TYPES 1) Chi Square Goodness of Fit – when we wish to compare an observed frequency to an expected one.
Suppose we know that the percentage of females in the population is 51% and we want to see if this percentage is also present in our class. In other words we wish to see if ~51% of our class are female as would be expected based on their proportion of the population.
#dataset
data <- c(20, 30)
data## [1] 20 30summary(data)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 20.0 22.5 25.0 25.0 27.5 30.0#TYPE 1 - Chi Sq Goodness of Fit
res <- chisq.test(data, p = c(1/2, 1/2)) #1/2 = 50%
res##
## Chi-squared test for given probabilities
##
## data: data
## X-squared = 2, df = 1, p-value = 0.1573#Chi Sq Goodness of Fit Test shows that there is no significant differenc ebetween what we expected and what we see in our dataTYPE 2) Chi Square Test of Independence – when we wish to see if two groups differ in their observed frequencies across a categorical dependent variable.
Imagine we have run a marketing study where we are interested in whether one of our two conditions increases the likelihood that a person buys a product.
#datset2
AD1 <- c(25, 25) # Creating AD 1 Row
AD2 <- c(35, 15) # Creating AD 2 Row
#Converting dataset into data.frame
data2 <- as.data.frame(rbind(AD1, AD2)) #rbind function for row bind or frame
# Labeling Columns
names(data2) = c('Bought', 'No')
data2## Bought No
## AD1 25 25
## AD2 35 15summary(data2)## Bought No
## Min. :25.0 Min. :15.0
## 1st Qu.:27.5 1st Qu.:17.5
## Median :30.0 Median :20.0
## Mean :30.0 Mean :20.0
## 3rd Qu.:32.5 3rd Qu.:22.5
## Max. :35.0 Max. :25.0#TYPE 2) Chi Square Test of Independence
chisq.test(data2) #AKA Pearson's Chi Sq Test##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: data2
## X-squared = 3.375, df = 1, p-value = 0.06619#Chi Sq Test of Independnce shows that there is almost a significant difference between AD1 and AD2 outcomes on purchase