# How to Find Outliers in R (3 Methods)

There are three common ways to identify outliers in a data frame in R:

Method 1: Use the Interquartile Range

We can define an observation to be an outlier if it is 1.5 times the interquartile range greater than the third quartile (Q3) or 1.5 times the interquartile range less than the first quartile (Q1).

```#find Q1, Q3, and interquartile range for values in points column
Q1 <- quantile(df\$points, .25)
Q3 <- quantile(df\$points, .75)
IQR <- IQR(df\$points)

#subset data where points value is outside 1.5*IQR of Q1 and Q3
outliers <- subset(df, df\$points<(Q1 - 1.5*IQR) | df\$points>(Q3 + 1.5*IQR))```

Method 2: Use Z-Scores

We can also define an observation to be an outlier if it has a z-score less than -3 or greater than 3.

```#create new column that calculates z-score of each value in points column
df\$z <- (df\$points-mean(df\$points))/sd(df\$points)

#subset data frame where z-score of points value is greater than 3
outliers <- df[df\$z>3, ]```

Method 3: Use Hampel Filter

We can also define an observation to be an outlier if it has a value outside of the median ± 3 median absolute deviations. This is known as the Hampel Filter.

```#calculate low and high bounds
low <- median(df\$points) - 3 * mad(df\$points, constant=1)
high <- median(df\$points) + 3 * mad(df\$points, constant=1)

#subset dataframe where points value is outside of low and high bounds
outliers <- subset(df, df\$points<low | df\$points>high)
```

The following examples show how to use each method in practice with the following data frame in R that shows the number of points scored by various basketball players:

```#create data frame
df <- data.frame(player=LETTERS[0:15],
points=c(7, 12, 7, 8, 8, 10, 72, 12, 6, 6, 24, 7, 13, 4, 12))

#view data frame
df

player points
1       A      7
2       B     12
3       C      7
4       D      8
5       E      8
6       F     10
7       G     72
8       H     12
9       I      6
10      J      6
11      K     24
12      L      7
13      M     13
14      N      4
15      O     12
```

## Example 1: Find Outliers Using Interquartile Range

We can use the following code to identify rows with outliers in the points column based on the interquartile range method:

```#find Q1, Q3, and interquartile range for values in points column
Q1 <- quantile(df\$points, .25)
Q3 <- quantile(df\$points, .75)
IQR <- IQR(df\$points)

#subset data where points value is outside 1.5*IQR of Q1 and Q3
outliers <- subset(df, df\$points<(Q1 - 1.5*IQR) | df\$points>(Q3 + 1.5*IQR))

#view outliers
outliers

player points
7       G     72
11      K     24
```

Using this method, we identify 2 rows as outliers in the data frame.

## Example 2: Find Outliers Using Z-Scores

We can use the following code to identify rows with outliers in the points column based on the interquartile range method:

```#create new column that calculates z-score of each value in points column
df\$z <- (df\$points-mean(df\$points))/sd(df\$points)

#subset data frame where z-score of points value is greater than 3
outliers <- df[df\$z>3, ]

#view outliers
outliers

player points       z
7      G     72 3.46542
```

Using this method, we identify 1 row as an outlier in the data frame.

## Example 3: Find Outliers Using Hampel Filter

We can use the following code to identify rows with outliers in the points column based on the Hampel Filter:

```#calculate low and high bounds
low <- median(df\$points) - 3 * mad(df\$points, constant=1)
high <- median(df\$points) + 3 * mad(df\$points, constant=1)

#subset dataframe where points value is outside of low and high bounds
outliers <- subset(df, df\$points<low | df\$points>high)

#view outliers
outliers

player points
7       G     72
11      K     24
```

Using this method, we identify 2 rows as outliers in the data frame.