RACHELLE FORMILLES GROUP STATISTICAL ANALYSIS
Kyle Kenneth Ruaya
2024-02-14
Data
1. What is the demographic profile of the respondents in terms of:
Attaching package: 'dplyr'The following objects are masked from 'package:stats':
filter, lagThe following objects are masked from 'package:base':
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 57 females and 43 males; 20 of which are from ABM, 20 from GAS, 40 from HUMSS, and 20 from STEM.
2. Is there a significant difference on the perceptions of the students towards mandatory ROTC in terms of physical capabilities, psychological capabilities, and attitude when grouped according to:
2.1 Sex
Call:
lm(formula = Attitude ~ `Physical Capabilities` + `Psychological Capabilities`,
data = Data)
Coefficients:
(Intercept) `Physical Capabilities`
1.73497 0.05187
`Psychological Capabilities`
0.27566 
From this, we may deduce that the data fail to satisfy the two assumptions – Linearity and Homogeneity of Variance.
2.1.1 Sex and Physical Capabilities
`summarise()` has grouped output by 'Sex'. You can override using the `.groups`
argument.
Attaching package: 'rstatix'The following object is masked from 'package:stats':
filterThe mean for male and female is 3.121 and 2.989, respectively.
The above graph shows the plotting of data by sex, which contains two sexes – male and female.
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsWarning: The following aesthetics were dropped during statistical transformation: fill
ℹ This can happen when ggplot fails to infer the correct grouping structure in
the data.
ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
variable into a factor?
It clearly shows that there is difference between the perception of students towards mandatory ROTC in terms of physical capabilities when grouped according to their sex.
Loading required package: carData
Attaching package: 'car'The following object is masked from 'package:purrr':
someThe following object is masked from 'package:dplyr':
recode
The histogram does not resemble a bell curve as seen above, means that the residuals do not have a normal distribution. Moreover, the points in the QQ-plots roughly follow the straight line, with the majority of them falling within the confidence bands. However, this does not guarantee that residuals follow a normal distribution since when based on the diagram on the left, it is the exact opposite of it. Thus, it is more convenient to observe the two.
Normality Test
Shapiro-Wilk normality test
data: res_aov$residuals
W = 0.96825, p-value = 0.01626The Shapiro-Wilk p-value = 0.01626 on the residuals is less than the usual significance level of 0.05. Thus, we reject the hypothesis that residuals have a normal distribution.
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 0.1493 0.7
98 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Wilcoxon Rank Sum Test
Wilcoxon rank sum test
data: a and b
W = 1469, p-value = 0.08476
alternative hypothesis: true location shift is not equal to 0Since the p-value is larger than 0.05, we fail to reject the null hypothesis, that is, there is no significant difference on the perception of the students in terms of physical capabilities when grouped according to sex.
2.1.2 Sex and Psychological Capabilities
`summarise()` has grouped output by 'Sex'. You can override using the `.groups`
argument.# A tibble: 20 × 3
# Groups: Sex [2]
Sex `Psychological Capabilities` count
<fct> <dbl> <int>
1 Female 2.2 1
2 Female 2.4 4
3 Female 2.6 5
4 Female 2.8 3
5 Female 3 16
6 Female 3.2 9
7 Female 3.4 8
8 Female 3.6 6
9 Female 3.8 2
10 Female 4 3
11 Male 2.2 2
12 Male 2.4 2
13 Male 2.6 1
14 Male 2.8 9
15 Male 3 6
16 Male 3.2 7
17 Male 3.4 5
18 Male 3.6 6
19 Male 3.8 3
20 Male 4 2The mean for male and female is 3.149 and 3.130, respectively.
The above graph shows the plotting of data by sex, which contains two sexes – male and female.
Warning: The following aesthetics were dropped during statistical transformation: fill
ℹ This can happen when ggplot fails to infer the correct grouping structure in
the data.
ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
variable into a factor?
The histogram does not resemble a bell curve as seen above, means that the residuals do not have a normal distribution. Moreover, the points in the QQ-plots roughly follow the straight line, with the majority of them falling within the confidence bands. However, this does not guarantee that residuals follow a normal distribution since when based on the diagram on the left, it is the exact opposite of it. Thus, it is more convenient to observe the two.
Normality Test
Shapiro-Wilk normality test
data: res_aov$residuals
W = 0.97513, p-value = 0.05525The Shapiro-Wilk p-value = 0.05525 on the residuals is greater than the usual significance level of 0.05. Thus, we fail to reject the hypothesis that residuals have a normal distribution.
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 0.3591 0.5504
98 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Two Sample T-test
Welch Two Sample t-test
data: c and d
t = 0.21253, df = 87.075, p-value = 0.8322
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.1587920 0.1968173
sample estimates:
mean of x mean of y
3.148837 3.129825 Since the p-value= 0.8322 is greater than 0.05, we fail to reject the null hypothesis. Hence, there is no significant difference on the perception of the students towards mandatory ROTC in terms of psychological capabilities when grouped according to their sex.
2.1.3 Sex and Attitude
`summarise()` has grouped output by 'Sex'. You can override using the `.groups`
argument.# A tibble: 21 × 3
# Groups: Sex [2]
Sex Attitude count
<fct> <dbl> <int>
1 Female 1.6 1
2 Female 1.8 2
3 Female 2.2 6
4 Female 2.4 3
5 Female 2.6 14
6 Female 2.8 7
7 Female 3 12
8 Female 3.2 3
9 Female 3.4 5
10 Female 3.6 3
# ℹ 11 more rowsThe mean for male and female is 2.716 and 2.789, respectively.
The above graph shows the plotting of data by sex, which contains two sexes – male and female.
The histogram does not resemble a bell curve as seen above, means that the residuals do not have a normal distribution. Moreover, the points in the QQ-plots roughly follow the straight line, with the majority of them falling within the confidence bands. However, this does not guarantee that residuals follow a normal distribution since when based on the diagram on the left, it is the exact opposite of it. Thus, it is more convenient to observe the two.
Normality Test
Shapiro-Wilk normality test
data: res_aov$residuals
W = 0.98744, p-value = 0.4682The Shapiro-Wilk p-value = 0.4682 on the residuals is less than the usual significance level of 0.05. Thus, we reject the hypothesis that residuals have a normal distribution.
Equality of Variance
Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.1559 0.6938
98 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Two Sample T-test
Welch Two Sample t-test
data: e and f
t = -0.7768, df = 92.437, p-value = 0.4393
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.2603230 0.1139338
sample estimates:
mean of x mean of y
2.716279 2.789474 Since the p-value= 0.4393 is greater than 0.05, we fail to reject the null hypothesis. Hence, there is no significant difference on the perception of the students towards mandatory ROTC in terms of attitude when grouped according to their sex.
2.2 Strand
2.2.1 Strand and “Physical Capabilities”
Normality Test
Shapiro-Wilk normality test
data: Data$`Physical Capabilities`
W = 0.95467, p-value = 0.001708Since p-value = 0.001708 < 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 0.6565 0.5808
96 The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.
Attaching package: 'gplots'The following object is masked from 'package:stats':
lowessWarning 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
a graphical parameterWarning 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 GAS Physical Capabi… 20 2.6 3.8 3 0.45 3.15 0.343 0.077 0.16
2 HUMSS Physical Capabi… 40 1.8 4 3 0.45 3.02 0.435 0.069 0.139
3 ABM Physical Capabi… 20 2 3.8 2.9 0.45 2.87 0.491 0.11 0.23
4 STEM Physical Capabi… 20 2.6 3.8 3.1 0.45 3.18 0.394 0.088 0.184The mean of GAS, HUMSS, ABM, and STEm is 3.150, 3.015, 2.870, and 3.180, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Physical Capabilities 100 6.48 3 0.0905 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 Physical Capabi… GAS HUMSS 20 40 -1.19 0.232 1 ns
2 Physical Capabi… GAS ABM 20 20 -2.03 0.0426 0.255 ns
3 Physical Capabi… GAS STEM 20 20 0.191 0.848 1 ns
4 Physical Capabi… HUMSS ABM 40 20 -1.15 0.251 1 ns
5 Physical Capabi… HUMSS STEM 40 20 1.42 0.157 0.941 ns
6 Physical Capabi… ABM STEM 20 20 2.22 0.0265 0.159 ns There is a significant difference between GAS and ABM, ABM and STEM.
2.2.2 Strand and Psychological Capabilities
Normality Test
Shapiro-Wilk normality test
data: Data$`Psychological Capabilities`
W = 0.97033, p-value = 0.02343Since p-value = 0.02343 < 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 0.1167 0.9501
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
graphical parameterWarning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
a graphical parameterWarning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameter
# 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 GAS Psychological C… 20 2.6 4 3.1 0.8 3.21 0.408 0.091 0.191
2 HUMSS Psychological C… 40 2.2 4 3.2 0.6 3.06 0.458 0.072 0.147
3 ABM Psychological C… 20 2.2 4 3.1 0.45 3.19 0.47 0.105 0.22
4 STEM Psychological C… 20 2.4 3.8 3.1 0.4 3.16 0.393 0.088 0.184The mean of GAS, HUMSS, ABM, and STEM is 3.210, 3.065, 3.190, and 3.160, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Psychological Capabilities 100 1.25 3 0.741 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 Psychological Ca… GAS HUMSS 20 40 -0.903 0.366 1 ns
2 Psychological Ca… GAS ABM 20 20 -0.0330 0.974 1 ns
3 Psychological Ca… GAS STEM 20 20 -0.179 0.858 1 ns
4 Psychological Ca… HUMSS ABM 40 20 0.865 0.387 1 ns
5 Psychological Ca… HUMSS STEM 40 20 0.696 0.486 1 ns
6 Psychological Ca… ABM STEM 20 20 -0.146 0.884 1 ns 2.2.3 Strand and Attitude
Normality Test
Shapiro-Wilk normality test
data: Data$Attitude
W = 0.97951, p-value = 0.1217Since p-value = 0.1217 < 0.05, it is conclusive that we fail to reject the null hypothesis. That is, we can 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 0.879 0.4549
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
graphical parameterWarning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
a graphical parameterWarning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameter
# 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 GAS Attitude 20 2.2 3.6 2.8 0.6 2.84 0.382 0.085 0.179
2 HUMSS Attitude 40 1.4 4 2.8 0.4 2.75 0.485 0.077 0.155
3 ABM Attitude 20 1.6 3.4 2.5 0.8 2.53 0.512 0.115 0.24
4 STEM Attitude 20 2.2 3.8 2.8 0.45 2.92 0.402 0.09 0.188The mean of GAS, HUMSS, ABM, and STEM is 2.84, 2.75, 2.53, and 2.93, respectively.
One WAY ANOVA
Df Sum Sq Mean Sq F value Pr(>F)
Strand 3 1.702 0.5672 2.722 0.0486 *
Residuals 96 20.002 0.2084
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1It is conclusive that there is a significant difference on the perception of the students towards mandatory ROTC in terms of attitude when grouped according to strand.
3. Is there a significant relationship between physical capabilities, psychological capabilities, and attitude in terms of the perception of the students towards mandatory ROTC?
Normality Test
Shapiro-Wilk normality test
data: Data1$`Scores in terms of the perception of the students towards mandatory ROTC`
W = 0.97705, p-value = 9.754e-05Since p-value = 9.754e-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 2 0.437 0.6464
297 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
a graphical parameterWarning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameter
# A tibble: 3 × 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 Capa… Scores … 100 1.8 4 3 0.6 3.05 0.431 0.043 0.086
2 Psychological… Scores … 100 2.2 4 3.2 0.6 3.14 0.436 0.044 0.087
3 Attitude Scores … 100 1.4 4 2.8 0.4 2.76 0.468 0.047 0.093The mean of physical capabilities, psychological capabilities, and attitude is 3.046, 3.138, and 2.758, respectively.
Kruskal-wallis Test
# A tibble: 1 × 6
.y. n statistic df p method
* <chr> <int> <dbl> <int> <dbl> <chr>
1 Scores in terms of the perception of the… 300 34.0 2 4.07e-8 Krusk…Based on the p-value, there is a significant difference was observed between the group pairs.
Pairwise Comparisons
# A tibble: 3 × 9
.y. group1 group2 n1 n2 statistic p p.adj p.adj.signif
* <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <chr>
1 Scores in te… Physi… Psych… 100 100 1.45 1.47e-1 4.40e-1 ns
2 Scores in te… Physi… Attit… 100 100 -4.17 3.08e-5 9.25e-5 ****
3 Scores in te… Psych… Attit… 100 100 -5.62 1.92e-8 5.75e-8 **** Pairwise, there is significant difference.
4. Which have the most significant impact?
Based on the provided output above, it can be seen that the main factor of the perception of the students is psychological capabilities.