This example involves analysis of activity data from a activity monitor (e.g. a fitbit) worn daily. The individual’s steps were measured in 5 second intervals. Some data is missing and so it was imputed using a function I show within this document. The imputation function was chosen to randomly generate numbers within a reasonable distribution of the mean of this data set. You will notice that most of the imputed values are within 1-2 standard deviations of the mean. There are other ways to imput missing data, but rather than just adding data to the mean, I used a statistical function which infers activity based on the data distribution.

The first question was how to load and prepare the data. I did so as follows:

activity <- read.csv("~/Documents/Reproducible Research/activity.csv", na.strings="NA")

#mean number of steps taken will need to exclude NA
activity$steps <- as.numeric(activity$steps)
activity$interval <- as.numeric(activity$interval)

A histogram of the raw data as well as summary statistics (including mean and median), were included in the initial analyses:

StepsTotal <- aggregate(steps ~ date, data=activity, sum, na.rm=TRUE)
hist(x=StepsTotal$steps, col = "blue", breaks=50, xlab="Steps Per Day", main="Daily Number of Steps", cex=1, cex.lab=0.75, cex.axis=0.75, cex.main=0.95, cex.sub=0.75, font=2, font.lab=2)

summary(StepsTotal$steps)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      41    8841   10760   10770   13290   21190

Next a time-series plot was made which shows the 5-minute interval average of number of steps taken and averaged across all days. You will also see which 5-minute interval across all days contained the maximum number of steps. I also calculate the number of missing values for steps.

library(lattice)
activity$date <- as.character(activity$date)
time_series <- tapply(activity$steps, activity$interval, mean, na.rm = TRUE)
plot(row.names(time_series), time_series, type = "l", xlab = "5 minute Intervals", ylab="Average All Days", main="Average Steps Taken", col="blue", cex=1, cex.axis=0.75, cex.lab=0.75, cex.main=0.95, font.lab=2, font=2)

max_interval <- which.max(time_series) #queries time series for max steps
names(max_interval) #gives the 5-min interval with max steps
## [1] "835"
sum(is.na(activity)) #calculates the total number of missing values
## [1] 2304

Next to give more accurate assessment for time-series analyses I created a function to impute data for the steps. This is a randomized function that generates data points within a subset of already present points. See below. Also see Statistics reference site of Columbia University: http://www.stat.columbia.edu/~gelman/arm/missing.pdf

#call the function random.imp to make random values to add to the missing data points in steps

source("~/Documents/Reproducible Research/imputeValues.R")
#R function to imput missing values for daily steps analysis
random.imp <- function (a){
    missing <- is.na(a)
    n.missing <- sum(missing)
    a.obs <- a[!missing]
    imputed <- a
    imputed[missing] <- sample(a.obs, n.missing, replace=TRUE)
    return(imputed)
}

After the function is called, the data can be appended as a new column to the dataframe. This allows me to analyze the same data set using imputed data. I also report the new mean and median based on the imputed data. Its always a good idea to keep all of your data in case later one wants to determine whether the imputed data was appropriate or another inference technique should be used.

df.steps <- random.imp(activity$steps) #now you have data to add to missing points
activity$imputed = paste(random.imp(activity$steps)) #pasted a column into the dataframe with the randomly imputed data based on original steps data

####repeat of analysis with imputed data
activity$imputed <- as.numeric(activity$imputed)
StepsTotal <- aggregate(imputed ~ date, data=activity, sum, na.rm=TRUE)
hist(x=StepsTotal$imputed, col = "blue", breaks=50, xlab="Steps Per Day + Imputed", main="Daily Number of Steps with Imputed Values", cex=1, cex.lab=0.75, cex.axis=0.75, cex.main=0.95, cex.sub=0.75, font=2, font.lab=2)

summary(StepsTotal$imputed)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      41    9293   10570   10720   12880   21190

Next, using the real and imputed data, I determine a time-series for the number of steps taken on average on the weekend versus the weekday by this individual.

activity$date <- as.Date(activity$date) #now you need to change activity date to POSIXt date object
activity$date <- strptime(paste(activity$date), format="%Y-%m-%d", tz="UTC")
activity$weekday <- paste(weekdays(activity$date)) #add the day of the week based on time-stamp
weekdays <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")
activity$weekday = as.factor(ifelse(is.element(weekdays(as.Date(activity$date)), weekdays), "Weekday", "Weekend"))
StepsImputedInterval <- aggregate(imputed ~ interval + weekday, activity, mean)
library(lattice)
xyplot(StepsImputedInterval$imputed ~ StepsImputedInterval$interval | StepsImputedInterval$weekday, main="Average Steps (Imputed) per Day by Interval", xlab="Interval (5 seconds each)", ylab="Imputed Steps", layout=c(1,2), type="l", cex=1, cex.axis=0.75, font=2, font.lab=2, font.main=2, font.sub=2, font.lab=2)

From the analysis one can tell that this individual is more active on the weekend. Interestingly though they seem to have certain hours during the week-day in which they are more active. Its important to keep in mind whether the fitness data was gathered at the same time each day – did the individual wake at the same time, or not? Just a few caveats to think about when looking at fitness and health data.