Research Methods for Statistical Analysis - Desklib

This article discusses various research methods for statistical analysis, including ANOVA, t-tests, and factor analysis. It provides detailed explanations of each method and their assumptions, strengths, and limitations. The article also includes examples of each method in different scenarios. The content is relevant for students studying statistics and research methods in various courses and universities.

RUNNING HEADER: RESEARCH METHODS 1
Research Methods
Student’s Name:
Student’s ID:
Institution:

Research Methods 2
Scenario 1
To carry out this test for scenario 1 a one-way ANOVA was used. The statistical method was
adopted since it establishes whether there are any statistically significant differences between
the means of two or more unrelated (independent) groups.
The assumptions that were made entailed the independent variables consisted of more than
two categorical and independent groups. Consequently, it was assumed that there was the
independence of observation in that there was no relationship between observations of the
groups themselves. The final assumption was the test of homogeneity which was shown that
the variance for time for each group was not equal, F(3, 56) = 6.247, p= 0.001.
From the test, it was established that there was a statistically significant difference between
the four groups (F=3,56) = 66.725,p = 0.00). The Tukey post hoc test showed that the time to
complete a 30m sprint was statistically different for the 1st and 2nd team, 1st and 3rd and the 1st
and 4th team. A similar observation could also be made for the 2nd team with respect to team
1, 3 and 4. However, there was no statistically significant difference between the 3rd and the
4th team (p=0.213).
Scenario 2
To determine the limits of agreement between methods and is the automatic system, a
suitable method for evaluating blood pressure, a paired sample t-test was used. The method
was chosen since it is suitable in comparing the means of two related groups on the same
dependent and continuous variable (Lakens, 2013). The strength of this method is that it
controls for the effect of the environment (Wellek, 2010). However, with the lower degrees
of freedom, it is harder to reject the null hypothesis (De Winter, 2013).

Research Methods 3
The assumptions made was that the independent variables consisted of two categorical and
related groups. Consequently, it was assumed that there was no significant outlier in the
differences between the two groups and that the distribution differences between the two
related groups were approximately normally distributed.
From the results of the paired sample t-test, it was found out that there was no statistically
significant improvement in the limits of the agreement since t(24) = -0.44, p>0.05. Thus, the
automatic system used is not as good as the manual system.
Scenario 3
To measure the effects of the two methods of warm-up on the cyclist for the three groups of
athletes, a repeated measure ANOVA was adopted. The method was chosen since it
compares three or more group mean where the participants in each group are the same. In this
scenario, the participants were subjected to more than one conditions and the response to
each condition was desired to be compared.
The main strength of this method is that the method’s design is very powerful since it
controls for factors which cause variability between subjects (Cardinal & Aitken, 2013).
However, the method is at risk of being influenced by the exposure of subjects to multiple
treatments (Levine, 2013).
The assumptions made were that the dependent variable was continuous while the
independent variables consisted of at least two categorical matched groups. Moreover, the
assumption of sphericity was upheld. However, the Maulchy test showed that the assumption
sphericity was violated (p<0.05). Thus, the focus will be on the Greenhouse-Geisser
correction. From the tests of within-subject effects, it was observed that with the Greenhouse
–Geisser correction, the mean scores were statistically different (F(1.524, 13.717 ) = 444.54,
P <0.00).

Research Methods 4
The pairwise comparison shows that there was no significant difference in performance
between the elite cyclist who undertook the passive warm up and the active warm up, the
club cyclist who took the passive and the active warmups, and the novice cyclists who took
the passive and the active warmups. However, there was a significant difference between the
treatments 1 and 3, 4, 5 and 6; treatment 2 and 3, 4,5,6; treatment 3 and 1, 2, 4,6; treatment 5
and 1,2,3,and 4; and treatment 6 and treatment 1,2,3,and 4. Thus, the type of warm-up affects
the performance of cyclists and it is dependent on their level of ability.
Scenario 4
To explore the connection between illegal performance, body image and appearance-
enhancing substance use and regular exercise, an exploratory factor analysis will be used.
The method was chosen since it measures many variables. Moreover, some of the variables
are believed to be measuring the same underlying construct (Williams, Onsman & Brown,
2010). The advantage of this method is that it is easy to use, encompasses a lot of survey
questions and it is the basis of other instruments such as regression analysis (Kline, 2014).
However, the method is limited in that its variables have to be interval-scaled. The
assumptions made is that there is a linear relationship between all variables, there is adequacy
in sampling, the data is suitable for data reduction and there are no significant outliers.

Research Methods 5
Reference
Cardinal, R. N., & Aitken, M. R. (2013). ANOVA for the behavioral sciences researcher.
Psychology Press.
De Winter, J. C. (2013). Using the Student's t-test with extremely small sample
sizes. Practical Assessment, Research & Evaluation, 18(10).
Kline, P. (2014). An easy guide to factor analysis. Routledge.
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a
practical primer for t-tests and ANOVAs. Frontiers in psychology, 4, 863.
Levine, G. (2013). A Guide to SPSS for Analysis of Variance. Psychology Press.
Wellek, S. (2010). Testing statistical hypotheses of equivalence and noninferiority. Chapman
and Hall/CRC.
Williams, B., Onsman, A., & Brown, T. (2010). Exploratory factor analysis: A five-step
guide for novices. Australasian Journal of Paramedicine, 8(3).

Research Methods 6
Appendix
Scenario 1
Table 1: Test of Homogeneity of Variances
Levene Statistic df1 df2 Sig.
6.25 3 56 0.00
Table 2: ANOVA
Sum of
Squares df
Mean
Square F Sig.
Between Groups 46.85 3 15.62 66.72 0.00
Within Groups 13.11 56 0.23
Total 59.96 59
Table 3: Tukey HSD
Lower Bound Upper Bound
1 2 -1.04 0.177 0.000 -1.512 -0.577
3 -1.94 0.177 0.000 -2.403 -1.468
4 -2.28 0.177 0.000 -2.750 -1.815
2 1 1.04 0.177 0.000 0.577 1.512
3 -0.89 0.177 0.000 -1.358 -0.423
4 -1.24 0.177 0.000 -1.706 -0.770
3 1 1.94 0.177 0.000 1.468 2.403
2 0.89 0.177 0.000 0.423 1.358
4 -0.35 0.177 0.213 -0.815 0.120
4 1 2.28 0.177 0.000 1.815 2.750
2 1.24 0.177 0.000 0.770 1.706
3 0.35 0.177 0.213 -0.120 0.815
Sig.
95% Confidence Interval
(I) Team
Mean
Difference (I-J) Std. Error
Scenario 2
Table 4: Paired sample t-test
Lower Upper
Pair 1 Manual - Automatic -0.76 8.633 1.727 -4.323 2.803 -0.44 24 0.664
Sig. (2-
tailed)
Paired Differences
95% Confidence Interval of
the Difference
Mean
Std.
Deviation
Std. Error
Mean t df

Research Methods 7
Table 5: Within-Subjects Factors
treatment
Dependent
Variable
1 Elite_passive
2 Elite_active
3 Club_passive
4 Club_active
5 Novice_passive
6 Novice_active
Table 6: Mauchly's Test of Sphericity
Greenhouse-Geisser Huynh-Feldt Lower-bound
treatment 0.00 66.63 14 0.00 0.30 0.35 0.20
Epsilon b
Within Subjects
Effect Mauchly's W Approx. Chi-Square df Sig.
Table 7: Tests of Within-Subjects Effects
Source
Type III Sum of
Squares df Mean Square F Sig.
Sphericity Assumed 2083890.2 5 416778.03 444.54 0.00
Greenhouse-Geisser 2083890.2 1.52 1367287.18 444.54 0.00
Huynh-Feldt 2083890.2 1.77 1176563.39 444.54 0.00
Lower-bound 2083890.2 1 2083890.15 444.54 0.00
Sphericity Assumed 42189.7 45 937.55
Greenhouse-Geisser 42189.7 13.72 3075.73
Huynh-Feldt 42189.7 15.94 2646.70
Lower-bound 42189.7 9 4687.74
treatment
Error(treatment)
Table 8: Pairwise Comparisons

Research Methods 8
Lower Bound Upper Bound
2 31.3 18.717 1.00 -42.71 105.31
3 127.9 22.108 0.00 40.48 215.32
4 135 22.707 0.00 45.21 224.79
5 454.8 21.382 0.00 370.25 539.35
6 456.1 21.289 0.00 371.92 540.28
1 -31.3 18.717 1.00 -105.31 42.71
3 96.6 9.698 0.00 58.25 134.95
4 103.7 10.519 0.00 62.11 145.29
5 423.5 5.945 0.00 399.99 447.01
6 424.8 5.09 0.00 404.67 444.93
1 -127.9 22.108 0.00 -215.32 -40.48
2 -96.6 9.698 0.00 -134.95 -58.25
4 7.1 1.835 0.06 -0.15 14.35
5 326.9 7.651 0.00 296.65 357.16
6 328.2 7.804 0.00 297.34 359.06
1 -135 22.707 0.00 -224.79 -45.21
2 -103.7 10.519 0.00 -145.29 -62.11
3 -7.1 1.835 0.06 -14.35 0.15
5 319.8 8.52 0.00 286.11 353.49
6 321.1 8.926 0.00 285.80 356.40
1 -454.8 21.382 0.00 -539.35 -370.25
2 -423.5 5.945 0.00 -447.01 -399.99
3 -326.9 7.651 0.00 -357.16 -296.65
4 -319.8 8.52 0.00 -353.49 -286.11
6 1.3 2.556 1.00 -8.81 11.41
1 -456.1 21.289 0.00 -540.28 -371.92
2 -424.8 5.09 0.00 -444.93 -404.67
3 -328.2 7.804 0.00 -359.06 -297.34
4 -321.1 8.926 0.00 -356.40 -285.80
5 -1.3 2.556 1.00 -11.41 8.81
1
2
3
4
5
6
95% Confidence Interval for Difference
(I) treatment (J) treatment Mean Difference (I-J) Std. Error Sig.b