Paired T-Test

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)
CerinaData <- read_excel("C:/yeah/CerinaData.xlsx")
View(CerinaData)

shaira<- CerinaData %>%
  na.omit()
shaira

## # A tibble: 23 x 29
##      NO. Sex   CS      Age Enrolled Grade `Describing Sets` `Finite/Infinite Se~
##    <dbl> <chr> <chr> <dbl> <chr>    <dbl> <chr>             <chr>               
##  1     2 F     S        14 yes          8 No idea           No idea             
##  2     5 F     S        14 yes          9 No idea           Very low            
##  3     6 F     S        13 yes          8 Low               Low                 
##  4     7 M     S        17 yes         11 No idea           No idea             
##  5     8 F     S        14 yes          8 Very low          Very low            
##  6     9 F     S        14 yes          9 No idea           No idea             
##  7    10 F     S        16 yes         10 No idea           Very low            
##  8    11 F     S        14 yes          8 No idea           No idea             
##  9    12 M     S        15 yes          9 No idea           No idea             
## 10    13 F     S        14 No           8 No idea           No idea             
## # ... with 13 more rows, and 21 more variables: Equality of Sets <chr>,
## #   Subset <chr>, Power Set <chr>, Equi Sets <chr>, Set Operations <chr>,
## #   Venn Diagram <chr>, Real No System <chr>, Addn of AE <chr>,
## #   Subn of AE <chr>, Laws of Exp <chr>, Multn of AE <chr>,
## #   Rem'l of Grp Sym <chr>, Div'n of AE <chr>, Synthetic Div'n <chr>,
## #   Pre-test Score <dbl>, Post-test Score <dbl>,
## #   Relevance of the topics discussed <chr>, ...

klarice <- select(shaira, "Pre-test Score", "Post-test Score")
klarice

## # A tibble: 23 x 2
##    `Pre-test Score` `Post-test Score`
##               <dbl>             <dbl>
##  1               10                 9
##  2                8                14
##  3               12                10
##  4               13                11
##  5                7                10
##  6               10                 7
##  7                9                 8
##  8                7                 9
##  9               13                11
## 10                8                11
## # ... with 13 more rows

mean(shaira$'Pre-test Score')

## [1] 9.086957

mean(shaira$'Post-test Score')

## [1] 10.04348

sd(shaira$'Pre-test Score')

## [1] 2.466375

sd(shaira$'Post-test Score')

## [1] 1.8703

t.test(shaira$'Post-test Score', shaira$'Pre-test Score', alternative = "two.sided", var.equal = TRUE, paired = TRUE )

## 
##  Paired t-test
## 
## data:  shaira$"Post-test Score" and shaira$"Pre-test Score"
## t = 1.6361, df = 22, p-value = 0.1161
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.2559605  2.1690040
## sample estimates:
## mean of the differences 
##               0.9565217

Since the p-value is 0.1161, we conclude that there is no significant difference between the Pre-test Score and Post-test Score.