ROAN CONGRESO GROUP STATISTICAL ANALYSIS
Kyle Kenneth Ruaya
2024-02-19
Data
1. What is the demographic profile of the respondents in terms of:
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intersect, setdiff, setequal, unionSex
Strand
The tables above provides the distributions of respondents in terms of sex, year level, and strand. It can be seen that there are 58 females and 42 males; 23 of which are from ABM, 22 from GAS, 31 from HUMSS, and 24 from STEM.
2. Is there a significant difference on the variables physical health and mental health when grouped according to:
2.1 Sex
Call:
lm(formula = `Physical Health` ~ `Mental Health`, data = Data)
Coefficients:
(Intercept) `Mental Health`
1.1373 0.6103 
From this, we may deduce that the data fail to satisfy two assumptions – Linearity and Homogeneity of Variance.
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filter2.1.1 Sex and Physical Health
Normality Test
Shapiro-Wilk normality test
data: Data$`Physical Health`
W = 0.95947, p-value = 0.003686Since p-value = 0.003686 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.
Equality of Variance
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Df F value Pr(>F)
group 1 0.2379 0.6268
98 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
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# A tibble: 2 × 11
Sex variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Female Physical Health 58 2 3.8 3 0.4 2.92 0.4 0.053 0.105
2 Male Physical Health 42 2.2 4 2.8 0.2 2.90 0.383 0.059 0.119The mean of female and male is 2.917 and 2.905, respectively.
Mann Whitney U Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Physical Health 100 0.0830 1 0.773 Kruskal-WallisBased on the p-value, there is no significant difference on the physical health when grouped according to sex.
2.1.2 Sex and Mental Health
Normality Test
Shapiro-Wilk normality test
data: Data$`Mental Health`
W = 0.95781, p-value = 0.002816Since p-value = 0.002816 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.
Equality of Variance
Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.8262 0.3656
98 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
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# A tibble: 2 × 11
Sex variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Female Mental Health 58 2 3.8 3 0.4 2.91 0.352 0.046 0.092
2 Male Mental Health 42 1.8 4 2.9 0.35 2.90 0.44 0.068 0.137The mean of female and male is 2.910 and 2.905, respectively.
Mann Whitney U Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Mental Health 100 0.00325 1 0.955 Kruskal-WallisBased on the p-value, there is no significant difference on the physical health when grouped according to sex.
2.2 Strand
2.2.1 Strand and Physical Health
Normality Test
Shapiro-Wilk normality test
data: Data$`Physical Health`
W = 0.95947, p-value = 0.003686Since p-value = 0.003686 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.
Equality of Variance
Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 3 0.072 0.9748
96 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
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# A tibble: 4 × 11
Strand variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 STEM Physical Health 24 2.6 4 3 0.3 3.13 0.371 0.076 0.157
2 ABM Physical Health 23 2.2 3.6 2.8 0.4 2.78 0.366 0.076 0.158
3 HUMSS Physical Health 31 2 3.6 2.8 0.4 2.86 0.384 0.069 0.141
4 GAS Physical Health 22 2.2 3.6 3 0.35 2.88 0.374 0.08 0.166The mean of STEM, ABM, HUMSS, and GAS is 3.133, 2.783, 2.858, and 2.882, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Physical Health 100 11.1 3 0.0114 Kruskal-WallisBased on the p-value, there is significant difference was observed between the group pairs.
Pairwise Comparisons
# A tibble: 6 × 9
.y. group1 group2 n1 n2 statistic p p.adj p.adj.signif
* <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr>
1 Physical Heal… STEM ABM 24 23 -3.14 0.00170 0.0102 *
2 Physical Heal… STEM HUMSS 24 31 -2.58 0.00984 0.0591 ns
3 Physical Heal… STEM GAS 24 22 -1.91 0.0559 0.335 ns
4 Physical Heal… ABM HUMSS 23 31 0.777 0.437 1 ns
5 Physical Heal… ABM GAS 23 22 1.18 0.239 1 ns
6 Physical Heal… HUMSS GAS 31 22 0.493 0.622 1 ns There is significant difference between STEM and ABM, STEM and HUMSS.
2.2.2 Strand and Mental Health
Normality Test
Shapiro-Wilk normality test
data: Data$`Mental Health`
W = 0.95781, p-value = 0.002816Since p-value = 0.002816 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.
Equality of Variance
Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 3 0.3016 0.8242
96 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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# A tibble: 4 × 11
Strand variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 STEM Mental Health 24 2.4 4 3 0.4 3.02 0.377 0.077 0.159
2 ABM Mental Health 23 2 3.8 2.8 0.4 2.87 0.416 0.087 0.18
3 HUMSS Mental Health 31 1.8 3.6 2.8 0.4 2.81 0.363 0.065 0.133
4 GAS Mental Health 22 2.2 3.8 3 0.35 2.97 0.392 0.084 0.174The mean of STEM, ABM, HUMSS, and GAS is 3.017, 2.870, 2.806, and 2.973, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Mental Health 100 5.62 3 0.132 Kruskal-WallisBased on the p-value, there is no significant difference was observed between the group pairs.
Pairwise Comparisons
# A tibble: 6 × 9
.y. group1 group2 n1 n2 statistic p p.adj p.adj.signif
* <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr>
1 Mental Health STEM ABM 24 23 -1.42 0.154 0.926 ns
2 Mental Health STEM HUMSS 24 31 -2.15 0.0314 0.188 ns
3 Mental Health STEM GAS 24 22 -0.439 0.660 1 ns
4 Mental Health ABM HUMSS 23 31 -0.616 0.538 1 ns
5 Mental Health ABM GAS 23 22 0.959 0.338 1 ns
6 Mental Health HUMSS GAS 31 22 1.63 0.102 0.614 ns There is significant difference between STEM and HUMSS.
3. Is there a significant relationship between physical health and mental health?
Normality Test
Shapiro-Wilk normality test
data: Data1$Scores
W = 0.96029, p-value = 2.126e-05Since p-value = 2.126e-05 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.
Equality of Variance
Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.012 0.913
198 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameterWarning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
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# A tibble: 2 × 11
Variables variable n min max median iqr mean sd se ci
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Physical Heal… Scores 100 2 4 2.9 0.4 2.91 0.391 0.039 0.078
2 Mental Health Scores 100 1.8 4 3 0.4 2.91 0.389 0.039 0.077The mean of physical health and mental health is 2.912 and 2.908, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Scores 200 0.00675 1 0.935 Kruskal-WallisBased on the p-value, there is no significant difference between physical health and mental health.
4. On which variable does academic workload have the most significant impact?
Based on the provided output above, we can say that it is the physical health.