Airline Delays in the First Course (part 2: processing the data)
========================================================
Nicholas Horton, nhorton@amherst.edu, January 17, 2014
------------------------------------------------------

#### Accessing the data
```{r, message=FALSE}
require(mosaic)
```

```{r,eval=TRUE}
# reads in ds2 from part 1
load(url("http://www.amherst.edu/~nhorton/airlines/GRB.Rd"))
ds2 = na.omit(ds2)  # get rid of missing values
alleagle = subset(ds2, UniqueCarrier=='OO')
allmesa = subset(ds2, UniqueCarrier=='MQ')
```

### Define a rule (then test it)
```{r}
compareI = function(airlinea, airlineb) {
  # difference in means greater than 30 minutes and both standard deviations < 60
  meana = mean(airlinea); meanb = mean(airlineb); diffmeans = meana - meanb;
  sda = mean(airlinea); sdb = sd(airlineb)
  if ((max(c(sda, sdb) >= 60)) | (abs(diffmeans) < 30)) { return("NEITHER") 
  } else return(ifelse(diffmeans < 0, "Airline A", "Airline B"))
}  
compareI(c(10, 10), c(-40, -40))
compareI(c(10, 10), c(-10, -10))
compareI(c(10, 10), c(-10, 1000))
```

```{r}
# observed result
americaneagle = c(-10, -9, -2, -1, 9, 13, 17, 54, 98, 236)
mesa = c(-22, -16, -14, -8, -5, 0, 0, 3, 4, 28)
mean(americaneagle); sd(americaneagle)
mean(mesa); sd(mesa)
compareI(americaneagle, mesa)
```

```{r}
compareI(sample(alleagle$ArrDelay, 10), sample(allmesa$ArrDelay, 10))
compareI(sample(alleagle$ArrDelay, 10), sample(allmesa$ArrDelay, 10))
```

```{r}
res = do(2000) * compareI(sample(alleagle$ArrDelay, 10), sample(allmesa$ArrDelay, 10))
tally(~ result, data=res)
```

### Define another rule (then test it)

```{r}
compareII = function(airlinea, airlineb) {
  # difference in means greater than 30 minutes and 10% more delays
  meana = mean(airlinea); meanb = mean(airlineb); diffmeans = meana - meanb;
  propdelays = mean(airlinea > 15) - mean(airlineb > 15)
  if (diffmeans > 30 & propdelays >= .1) { return("Airline B")
  } else if (diffmeans < -30 & propdelays <= -.1) { return("Airline A") 
  } else return("NEITHER") 
}  
compareII(c(0,0,0,0,0,0,20,20,20,20), c(0,0,0,0,200,200,200,200,200,200))
compareII(c(0,0,0,0,200,200,200,200,200,200), c(0,0,0,0,0,0,20,20,20,20))
compareII(c(0,0,0,0,200,200,200,200,200,200), c(0,0,0,20,20,20,20,20,20,20))
```

```{r}
compareII(americaneagle, mesa)
res = do(2000) * compareII(sample(alleagle$ArrDelay, 10), sample(allmesa$ArrDelay, 10))
tally(~ result, data=res)
```