page 128 of the Green and
Salkind text)
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Independent Samples T-Test Exemplar Template
Research Question
Does the average amount of time spent talking differ under low-stress versus
high-stress conditions?
Hypotheses
H0: The average amount of time spent talking does not differ under low-stress
versus high-stress conditions?
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H1: The average amount of time spent talking does differ under low-stress versus
high-stress conditions?
Results
An independent-samples t-test was conducted to evaluate the hypothesis that
students talk more under a high stress condition (anticipating questions from a panel of
measurement specialists) as opposed to low-stress condition (anticipating taking a
personality measure). The independent variable was stress condition, with two levels,
low-stress condition and high-stress condition. The dependent variable was time spent
talking. The test was significant, t(28) = 2.43, p = .02, but the results were counter to the
research hypotheses. Students in the high-stress condition (M = 22.07, SD = 27.14), on
average, talked less than those in the low-stress condition. The 95% confidence interval
or the difference in means was quite wide, ranging 3.63 to 42.64. The ets square index
indicated that 17% of the variance of the talk variable was accounted for by whether a
student was assigned to a low-stress or high-stress condition. Table 1 depicts the
descriptive statistics for the time spent talking by stress condition. Figure 1 is a box-plot
of stress conditions. The appendix depicts the SPSS independent-samples t-test output
generated from the analysis.
Table 1
Descriptive Statistics for Time Spent Talking
Variable
M
SD
Low Stress Condition
45.20
25.00
High Stress Condition
22.07
27.12
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Figure 1. Boxplot depicting time spent talking by stress condition.
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Appendix
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The t Test for Independent Samples
The t Test for Independent Samples Program Transcript
JENNIFER ANN MORROW: Welcome to the T-test for Independent Samples. My name is Dr.
Jennifer Ann Morrow. In today's demonstration, I will go with you the definition for a t-test for
independent samples. I'll give you the alternative names for this test. I will go over some
sample research questions that can be addressed using a t-test for independent samples. I'll
give you the formulas. I'll go over the assumptions, discuss effect size, and then give you
examples using both the formula and SPSS. OK, let's get started. A t-test for independent
samples is a statistic that is used when you have two separate groups-- levels of your
independent variable-- and you want to compare them on your dependent variable. These
separate groups have different participants within them. There are many different names for
this particular statistic-- independent t-test, independent samples t-test, between subjects ttest, and between groups t-test. All of these are different names for the t-test for independent
samples. Here are a couple of sample research questions that can be addressed using a t-test
for independent samples. The first research question is, is there a difference in level of self
esteem between participants in the control group and those in the experimental group? In this
case, my independent variable would be group, and my levels or groups would be control and
experimental. And my dependent variable is self-esteem. My second question that can be
addressed using a t-test for independent samples is, is there a gender difference in spirituality?
In this case, my independent variable would be gender and my levels or groups would be
female and male. And my dependent variable would be spirituality. The basic formula for a t-
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test for independent samples is as follows-- x sub 1 minus x sub 2 divided by the standard error,
where x sub 1 is the mean for the first group and x sub two is the mean for the second group.
And your standard error is equal to the pooled variance divided by the sample size for the first
group plus the pooled variance divided by the sample size for the second group. And you take
the square root of that. To find a pooled variance, all you have to do is take the sum of squares
for the first group, add it to the sum of squares for the second group, and divide that by the
degrees of freedom for the first group plus the degrees of freedom for the second group. And
for this statistic, the t-test for independent samples, the degrees of freedom equals the sample
size for the first group minus 1 plus the sample size for the second group minus 1. The t Test for
Independent Samples © 2014 Laureate Education, Inc. 2 There are also additional formulas that
you can use to calculate a t-test for independent samples. You can use the raw score formula,
where you have the mean of the first group minus the mean of the second group divided by the
square root of the multiplication of sum of squares for the first group plus the sum of squares
for the second group divided by the sample size for the first group plus the sample size for the
second group minus 2. You multiply that by the addition of 1 over the sample size for the first
group plus 1 over the sample size for the second group. And the formula for the sum of squares
is below, where you take the sum of all of the x squareds for the first group minus the sum of all
the values. And you square that, and you divide that by the sample size for the first group. And
that will give you the sum of squares for the first group. Using the same formula, plug in the
information for your second group and you'll get the sum of squares for the second group.
There's also another formula that you can use. The next formula is called the deviation formula.
And here, you take the mean of the first group, subtract the mean of the second group, and you
divide it by the square root of the sum of the deviations for the first group, each score minus
the mean of that group, and the deviations for the second group, each score minus the mean of
that group. Those are both squared. You divide that by the sample size for the first group plus
the sample size for the second group minus 2. Multiply that by the sum of 1 over the sample
size for the first group, 1 over the sample size for the second group. And then you take the
square root of that. All these formulas will give you the same result. Choose the one that's
easiest for you to use. Let's recap. So far, we've learned the definition for a t-test for
independent samples, we've learned some different names for this particular statistic, we've
gone over some sample research questions that can be addressed using this analysis, and we've
learned the different formulas that we need to use to analyze using a t-test for independent
samples. Now, let's go over t-tests for independent samples in more detail. There are three
basic assumptions that must be met in order to use a t-test for independent samples. The first
assumption is, the observations within each sample must be independent. The scores cannot be
related to other scores in your sample. The second assumption is the two populations from
which the samples are selected must be normally distributed. And lastly, the two populations
from which the samples are selected must have equal variances. And this is known as
homogeneity of variance. If you violate any of these assumptions, you should not use the t-test
for independent samples. The t Test for Independent Samples © 2014 Laureate Education, Inc.
3 For a t-test for independent samples, you can report two measures of the effect size-Cohen's d and the percentage of variance explained, or r squared. To calculate Cohen's d, you
take the mean of the first group minus the mean of the second group and divide that by the
square root of your pooled variance. To get the percentage of variance explained, you take your
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t value, you square it, and divide that by your t value squared plus your degrees of freedom.
Let's do an example of using the formula. My research question is, do girls perform better on a
math test compared to boys? My null hypothesis is mu1 minus mu2 equals 0. There is no
difference in math performance between girls and boys. My alternative hypothesis or my
research hypothesis is mu1 minus mu2 does not equal zero. There is a difference in math
performance between girls and boys. I have 10 scores for the boys-- 24, 23, 16, 17, 19, 13, 17,
20, 15, and 26. And I also have 10 scores for the girls-- 18, 19, 23, 29, 30, 31, 29, 26, 21, and 24.
My mean for the boys equals 19. And my sum of squares for the boys equals 160. My mean for
the girls equals 25. And my sum of squares for the girls equals 200. My degrees of freedom for
this analysis again is n1 plus n2 minus 2, which is 20 minus 2-- 18. And when I look at my t
distribution table for the critical value for a t-test with 18 degrees of freedom, an alpha level of
0.05 and a two tailed test, I find that the critical value that I need to surpass is equal to plus or
minus 2.101. So my t value needs to surpasses that in order for it to be significant. Now let's
calculate the t statistic. So again, my t tests for independent samples equals the mean of the
first group minus the mean of the second group over the standard error. And to calculate my
standard error, I need to find my pool variance. And my pooled variance is equal to my sum of
squares for the first group plus my sum of squares for the second group divided by my degrees
of freedom for the first group and my degrees of freedom for the second group. My pooled
variance is equal to 20. And to get your standard error, is my pooled variance divided by the
sample size for the first group and my pooled variance divided by the sample size for the
second group. You take the square root of that. And so my standard error is 2.00. So let's plug
in this information in my t statistic. So t equals the mean of the first group for boys is 19, the
mean my second group, girls, is 25, divided by my standard error, which is 2. I get a t value of
negative 0.300. So here in this case, my value has surpassed the critical value. The t Test for
Independent Samples © 2014 Laureate Education, Inc. 4 And remember, my critical value is
2.101, plus or minus. So to write that up, I would be t, my degrees of freedom, which is 18,
equals my t value, negative 3.00, comma p less than 0.05, again, the alpha level that I chose a
priori, comma two tailed. So what this would say is that girls perform significantly better on a
math test compared to boys. So I could put girls, mean equals 25, performed significantly better
than the boys. And their mean was 19. I can also calculate effect size for this example. My
Cohen's d again is the mean difference, which would be minus 6 divided by the square root of
your pooled variance, which in this case is 20. So my Cohen's d is negative 1.34, which is a large
effect size. I could also calculate my percent of variance, which again is t squared divided by t
squared plus your degrees of freedom. And in this case, my percent of variance is equal to 0.33.
Now, let's use an example using SPSS. First, open up your SPSS program and find the file that
you want to use to conduct your analysis. Click on File, click on Open, click on Data, and find the
data set that you want to use. Once you've found the data set, click on it. And click on Open.
And make sure your Data View window appears on the screen. Now, for this example, I want to
conduct an independent samples t-test looking at gender differences in stress. So in this case,
my independent variable would be gender. And my dependent variable would be stress. Let me
show you how to do that. I'm going to click on Analyze, Compare Means. Click on Independent
Samples T-test, and your Independent Samples T-test dialog box will appear on the screen. The
first thing you should do is input your independent variable. In this case, it's gender. So in the
box on the left, find Gender, click on it. And click on the right arrow key, where it says Grouping
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Variable. That as another name for your independent variable. Once you click on that, you'll see
that these two question marks appear in the box. What you have to do is you have to tell SPSS
what the values you have for each of your levels in your independent variable. So click on
Define Groups. Now, I know that for my values of female and male, females are 0 and males are
1. And if you don't remember that, you can go back to data set and check that. So here, you put
0 for group one and 1 for group two and click on Continue. The next thing you need to do is find
your dependent variable here on the box on the left, scroll down so you could see the variable
Stress. Click on Stress. Click on the right arrow key to move that to the variable box that says
Test Variables. The t Test for Independent Samples © 2014 Laureate Education, Inc. 5 And now
the variable Stress has appeared in the dialog box here on the right. Now click OK. As you can
see, SPSS is now giving you an independent samples t-test, where you have the dependent
variable of Stress, you have the independent variable of Gender of Participation, where 0 are
females and 1 are males. You have 97 females and 51 males. For your females, the means for
stress is 2.43. And the mean for males is 2.45. Your standard deviation for females is 0.73. And
your standard deviation for males is 0.70. And you have your standard error of the mean for
females is 0.07. And the standard error of the mean for males is, if you round this up, 0.10. In
your next table, SPSS will give you the results of the independent samples ttest. The first thing
that you should look at is something called a Levines tests for quality of variances. This is testing
out your assumptions of homogeneity of variance. You want this here, where it says SIG, the
significance for this particular assumption test, to be non-significant. You do not want a
significance here. If you have non-significance, if it's greater than p less than 0.05-- in this case,
it is. It says not go below p less than 0.05. Saying that yes we do have equal variances assumed
for this analysis. So then you focus on the first row in this table. And that is your t statistic
result. So here in this case, we have a t value of negative 0.104. We'll just round that to
negative 0.10. We have 146 degrees of freedom. And my significance, again for two tailed tests,
alpha level of 0.05, the value is 0.917. Here, this is nonsignificant because it's not p less than
0.05. So how would I write this up? You would put t, 146 degrees of freedom, equals negative
0.10, which is your t value, comma, ns, which stands for non significant, comma two tailed. And
what this would be saying is that there are no significant differences between the means for
females for stress and the mean for males for stress. So I would write that up as females-- and
here, the mean equals 2.43, and my standard deviation is 0.73-- report similar levels of stress
compared to males. And my mean is equal to 2.45. And a standard deviation is 0.71. So here, I
did not achieve significance for this t statistic. I can also calculate the percent of variance
accounted for. Again, that's just t squared divided by t squared plus your degrees of freedom.
And here, in this case, it would be negative 0.10 squared divided by negative 0.10 squared plus
your degrees of freedom and my percent of variance accounted for actually would be equal to
0.00. The t Test for Independent Samples © 2014 Laureate Education, Inc. 6 There is no effect
size, which makes sense because we have a very low t value and we have a non-significant
result. OK, let's recap. We learned about the assumptions of the t-test for independent
samples. We went over how to calculate two measures of effect size. And we did an example
using the formula and an example using SPSS. We have now come to the end of our
demonstration. Practice conducting a t-test for independent samples on your own. Refer to the
Webliography for more information on t-tests for independent samples. Thank you, and have a
great day.
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