Quantitative Analysis of Advanced Research Methods Assignment

This assignment presents a quantitative assessment of advanced research methods, focusing on two primary analyses: an independent samples t-test and multiple linear regression. The t-test is employed to compare heart rates under different experimental conditions (thinking about running vs. solving math problems), revealing statistically significant differences in the task phase but not in the baseline or resting phases. The analysis includes descriptive statistics, t-test results, and considerations for effect size and assumptions (normality, outliers). The second part utilizes multiple linear regression to identify predictors of baseline heart rate, with variables including BMI, smoking, age, alcohol, and dominance personality traits. The regression analysis indicates that none of these variables significantly predict baseline heart rate, though the constant term is significant. The assignment also includes a discussion of model assumptions, such as normality of residuals and homoscedasticity, and suggests further research questions related to gender and personality traits.

Running head: ADVANCED RESEARCH METHODS 1
Advanced Research Methods – Quantitative Assessment
Name
Institution

ADVANCED RESEARCH METHODS 2
Advanced Research Methods – Quantitative Assessment
Question 1
a. The method of analysis is the independent sample t-test as the independent
variable (condition) has two factors. The approach is suitable for comparing the
means between two separate groups on the same continuous, dependent variable.
The continuous dependent variable is heart rate.
b. Table 1 shows the descriptive statistics of the variables.
Table 1
Descriptive Statistics for Variables
Thinking about going
for a run
Thinking about solving
some math problems
Phase of
Experiment Mean SD Mean SD
Baseline 73.21 12.75 71.88 10.29
Task 85.99 14.26 79.13 10.26
Resting 73.66 12.29 72.06 9.79
The average heart rate when thinking about going for a run differs from baseline
to resting at a higher rate when performing the task. Similarly, the average heart
rate when thinking about solving some math problems differs from baseline to
resting at a higher rate when performing the task. However, the heart rates are
slightly higher when thinking about going for a run than
solving some math problems. Table 2 shows the test results.
Table 2

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Independent Samples t-test Results
Phase of Experiment t-statistic df P-value
Baseline 0.277 79 0.783
Task 2.231 77 0.029
Resting 0.263 80 0.793
The analysis found that the participants at 95% confidence level had statistically
significantly different heart rate when thinking about going for a run (mean =
85.99, SD = 14.26) and when thinking about solving some math problems (mean
= 79.13, SD = 10.26), t (77)=2.231 , p=0.029 in the task phase. However, at a
95% confidence level, there was no statistically significant difference in the heart
rate during the baseline and resting phase of the experiment. The test results were
t ( 79 )=0.277 , p=0.783 and t ( 80 )=0.263 , p=0.793, for baseline and resting,
respectively.
c. It will be of interest to know if the observed differences in the average heart rate
in the task phase are significant enough to warrant practical meaning. Further
analysis of the results should be performed, such as “Effect size” for the t-test.
This test indicates whether or not the difference between the two groups’ averages
is large enough to have practical meaning, whether or not it is statistically
significant. In SPSS, Cohen’s d tests show the effect sizes. In addition to the test
of effect sizes, the assumption underlying independent t-test should be checked to
improve the credibility of the results.
These assumptions include the independence of the phase of the experiment,
normality of the average heart rate, and the existence of outliers. The normality

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of the response variable can be checked using a histogram with a standard
probability plot and confirmed by the Shapiro-Wilk test. If the normality
assumption is violated, then the non-parametric equivalent test should be
performed (Mann-Whitney test). Outliers are values that do not follow the general
pattern of the data, and they significantly affect the mean. Thus, affecting the
estimated t-statistics. In checking for the existence of outliers, a boxplot of the
response variable is examined, and if any outlier exists, it is then removed from
the data.
Question 2
a. The method suitable for this analysis is multiple linear regression, as the response
variable is continuous (baseline heart rate). Further, the researcher is interested in
identifying the significant predictors of heart rate, making the task a regression
problem. The independent variables are more than one, thus making multiple
regression suitable.
b. The regression model takes the form:
Y i=β0 +β1 X1 i+ β2 X2 i+ β3 X3 i +β4 X 4 i+ β5 X5 i +ei
Where:
Y i=¿ Baseline heart rate
β0 , β1 , … , β5=¿ intercept and slope estimates (parameter estimates)
X1 i=¿ BMI score
X2 i=¿ Smoking
X3 i=¿ Age
X 4 i=¿ Alcohol

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X5 i=¿ Dominance personality trait
ei=¿ Residuals (assumed to be normally distributed with constant variance)
Table 3 shows the regression estimates.
Table 3
Regression Estimates for Baseline Heart Rate (Response)
Variable Estimate Std. Error t-statistic P-vale
Constant 80.938 10.676 7.581 0.000
BMI -0.320 0.438 -0.730 0.468
Smoking 0.453 0.321 1.412 0.162
Age 0.108 0.235 0.458 0.648
Alcohol -0.236 0.268 -0.883 0.380
Dominance -4.477 2.520 -1.777 0.080
The estimated equation is
^Y =80.938−0.320 X1 +0.453 X 2+0.108 X3−0.236 X 4−4.477 X5
All the slope parameters are statistically insignificant at a 95% confidence level since
the p-values are greater than α=0.05. However, the constant term is significant (p =
0.00), indicating that other factors not included in the model affect the baseline heart
rate. Therefore, BMI, smoking, age, alcohol, and dominant personality does not
predict the baseline heart rate. These results might not be valid if some of the
assumptions of multiple regression analysis are violated. Figure 1 shows the
histogram plot of the residuals.

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Figure 1. Histogram plot with standard normal probability density overlay
The plot shows that the residuals are approximately normal, as the histogram is bell-
shaped. Shapiro-Wilk normality test further confirms that the residuals are
approximately normally distributed at a 5% significance level,
W ( 74 )=0.985 , p=0.505. The p-value is greater than 0.05, hence fail to reject the null
hypothesis of normality. Therefore, the results obtained from the regression are valid
and can be generalized. Another assumption that could be checked is the constant
variance of the residuals (homoscedasticity). Figure 2 shows a plot of residuals and
predicted values.

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Figure 2. Scatter plot of standardized residuals and the predicted values
The plots are random without any observable patter indicating that the assumption of
homoscedasticity is met. Finally, the observations were selected independently, thus
satisfying the assumption of independence of the observations.
c. The research team should look into the following hypotheses:
1) Whether there is a difference in baseline heart rate among the gender.
2) Whether there is a difference in task heart rate among the gender.
3) Whether there is a difference in resting heart rate among the gender.
4) Characteristics (openness, conscientiousness, extraversion, agreeableness, and
neuroticism) different significantly among the gender
5) Characteristics (openness, conscientiousness, extraversion, agreeableness, and
neuroticism) different significantly among age groups

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These hypotheses can assist the team in gaining a better understanding of the data.
The age groups can be created from the dataset using intervals such as ten years apart
or five years apart. Gender is an essential demographic variable that has been shown
to affect the outcome of behaviors.