Data

library(dplyr)


Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

library(readxl)
Data <- read_excel("D:/SY 21-22 Second Sem/STAT 50/Data.xlsx")
Data

Answer as indicated

1. Provide the same output provided below

1.1 First output:

library(dplyr)
Data%>%
  group_by(`Course Taken`)%>%
  summarise(Frequency = n(), `Mean Age` = mean(Age))

1.2 Second output:

Consider the variables: In5, Ex4, TP3, and CP2

library(dplyr)
Data%>%
  group_by(`Course Taken`)%>%
  summarise(Frequency = n(), `Mean Intrinsic5` =  mean(`In5`),
            `Mean Extrinsic4` = mean(Ex4), `Mean TP3` = mean(TP3), `Mean CP2` = mean(CP2))

Recoding the responses in Variables “In1 and In2” with the following changes

"1 for "Strongly Disagree"
"2" for "Disagree"
"3" for "Moderately Disagree"
"4" for "Neutral"
"5" for "Moderately Agree"
"6" for Agree
"7" for "Strongly Agree"

library(dplyr)
Data<-Data%>%
  mutate(In1.1=recode(`In1`, 
                          "1" = "Strongly Disagree", "2" = "Disagree","3" = "Moderately Disagree", "4" = "Neutral", "5" = "Moderately Agree", "6" = "Agree","7" = "Strongly Agree"))%>%
 mutate(In1.2=recode(`In2`, 
                          "1" = "Strongly Disagree", "2" = "Disagree","3" = "Moderately Disagree", "4" = "Neutral", "5" = "Moderately Agree", "6" = "Agree","7" = "Strongly Agree"))

2. Answer the following:

    a. HOw many observations in Variable In1 that are strongly agree at the same time moderately disagree in variable In2?
    Answer: 0
    b. HOw many observations in Variable In2 that are strongly agree at the same time Neutral in variable In1?
    Answer: 3

library(gmodels)

Warning: package 'gmodels' was built under R version 4.1.3

Crosstable<-CrossTable(Data$In1.1, Data$In1.2)


 
   Cell Contents
|-------------------------|
|                       N |
| Chi-square contribution |
|           N / Row Total |
|           N / Col Total |
|         N / Table Total |
|-------------------------|

 
Total Observations in Table:  163 

 
                    | Data$In1.2 
         Data$In1.1 |               Agree |            Disagree |    Moderately Agree | Moderately Disagree |             Neutral |      Strongly Agree |   Strongly Disagree |           Row Total | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
              Agree |                  26 |                   0 |                   2 |                   0 |                   0 |                   9 |                   0 |                  37 | 
                    |              11.254 |               0.681 |               7.263 |               1.135 |               2.497 |               0.213 |               0.454 |                     | 
                    |               0.703 |               0.000 |               0.054 |               0.000 |               0.000 |               0.243 |               0.000 |               0.227 | 
                    |               0.433 |               0.000 |               0.042 |               0.000 |               0.000 |               0.265 |               0.000 |                     | 
                    |               0.160 |               0.000 |               0.012 |               0.000 |               0.000 |               0.055 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
           Disagree |                   0 |                   1 |                   2 |                   1 |                   0 |                   0 |                   0 |                   4 | 
                    |               1.472 |              11.657 |               0.574 |               6.273 |               0.270 |               0.834 |               0.049 |                     | 
                    |               0.000 |               0.250 |               0.500 |               0.250 |               0.000 |               0.000 |               0.000 |               0.025 | 
                    |               0.000 |               0.333 |               0.042 |               0.200 |               0.000 |               0.000 |               0.000 |                     | 
                    |               0.000 |               0.006 |               0.012 |               0.006 |               0.000 |               0.000 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
   Moderately Agree |                  20 |                   0 |                  17 |                   1 |                   2 |                   7 |                   0 |                  47 | 
                    |               0.421 |               0.865 |               0.721 |               0.135 |               0.433 |               0.802 |               0.577 |                     | 
                    |               0.426 |               0.000 |               0.362 |               0.021 |               0.043 |               0.149 |               0.000 |               0.288 | 
                    |               0.333 |               0.000 |               0.354 |               0.200 |               0.182 |               0.206 |               0.000 |                     | 
                    |               0.123 |               0.000 |               0.104 |               0.006 |               0.012 |               0.043 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
Moderately Disagree |                   0 |                   0 |                   4 |                   1 |                   0 |                   1 |                   0 |                   6 | 
                    |               2.209 |               0.110 |               2.822 |               3.617 |               0.405 |               0.051 |               0.074 |                     | 
                    |               0.000 |               0.000 |               0.667 |               0.167 |               0.000 |               0.167 |               0.000 |               0.037 | 
                    |               0.000 |               0.000 |               0.083 |               0.200 |               0.000 |               0.029 |               0.000 |                     | 
                    |               0.000 |               0.000 |               0.025 |               0.006 |               0.000 |               0.006 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
            Neutral |                   9 |                   2 |                  22 |                   1 |                   8 |                   3 |                   0 |                  45 | 
                    |               3.454 |               1.658 |               5.776 |               0.105 |               8.112 |               4.345 |               0.552 |                     | 
                    |               0.200 |               0.044 |               0.489 |               0.022 |               0.178 |               0.067 |               0.000 |               0.276 | 
                    |               0.150 |               0.667 |               0.458 |               0.200 |               0.727 |               0.088 |               0.000 |                     | 
                    |               0.055 |               0.012 |               0.135 |               0.006 |               0.049 |               0.018 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
     Strongly Agree |                   5 |                   0 |                   1 |                   0 |                   0 |                  13 |                   0 |                  19 | 
                    |               0.568 |               0.350 |               3.774 |               0.583 |               1.282 |              20.606 |               0.233 |                     | 
                    |               0.263 |               0.000 |               0.053 |               0.000 |               0.000 |               0.684 |               0.000 |               0.117 | 
                    |               0.083 |               0.000 |               0.021 |               0.000 |               0.000 |               0.382 |               0.000 |                     | 
                    |               0.031 |               0.000 |               0.006 |               0.000 |               0.000 |               0.080 |               0.000 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
  Strongly Disagree |                   0 |                   0 |                   0 |                   1 |                   1 |                   1 |                   2 |                   5 | 
                    |               1.840 |               0.092 |               1.472 |               4.673 |               1.301 |               0.002 |              61.261 |                     | 
                    |               0.000 |               0.000 |               0.000 |               0.200 |               0.200 |               0.200 |               0.400 |               0.031 | 
                    |               0.000 |               0.000 |               0.000 |               0.200 |               0.091 |               0.029 |               1.000 |                     | 
                    |               0.000 |               0.000 |               0.000 |               0.006 |               0.006 |               0.006 |               0.012 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|
       Column Total |                  60 |                   3 |                  48 |                   5 |                  11 |                  34 |                   2 |                 163 | 
                    |               0.368 |               0.018 |               0.294 |               0.031 |               0.067 |               0.209 |               0.012 |                     | 
--------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|---------------------|

Crosstable

$t
                     y
x                     Agree Disagree Moderately Agree Moderately Disagree
  Agree                  26        0                2                   0
  Disagree                0        1                2                   1
  Moderately Agree       20        0               17                   1
  Moderately Disagree     0        0                4                   1
  Neutral                 9        2               22                   1
  Strongly Agree          5        0                1                   0
  Strongly Disagree       0        0                0                   1
                     y
x                     Neutral Strongly Agree Strongly Disagree
  Agree                     0              9                 0
  Disagree                  0              0                 0
  Moderately Agree          2              7                 0
  Moderately Disagree       0              1                 0
  Neutral                   8              3                 0
  Strongly Agree            0             13                 0
  Strongly Disagree         1              1                 2

$prop.row
                     y
x                          Agree   Disagree Moderately Agree
  Agree               0.70270270 0.00000000       0.05405405
  Disagree            0.00000000 0.25000000       0.50000000
  Moderately Agree    0.42553191 0.00000000       0.36170213
  Moderately Disagree 0.00000000 0.00000000       0.66666667
  Neutral             0.20000000 0.04444444       0.48888889
  Strongly Agree      0.26315789 0.00000000       0.05263158
  Strongly Disagree   0.00000000 0.00000000       0.00000000
                     y
x                     Moderately Disagree    Neutral Strongly Agree
  Agree                        0.00000000 0.00000000     0.24324324
  Disagree                     0.25000000 0.00000000     0.00000000
  Moderately Agree             0.02127660 0.04255319     0.14893617
  Moderately Disagree          0.16666667 0.00000000     0.16666667
  Neutral                      0.02222222 0.17777778     0.06666667
  Strongly Agree               0.00000000 0.00000000     0.68421053
  Strongly Disagree            0.20000000 0.20000000     0.20000000
                     y
x                     Strongly Disagree
  Agree                      0.00000000
  Disagree                   0.00000000
  Moderately Agree           0.00000000
  Moderately Disagree        0.00000000
  Neutral                    0.00000000
  Strongly Agree             0.00000000
  Strongly Disagree          0.40000000

$prop.col
                     y
x                          Agree   Disagree Moderately Agree
  Agree               0.43333333 0.00000000       0.04166667
  Disagree            0.00000000 0.33333333       0.04166667
  Moderately Agree    0.33333333 0.00000000       0.35416667
  Moderately Disagree 0.00000000 0.00000000       0.08333333
  Neutral             0.15000000 0.66666667       0.45833333
  Strongly Agree      0.08333333 0.00000000       0.02083333
  Strongly Disagree   0.00000000 0.00000000       0.00000000
                     y
x                     Moderately Disagree    Neutral Strongly Agree
  Agree                        0.00000000 0.00000000     0.26470588
  Disagree                     0.20000000 0.00000000     0.00000000
  Moderately Agree             0.20000000 0.18181818     0.20588235
  Moderately Disagree          0.20000000 0.00000000     0.02941176
  Neutral                      0.20000000 0.72727273     0.08823529
  Strongly Agree               0.00000000 0.00000000     0.38235294
  Strongly Disagree            0.20000000 0.09090909     0.02941176
                     y
x                     Strongly Disagree
  Agree                      0.00000000
  Disagree                   0.00000000
  Moderately Agree           0.00000000
  Moderately Disagree        0.00000000
  Neutral                    0.00000000
  Strongly Agree             0.00000000
  Strongly Disagree          1.00000000

$prop.tbl
                     y
x                           Agree    Disagree Moderately Agree
  Agree               0.159509202 0.000000000      0.012269939
  Disagree            0.000000000 0.006134969      0.012269939
  Moderately Agree    0.122699387 0.000000000      0.104294479
  Moderately Disagree 0.000000000 0.000000000      0.024539877
  Neutral             0.055214724 0.012269939      0.134969325
  Strongly Agree      0.030674847 0.000000000      0.006134969
  Strongly Disagree   0.000000000 0.000000000      0.000000000
                     y
x                     Moderately Disagree     Neutral Strongly Agree
  Agree                       0.000000000 0.000000000    0.055214724
  Disagree                    0.006134969 0.000000000    0.000000000
  Moderately Agree            0.006134969 0.012269939    0.042944785
  Moderately Disagree         0.006134969 0.000000000    0.006134969
  Neutral                     0.006134969 0.049079755    0.018404908
  Strongly Agree              0.000000000 0.000000000    0.079754601
  Strongly Disagree           0.006134969 0.006134969    0.006134969
                     y
x                     Strongly Disagree
  Agree                     0.000000000
  Disagree                  0.000000000
  Moderately Agree          0.000000000
  Moderately Disagree       0.000000000
  Neutral                   0.000000000
  Strongly Agree            0.000000000
  Strongly Disagree         0.012269939

3. Consider the following:

Make a new variable named as “InAverage”, InAverage is the average of the responses in the variables In1, In2, IIn3, In4, and In5.

Data<-Data%>%
  mutate(InAverage = (In1+In2+In3+In4+In5)/5)

Make two groups of the variable “Age”,

Grouping:

Group 1 with age less than 21 years old

Group 2 with age more than 20 years old

Data1<-Data%>%
  filter(Age!=21)%>%
  filter(Age!=22)%>%
  mutate(Agegroup = ifelse(Age<21, "Less than 21 years old", "more than 22 years old"))
Data1

3.1 Is there a significant difference between the two groups of age in terms of the variable “InAverage”?

table(Data1$Agegroup)


Less than 21 years old more than 22 years old 
                    14                     13

var.test(Data1$InAverage~Data1$Agegroup)


    F test to compare two variances

data:  Data1$InAverage by Data1$Agegroup
F = 0.61956, num df = 13, denom df = 12, p-value = 0.4036
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
 0.1912667 1.9535909
sample estimates:
ratio of variances 
         0.6195631

Test of Difference

t.test(Data1$InAverage~Data1$Agegroup, var.equal = TRUE)


    Two Sample t-test

data:  Data1$InAverage by Data1$Agegroup
t = 1.4709, df = 25, p-value = 0.1538
alternative hypothesis: true difference in means between group Less than 21 years old and group more than 22 years old is not equal to 0
95 percent confidence interval:
 -0.3030324  1.8173182
sample estimates:
mean in group Less than 21 years old mean in group more than 22 years old 
                            4.957143                             4.200000

As shown in the above, the p-value is 0.1538. This means that the variances of the two groups are equal.

4. Is there a significant difference among the courses taken in terms of the variable “InAverage”?

res_aov <- aov(InAverage ~ `Course Taken`,  data = Data)

Normality Test

shapiro.test(res_aov$residuals)


    Shapiro-Wilk normality test

data:  res_aov$residuals
W = 0.96551, p-value = 0.00044

Equality of Variances Test

library(car)

Warning: package 'car' was built under R version 4.1.3

Loading required package: carData

Warning: package 'carData' was built under R version 4.1.3


Attaching package: 'car'

The following object is masked from 'package:dplyr':

    recode

leveneTest(InAverage ~ `Course Taken`, Data)

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

library(tidyverse)# data manipulation and visualization

Warning: package 'tidyverse' was built under R version 4.1.3

-- Attaching packages --------------------------------------- tidyverse 1.3.1 --

v ggplot2 3.3.5     v purrr   0.3.4
v tibble  3.1.6     v stringr 1.4.0
v tidyr   1.2.0     v forcats 0.5.1
v readr   2.1.2

Warning: package 'ggplot2' was built under R version 4.1.3

Warning: package 'tibble' was built under R version 4.1.3

Warning: package 'tidyr' was built under R version 4.1.3

Warning: package 'readr' was built under R version 4.1.3

Warning: package 'forcats' was built under R version 4.1.3

-- Conflicts ------------------------------------------ tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
x car::recode()   masks dplyr::recode()
x purrr::some()   masks car::some()

library(ggpubr)#creating easily publication ready plots

Warning: package 'ggpubr' was built under R version 4.1.3

library(rstatix)#pipe-friendly R functions for easy statistical analyses

Warning: package 'rstatix' was built under R version 4.1.3


Attaching package: 'rstatix'

The following object is masked from 'package:stats':

    filter

res.kruskal <- Data %>% kruskal_test(InAverage~`Course Taken`)
res.kruskal

No significant difference among the different courses in terms of their InAverage.

Stat 50 Last Activity

BS Math 3

5/22/2022

Data

Answer as indicated

1. Provide the same output provided below

1.1 First output:

1.2 Second output:

Consider the variables: In5, Ex4, TP3, and CP2

Recoding the responses in Variables “In1 and In2” with the following changes

2. Answer the following:

3. Consider the following:

Make a new variable named as “InAverage”, InAverage is the average of the responses in the variables In1, In2, IIn3, In4, and In5.

Make two groups of the variable “Age”,

Grouping:

Group 1 with age less than 21 years old

Group 2 with age more than 20 years old

3.1 Is there a significant difference between the two groups of age in terms of the variable “InAverage”?

Test of Difference

4. Is there a significant difference among the courses taken in terms of the variable “InAverage”?

Normality Test

Equality of Variances Test