Performing Fisher’s exact test

In this tutorial we will be using data provided by Freeman and Campbell from The University of Sheffield that examined whether intra-muscular magnesium better treated chronic fatigue syndrome compared to a placebo treatment in 32 patients. The results of the study are provided in the table below.

	Magnesium	Placebo
Felt better	12	3
Did not feel better	3	14

For this example we will manually put the data into R rather than reading it from a file. Using the data.frame() function we can build a data frame object where we input the data from top to bottom row-wise then left to right column-wise. We can do so by first providing a name for the column, placing an equal sign, then using c() to record the data row-wise. The row.names option can also be used to create a list of names for the rows in the data frame.

df <- data.frame(Magnesium = c(12, 3), Placebo = c(3, 14),
                row.names = c("Felt better", "Did not feel better"))

df

##                     Magnesium Placebo
## Felt better                12       3
## Did not feel better         3      14

We can now run the test by wrapping the data frame in the fisher.test() function. Like other functions we can change whether we want the test to be two- or one-sided through the alternative option, however because the magnesium treatment could have a better, worse, or no effect we should keep it to the default two.sided.

fisher.test(df)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  df
## p-value = 0.001033
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##    2.507119 159.407427
## sample estimates:
## odds ratio 
##   16.41917

From the results of the test we can see that with a p-value less than 0.05 (p-value = 0.001033) we can reject H_0</i> to conclude that the rows and columns are not independent. In the context of our data, we can conclude that patients given the magnesium treatment overall felt better than those who took the placebo.</p>

Full code block

# Create a data frame
df <- data.frame(Magnesium = c(12, 3),Placebo = c(3, 14),
                row.names = c("Felt better", "Did not feel better"))

df

# Run a two-sided Fisher's exact test
fisher.test(df)

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