1
Chi-Square Testing Hypothesis
Student’s Name
Institution Affiliation
Instructor
Date
2
1. “Is there a difference in infection proportions across the four education levels?”
No, there’s not much difference in the proportion of infection across the four education
levels.
2. “Is there a difference in infection proportions across the four sessions?”
Yes, the number of infections during the four sessions varied substantially, as highlighted
in the results section above.
3. “Is there a difference in infection proportions between people who are married or
unmarried?”
No, there is no statistically measurable difference between married and unmarried
populations regarding infection.
4. “Is the extraversion score different between those infected or not?”
Infected and non-infected persons do not show any significant differences in extraversion
scores.
5. “Is the total mucus weight different between those infected or not?”
Yes, a remarkable difference in the total weight of mucus in the infected was observed as
compared to the non-infected
6. “Is the extraversion score different across the four seasons?”
No, extraversion scores have no substantial variance across the four seasons.
7. “Is the total mucus weight different across the four seasons?”
Yes, there is a significant difference in total mucus weight for the four seasons.
3
Hypothesis testing report
This report assesses the variation in infection proportions, extraversion scores, and total
mucus weights depending on education levels, season, and marital status. The study's data
comprise nominal and interval variables to achieve the analysis's goals.
The Shapiro-Wilk test was applied to decide whether the data was normal or skewed in
the analyses. It was used to test for the normality of the data for both extraversion scores and
total mucus weights, and the results showed that the data was not normally distributed. This
conclusion was made based on the low p-values from the Shapiro-Wilk test analyses that showed
that the distribution of these variables is not normal (González-Estrada & Cosmes, 2019)
Education, session season, and marital status are categorical independent variables,
whereas the extraversion score and total mucus weight are continuous independent variables.
The only large limitation identified is that none of the datasets' assumptions or errors were
significantly violated. Still, some continuous variables needed to be more balanced, which could
indicate incorrect data entry, the presence of outliers, or the need to transform the data.
Based on the contingency, the measures derived from the statistical tests were used to
identify the type of contingency or the relationship between the categories. The Chi-square tests
for independence produced contingency tables that highlighted significant associations between
some categorical variables. For instance, a high Chi-Square value meant that there was a
relationship between session seasons and infection proportions, implying that the infection
proportions differ with the session's season.
While comparing the results of statistical analyses, the following tests have been
employed to compare two groups or more than two groups, and the Independent Samples T-Test
was applied to compare the means of two independent variables, such as the scores for
4
extraversion and total mucus weights between infected and non-infected people (Beyer, 2021).
The One-Way ANOVA was used to compare more than two means: self-extraversion and total
mucus weight in the four seasons. Chi-square tests were employed to determine if there were
differences in the proportion of infections between categories such as education level, the session
attended, and marital status.
These analyses revealed highly significant variations of infection proportions among
different sessions or in total mucus weights among different infection statuses and seasons. More
particularly, the Chi-Square test outcomes unveiled (𝜒2(3, 𝑁=406) =8. 869χ2(3, N=406) =8.
869, 𝑝=0. 031p=0. 031) suggested a meaningful variation in the share of infections by sessions,
and the results of the Independent Samples T-Test (𝑡 (403) =−3. 450t (403) =−3. 450, 𝑝<0.
001p<0. 001) the P value depicted in the following table indicated the difference in total mucus
weight between infected and non-infected persons were statistically significant.
The One-Way ANOVA results stood at F (3,402) =5. In addition, the study discovered a
statistically significant difference in mean number of refills among the groups (F3,402=5. 842F
(3,402) =5. 842, 𝑝=0. 001p=0. This corresponds to the marked result on the total mucus weight,
where a variation was perceived across the four seasons. On the other hand, there were no
observed statistical differences between the groups regarding how the proportion of infection is
impacted by education level (𝜒2(3, 𝑁=406) =0. 528χ2(3, N=406) =0. 528, 𝑝=0. 913p=0.
There were significant differences in mean scores between groups of people with
different numbers of children (F (2, 𝑁=442) = 2. 849χ2(1, N=406) =0. 849, 𝑝=0. 357p=0. The
result also indicates that the mean of the total score of the students in the experimental group is
significantly higher than that of the control group by performing the Independent Samples T-
Test, F (404) = -0. 954t (404) =−0. 954, 𝑝=0. 341p=0. 341) and One-Way ANOVA results (F (3,
5
402) = 1. 062F (3,402) =1. 062, 𝑝=0. 365p=0. Furthermore, in the study, it was found that there
were no significant variations in levels of extraversion based on whether subjects had a viral
infection or not or if the examinees were tested in one or another season.
Finally, the main findings shed light on the effects of session timing and season variation
on the rate of infections and mucus secretion, which would be valuable in public health.
Nonetheless, in the context of this study, factors such as education level, marital status, and
levels of extraversion do not influence this matter.
6
References
Beyer, A. (2021). Chapter 13: Independent Samples. Open.maricopa.edu.
https://open.maricopa.edu/psy230mm/chapter/chapter-13-independent-samples/
González-Estrada, E., & Cosmes, W. (2019). Shapiro–Wilk test for skew-normal distributions
based on data transformations. Journal of Statistical Computation and Simulation, 89(17),
3258–3272. https://doi.org/10.1080/00949655.2019.1658763
