Running head DATA ANALYSIS AND APPLICATION .docx

Running head: DATA ANALYSIS AND APPLICATION
1
DATA ANALYSIS AND APPLICATION
12
Data Analysis and Application (DAA): U02A1
MYSTERY STUDENT OF THE WEEK!
Capella University
In conducting an independent samples t test, it is important
to consider the assumptions, and to analyze the data to
determine if the assumptions have been met, especially with
regard to the variance between group means. Additionally, for
the purpose of this assignment, a post-hoc and priori power
analysis will assist in determining whether the data can be
credibility used in research. Type I and Type II errors can be
detrimental to research in the field of psychology and should be
carefully avoided; this assignment will address measures that
can be taken to avoid such errors.
Section 1: Reporting the t Test Results
In this particular analysis of the bpstudy.sav data set,
researchers investigated data from 65 participants. With gender
as a predictor variable and heart rate (HR1) as the outcome

variable, a t test analysis compared mean heart rates using
interval level data for both male and female participants. This
data set also contained participant’s smoking status
(categorical, nominal data), as well as their weight and
systolic/diastolic pressure (interval level data).
Using an independent samples t test, researchers were able to
compare mean female heart rates with mean male heart rates, to
determine if a significant difference exists among mean heart
rates as it relates to the gender variable. Gender, a traditionally
dichotomous variable, is a meaningless variable, and as Warner
(2013) explains, “it would be nonsense to add up scores for a
nominal variable… and calculate a mean… based on the sum of
those scores”; therefore, mean gender score was not analyzed in
this research (p. 7). Field (2014) explains that variables like
gender, ethnicity and other characteristic variables used to
identify participants are often collected using nominal, data and
in descriptive statistics is not usually relevant to the analysis
process (Field, 2013, p. 8). Of the 65 samples collected, 28
were male (N₁) and 36 were female (N₂) with one misidentified
gender; for the purpose of this research, participant 11, whose
gender is listed as “3”, is automatically selected out and will
not be considered for this t test analysis (Warner, 2013, p. 137).
As outlined in Table 1 below, the mean heart rate for males was
73.68 beats per minute (BPM) and the mean heart rate for
females was 74.97 BPM. The standard deviation for the male
heart rate was 9.77 (s₁), rounded to the nearest hundredth, and
for the female heart rate it was 7.87 (s₂). The mean difference,
(M₁-M₂) is -1.29. These values are essential for computing
effect size.
Table 1
Descriptive statistics for heart rate by gender
Group Statistics
GENDER
N
Mean

Std. Deviation
Std. Error Mean
HR1
male
28
73.68
9.772
1.847
female
36
74.97
7.865
1.311
The effect size is calculated using Cohen’s d, which is
computed by dividing the mean difference by the (average)
standard deviation, (M₁-M₂)/s₁ or (M₁-M₂)/s₂. Therefore, -1.29/
9.77 = -0.13 for s₁, rounded to the nearest hundredth, and -1.29/
7.87 = -0.16 for s₂. Averaging these two computations yields a
value of -0.145, or an absolute value of 0.15, rounded. In
accordance with Warner (2013), this value indicates a small
effect size (Warner, 2013, p. 208). Therefore, data analyzation
supports there is little difference between mean heart rates for
male and female participants, and the effect size is not of great
significance.
There are several assumptions that must be met in order to
conduct an independent samples t test. First, the outcome
variable should be quantitative and normally distributed.
Second, the variance should be generally similar or equal across
groups, also referred to as homogeneity of variance; finally,
there should be independent observations both between and
within groups, meaning that each group is independent of one
another (Warner, 2013, p.189-190). As explained in the last
assignment, and again detailed in the histogram below in Table
2, the data for heart rate is quantitative and normally distributed

with a mostly symmetrical, mesokurtic shape; there are no
extreme outliers. The assumption for independence of
observations is satisfied, both between and within groups,
because there is no group overlap with regard to the
participant’s gender.
Table 2
Heart rate histogram
Levene’s test for equality of variance, as detailed in Table 3,
indicates that the significance value of 0.125 is well above the
alpha value of 0.05, so equal variance is assumed for males and
females. This shows that the assumption for the equality of
variances has been satisfied, and equal variances assumed data
should be utilized. Levene’s test rationalizes that the data is
not significantly different, so it satisfies the assumption of
homogeneity of variance. Based on the equal variances
assumed data, the t value is -0.59, rounded to the nearest
hundredth with 62 df.
Table 3
Levene’s test for homogeneity of variance
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
Df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference

Lower
Upper
HR1
Equal variances assumed
2.421
.125
-.587
62
.559
-1.294
2.204
-5.699
3.112
Equal variances not assumed
-.571
51.062
.570
-1.294
2.265
-5.840
3.253
The null hypothesis for the purpose of this research is that there
is no difference between males and females with regard to their
heart rate, while the alternative hypothesis states there is a
difference between male and female heart rate. The alpha level
for the purpose of this analysis is 0.05 (Warner, 2013; George &

Mallery, 2014).
According to Table 3, the t ratio is -0.587 with 62 degrees of
freedom. The degrees of freedom are calculated using N-2
(Warner, 2013, p. 199). The critical t value, according to
Warner (2013), is 2.00 for a two-tailed test (p. 1057). The p
value is 0.559, which is significantly more that the alpha value
of 0.05, which justifies a failure to reject the null hypothesis.
Females have slightly higher mean heart rates than their male
counterparts in this data set, however, the mean values do not
indicate that the higher heart rates are statistically significant.
The data analysis in this report constitutes a failure to reject the
null hypothesis, which suggests that there is no difference
between males and females with regard to gender and their
mean heart rate. The alternative hypothesis that there is a
difference between the male and female heart rate is
subsequently rejected.
Section 2: Post-hoc Power Analysis
Warner (2013) defines statistical power as “the probability of
correctly rejecting the H₀ when H₀ is false” (p. 107). The
G*Power post-hoc power analysis gives the researcher insight
into how the two gender groups vary with regard to mean
differences, in this case, heart rate. Observation of the
distribution graph below in Table 4 shows a great deal of
overlap between males and females in this data set. Table 4
suggests that there is little difference between male and female
heart rates, and rejecting the null hypothesis is justifiable,
based on visual interpretation of this output graph.
Table 4
G*Power distribution graph for post-hoc power analysis
Table 5 below shows the critical t value is -1.9989715, or -2.00
rounded, which is in accordance with the findings in section 1.

The noncentrality parameter δ computes to a value of -0.52 and
the Power (1-β err prob) is 0.08; both are higher than the alpha
value of 0.05. A Type II error would be committed if it was
determined there was no difference between male and female
heart rates when, in fact, there was a difference between the
mean heart rates for males and females, which would be
indicative of a false negative (Field, 2013; Warner, 2013). In
the output in Table 5, the risk of committing such an error is
relatively low, but still higher than the alpha level.
Table 5
G*Power output values for post-hoc power analysis
t tests - Means: Difference between two independent means
(two groups)
Analysis: Post hoc: Compute achieved power
Input: Tail(s) = Two
Effect size d = -0.13
α err prob = 0.05
Sample size group 1 = 28
Output: Noncentrality parameter δ = -0.5159215
Critical t = -1.9989715
Df = 62
Power (1-β err prob)= 0.0800468
Section 3: A Priori Power Analysis
The G*Power priori power analysis gives the researcher insight
into how to ensure ample data collection will be necessary to
achieve sufficient results. In this particular research, increasing
the Power (1-β err prob) to 0.80 would require data collection
on a much larger scale N₁=930 and N₂=930. The larger sample
size would likely yield less overlap in the distribution of scores;
however, obtaining data from a large sample size is generally
more difficult (Warner, 2013, p. 103-104). Table 6 below
shows the decreased overlap when sample size is significantly
increased.
Table 6
G*Power distribution graph for priori power analysis

By increasing the Power (1-β err prob) to 0.80, the sample size
is also significantly increased, as shown in Table 7 below,
where N₁ and N₂ both equal 930. This is in line with findings
that increasing the sample size, effect size or alpha level
increases power; when Cohen’s d increases, so will the t ratio
because there is a greater likelihood to acquire a greater t value
when the effect size is greater (Warner, 2013, p. 109).
When N is increased, statistical power also increases; having a
high N value will reduce the risk of the researcher committing a
Type II error (Warner, 2013, p. 109). This is a logical
conclusion because the greater the sample size, the more
confidently a researcher can generalize. When the alpha level is
made smaller, statistical power decreases; contrarily, if the
alpha level is increased, statistical power also increases; the
smaller the threshold to reject the null, the more credible the
claims made by the researcher (Warner, 2013, p. 108).
Table 7
G*Power output values for priori power analysis
(two groups)
Analysis: A priori: Compute required sample size
α err prob = 0.05
Allocation ratio N2/N1 = 1
Critical t = -1.9612416
Df = 1858
Total sample size = 1860
Actual power = 0.8000757
By further manipulating the effect size to 0.50, Table 8 and

Table 9 show that it would be necessary to obtain equal sample
sizes, N₁=64 and N₂=64. The researcher can ensure valid data is
obtained in research by being aware of these principles in
advance, and compensating during data collection if necessary.
For example, if Cohen’s d is small, the necessary sample size to
receive the desired level of statistical power (80%) can be
determined prior to research; the development of tables, like
Table 3.3 in Warner (2013) assist in this process (p. 112-113).
Table 8
G*Power distribution output for priori power analysis with
medium effect size
Table 9
G*Power output values for priori power analysis with medium
effect size
(two groups)
Effect size d = 0.50
α err prob = 0.05
Output: Noncentrality parameter δ = 2.8284271
Critical t = 1.9789706
Df = 126

Conclusion
In conducting psychological research, it is imperative that
the data collected be, not only error-free, but statistically
significant; the data analysis should also provide sound insight
that will answer the research question. Setting alpha levels,
threshold values and gauging statistical power are all avenues of
rationalizing findings and providing accountability through
concrete and standardized values. Conducting priori power
analysis can ensure that ample data is collected, that alpha
levels are reasonable for the sample size and that the effect size
correctly measures the significance of the variance.
References
Field, A. (2013). Discovering statistics using IBM SPSS
statistics (4th ed.). Thousand Oaks, CA:
SAGE Publications, Inc.

George, D. & Mallery, P. (2014). IBM statistics 21 step by step:
A simple guide and reference
(13th ed.). Boston, MA: Pearson.
Warner, R. M. (2013). Applied statistics: From bivariate
through multivariate techniques (2nd
ed.). Los Angeles, CA: SAGE Publications, Inc.
DR.
BELOW IS A NOTE THAT MY PROFESSOR LEFT FOR ALL
STUDENTS
(I HAVE ATTACHED THE PAPER THAT HE SENT AS AN
EXAMPLE FROM A MYSTERY STUDENT)
CLASS, HERE IS ONE EXAMPLE OF A WELL PRESENTED
PAPER. PLEASE REMEMBER TO GIVE FULL AND
COMPLETE ANSWERS(NO BULLET POINTS), AND TO
REMOVE ANY INSTRUCTIONS FROM THE ASSIGNMENT
YOU HAND IN. SPSS TABLES SHOULD BE LABELED AND
DISCUSSED NEAR THE TABLE OR FIGURE.
BE SURE TO HAVE A ONE PARAGRAPH INTRODUCTION
AND A ONE PARAGRAPH CONCLUSION, IN ADDITION TO
THE OTHER SECTIONS OF THE DAA TEMPLATE. THANKS
EVERYONE.
THIS IS THE EXAMPLE OF WHAT HE WANTS THE
ASSIGNMENTS TO LOOK LIKE:
MYSTERY STUDENT OF THE WEEK!
Capella University

In conducting an independent samples t test, it is important
to consider the assumptions, and to analyze the data to
determine if the assumptions have been met, especially with
regard to the variance between group means. Additionally, for
the purpose of this assignment, a post-hoc and priori power
analysis will assist in determining whether the data can be
credibility used in research. Type I and Type II errors can be
detrimental to research in the field of psychology and should be
carefully avoided; this assignment will address measures that
can be taken to avoid such errors.
Section 1: Reporting the t Test Results
In this particular analysis of the bpstudy.sav data set,
researchers investigated data from 65 participants. With gender
as a predictor variable and heart rate (HR1) as the outcome
variable, a t test analysis compared mean heart rates using
interval level data for both male and female participants. This
data set also contained participant’s smoking status
(categorical, nominal data), as well as their weight and
systolic/diastolic pressure (interval level data).
Using an independent samples t test, researchers were able to
compare mean female heart rates with mean male heart rates, to
determine if a significant difference exists among mean heart
rates as it relates to the gender variable. Gender, a traditionally
dichotomous variable, is a meaningless variable, and as Warner
(2013) explains, “it would be nonsense to add up scores for a
nominal variable… and calculate a mean… based on the sum of
those scores”; therefore, mean gender score was not analyzed in
this research (p. 7). Field (2014) explains that variables like
gender, ethnicity and other characteristic variables used to
identify participants are often collected using nominal, data and
in descriptive statistics is not usually relevant to the analysis
process (Field, 2013, p. 8). Of the 65 samples collected, 28
were male (N₁) and 36 were female (N₂) with one misidentified
gender; for the purpose of this research, participant 11, whose

gender is listed as “3”, is automatically selected out and will
not be considered for this t test analysis (Warner, 2013, p. 137).
As outlined in Table 1 below, the mean heart rate for males was
73.68 beats per minute (BPM) and the mean heart rate for
females was 74.97 BPM. The standard deviation for the male
heart rate was 9.77 (s₁), rounded to the nearest hundredth, and
for the female heart rate it was 7.87 (s₂). The mean difference,
(M₁-M₂) is -1.29. These values are essential for computing
effect size.
Table 1
Descriptive statistics for heart rate by gender
Group Statistics
GENDER
N
Mean
Std. Deviation
Std. Error Mean
HR1
male
28
73.68
9.772
1.847
female
36
74.97
7.865
1.311
The effect size is calculated using Cohen’s d, which is
computed by dividing the mean difference by the (average)
standard deviation, (M₁-M₂)/s₁ or (M₁-M₂)/s₂. Therefore, -1.29/
9.77 = -0.13 for s₁, rounded to the nearest hundredth, and -1.29/
7.87 = -0.16 for s₂. Averaging these two computations yields a

value of -0.145, or an absolute value of 0.15, rounded. In
accordance with Warner (2013), this value indicates a small
effect size (Warner, 2013, p. 208). Therefore, data analyzation
supports there is little difference between mean heart rates for
male and female participants, and the effect size is not of great
significance.
There are several assumptions that must be met in order to
conduct an independent samples t test. First, the outcome
variable should be quantitative and normally distributed.
Second, the variance should be generally similar or equal across
groups, also referred to as homogeneity of variance; finally,
there should be independent observations both between and
within groups, meaning that each group is independent of one
another (Warner, 2013, p.189-190). As explained in the last
assignment, and again detailed in the histogram below in Table
2, the data for heart rate is quantitative and normally distributed
with a mostly symmetrical, mesokurtic shape; there are no
extreme outliers. The assumption for independence of
observations is satisfied, both between and within groups,
because there is no group overlap with regard to the
participant’s gender.
Table 2
Heart rate histogram
Levene’s test for equality of variance, as detailed in Table 3,
indicates that the significance value of 0.125 is well above the
alpha value of 0.05, so equal variance is assumed for males and
females. This shows that the assumption for the equality of
variances has been satisfied, and equal variances assumed data
should be utilized. Levene’s test rationalizes that the data is
not significantly different, so it satisfies the assumption of
homogeneity of variance. Based on the equal variances
assumed data, the t value is -0.59, rounded to the nearest
hundredth with 62 df.
Table 3

Levene’s test for homogeneity of variance
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
Df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
HR1
Equal variances assumed
2.421
.125
-.587
62
.559
-1.294
2.204
-5.699
3.112

Equal variances not assumed
-.571
51.062
.570
-1.294
2.265
-5.840
3.253
The null hypothesis for the purpose of this research is that there
is no difference between males and females with regard to their
heart rate, while the alternative hypothesis states there is a
difference between male and female heart rate. The alpha level
for the purpose of this analysis is 0.05 (Warner, 2013; George &
Mallery, 2014).
According to Table 3, the t ratio is -0.587 with 62 degrees of
freedom. The degrees of freedom are calculated using N-2
(Warner, 2013, p. 199). The critical t value, according to
Warner (2013), is 2.00 for a two-tailed test (p. 1057). The p
value is 0.559, which is significantly more that the alpha value
of 0.05, which justifies a failure to reject the null hypothesis.
Females have slightly higher mean heart rates than their male
counterparts in this data set, however, the mean values do not
indicate that the higher heart rates are statistically significant.
The data analysis in this report constitutes a failure to reject the
null hypothesis, which suggests that there is no difference
between males and females with regard to gender and their
mean heart rate. The alternative hypothesis that there is a
difference between the male and female heart rate is
subsequently rejected.
Section 2: Post-hoc Power Analysis
Warner (2013) defines statistical power as “the probability of
correctly rejecting the H₀ when H₀ is false” (p. 107). The
G*Power post-hoc power analysis gives the researcher insight

into how the two gender groups vary with regard to mean
differences, in this case, heart rate. Observation of the
distribution graph below in Table 4 shows a great deal of
overlap between males and females in this data set. Table 4
suggests that there is little difference between male and female
heart rates, and rejecting the null hypothesis is justifiable,
based on visual interpretation of this output graph.
Table 4
G*Power distribution graph for post-hoc power analysis
Table 5 below shows the critical t value is -1.9989715, or -2.00
rounded, which is in accordance with the findings in section 1.
The noncentrality parameter δ computes to a value of -0.52 and
the Power (1-β err prob) is 0.08; both are higher than the alpha
value of 0.05. A Type II error would be committed if it was
determined there was no difference between male and female
heart rates when, in fact, there was a difference between the
mean heart rates for males and females, which would be
indicative of a false negative (Field, 2013; Warner, 2013). In
the output in Table 5, the risk of committing such an error is
relatively low, but still higher than the alpha level.
Table 5
G*Power output values for post-hoc power analysis
(two groups)
Analysis: Post hoc: Compute achieved power
α err prob = 0.05

Critical t = -1.9989715
Df = 62
Section 3: A Priori Power Analysis
The G*Power priori power analysis gives the researcher insight
into how to ensure ample data collection will be necessary to
achieve sufficient results. In this particular research, increasing
the Power (1-β err prob) to 0.80 would require data collection
on a much larger scale N₁=930 and N₂=930. The larger sample
size would likely yield less overlap in the distribution of scores;
however, obtaining data from a large sample size is generally
more difficult (Warner, 2013, p. 103-104). Table 6 below
shows the decreased overlap when sample size is significantly
increased.
Table 6
G*Power distribution graph for priori power analysis
By increasing the Power (1-β err prob) to 0.80, the sample size
is also significantly increased, as shown in Table 7 below,
where N₁ and N₂ both equal 930. This is in line with findings
that increasing the sample size, effect size or alpha level
increases power; when Cohen’s d increases, so will the t ratio
because there is a greater likelihood to acquire a greater t value
when the effect size is greater (Warner, 2013, p. 109).
When N is increased, statistical power also increases; having a
high N value will reduce the risk of the researcher committing a
Type II error (Warner, 2013, p. 109). This is a logical
conclusion because the greater the sample size, the more
confidently a researcher can generalize. When the alpha level is
made smaller, statistical power decreases; contrarily, if the
alpha level is increased, statistical power also increases; the
smaller the threshold to reject the null, the more credible the
claims made by the researcher (Warner, 2013, p. 108).
Table 7
G*Power output values for priori power analysis

(two groups)
α err prob = 0.05
Critical t = -1.9612416
Df = 1858
By further manipulating the effect size to 0.50, Table 8 and
Table 9 show that it would be necessary to obtain equal sample
sizes, N₁=64 and N₂=64. The researcher can ensure valid data is
obtained in research by being aware of these principles in
advance, and compensating during data collection if necessary.
For example, if Cohen’s d is small, the necessary sample size to
receive the desired level of statistical power (80%) can be
determined prior to research; the development of tables, like
Table 3.3 in Warner (2013) assist in this process (p. 112-113).
Table 8
G*Power distribution output for priori power analysis with
medium effect size
Table 9

G*Power output values for priori power analysis with medium
effect size
(two groups)
Effect size d = 0.50
α err prob = 0.05
Output: Noncentrality parameter δ = 2.8284271
Critical t = 1.9789706
Df = 126
Conclusion
In conducting psychological research, it is imperative that
the data collected be, not only error-free, but statistically
significant; the data analysis should also provide sound insight
that will answer the research question. Setting alpha levels,
threshold values and gauging statistical power are all avenues of
rationalizing findings and providing accountability through
concrete and standardized values. Conducting priori power
analysis can ensure that ample data is collected, that alpha
levels are reasonable for the sample size and that the effect size
correctly measures the significance of the variance.

References
Field, A. (2013). Discovering statistics using IBM SPSS
statistics (4th ed.). Thousand Oaks, CA:
SAGE Publications, Inc.
George, D. & Mallery, P. (2014). IBM statistics 21 step by step:
A simple guide and reference
(13th ed.). Boston, MA: Pearson.
Warner, R. M. (2013). Applied statistics: From bivariate
through multivariate techniques (2nd
ed.). Los Angeles, CA: SAGE Publications, Inc.
Dr.
You will be using the wk5data.sav in SPSS for this assignment.
Please do not forget the introduction before you begin Step 1, as
indicated on the template. I thank you kindly. I am also
attaching the template to be used for this assignment, as each
assignment has different instructions within the template itself.
THIS IS THE ASSIGNMENT FOR THIS WEEK:
Step 1. Write Section 1 of the DAA. Provide a context of the
wk5data.sav data set. Specifically, imagine that you are a

clinical researcher studying a new treatment for anxiety. To
determine treatment efficacy, you monitor the anxiety levels of
clients over five weeks. Anxiety symptoms are quantified with a
symptom checklist, and the data are entered SPSS. Week 1
represents the baseline number of anxiety symptoms. Week 5
represents the number of anxiety symptoms at the conclusion of
treatment. In Section 1 of the DAA, articulate your within-
subjects factor and the outcome variable. Specify the sample
size of the data set. Based on your visual inspection of the raw
data in wk5data.sav, speculate on the overall trend in recorded
symptoms from Week 1 to Week 5.
Step 2. Write Section 2 of the DAA. Assume that the sample is
too small to assess multivariate normality. Instead, focus your
analysis in Section 2 on the sphericity assumption. Provide the
SPSS output for the Mauchly test. Report the results of the
Mauchly W and interpret it in terms of the sphericity
assumption. If sphericity is violated, analyze the three epsilon
estimates (Greenhouse-Geisser, Huynh-Feldt, and lower bound)
and justify your decision for selecting one of the three epsilon
corrections reported below in Section 4 Interpretation.
Step 3. Write Section 3 of the DAA. Specify a research question
related to the repeated measures ANOVA. Articulate the null
hypothesis and alternative hypothesis. Specify the alpha level.
Step 4. Write Section 4 of the DAA.
· To provide context, paste SPSS output of Weeks 1–5
descriptive statistics. Report these descriptive statistics in your
narrative.
· Next, paste SPSS output of the estimated marginal means plot
of Weeks 1–5. Provide an interpretation of this figure.
· Then paste the SPSS output for the test of within-subjects
effects.
· Report F, the degrees of freedom based on your epsilon
correction selected in Section 2 (if epsilon correction is not
necessary, report Sphericity Assumed df), the F value, the p
value, the effect size, and interpretation of the effect size.
· Interpret the results against the null hypothesis. Next, paste

the SPSS output for the tests of within-subjects contrasts if the
overall F null hypothesis is rejected.
· Make sure in SPSS that the contrast is designated as "simple"
with Week 1 set as the baseline comparison. Report the F tests
for the simple contrasts and interpret them.
Step 5. Write Section 5 of the DAA. Discuss the conclusions of
the repeated measures ANOVA as it relates to the research
question. Conclude with an analysis of the strengths and
limitations of repeated measures ANOVA.

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