09-t-test.Rmd

# T-tests 

As mentioned at the beginning of this course, I am not going to discuss which tests you should use, or why you should use them. I am simply going to show you HOW to use them in `R`

When running t-tests, there is a simple, built in function we can use. See `?t.test` for more information.

In this example we will use Crawley's t.test data from .296 of the R book. 

```{r}
t.test.data <- read.table(
     "http://www.bio.ic.ac.uk/research/mjcraw/therbook/data/t.test.data.txt",
     header = T
     )

t.test.data
```


Remember that we must always satisfy ourselves that the data are normally distributed before completing a t-test, if not, the assumptions of these tests do not hold. You should consider the other [assumptions](http://en.wikipedia.org/wiki/Student%27s_t-test#Assumptions) of a t-test too, before you run the test.

```{r T-test1}
gardenA <- t.test.data$gardenA
gardenB <- t.test.data$gardenB

par(mfrow=c(1,2))
qqnorm(gardenA)
qqline(gardenA)
qqnorm(gardenB)
qqline(gardenB)
par(mfrow=c(1,1))
```

OK great...this data looks pretty normal. Let's complete the `t.test()`

In this example we have assumed that the gardens are paired plots, and that we are interested in a two sided test. If you are not sure what is meant by these terms, you should read up on it before attempting to complete the test: [Wikipedia](http://en.wikipedia.org/wiki/Student%27s_t-test) is a surprisingly good resource for statistical information.


```{r}
t.test(
     x = gardenA,
     y = gardenB,
     alternative = "two.sided",
     paired = TRUE
     )
```

The output gives us the test statistic, the degrees of freedom, and the -value - simple.

Note that if you want to automate `t.test`, or another test, you can extract the results from the test object like so:

```{r}
example_test <-t.test(
     x = gardenA,
     y = gardenB,
     alternative = "two.sided",
     paired = TRUE
     )

example_test$statistic
example_test$parameter
example_test$.value

```


So yes....it appears that our two samples are significantly different, because the test statistic is greater than our critical t value. We can can calculate the critical t value to check this:

```{r}
qt(
     0.975, # 0.975 because it is a two tailed test and 2*(1-0.975) = 0.05!          
     df = 9
     )

# We ignore signs in a two-sided t-test, hence if the absolute value of the test
# statistic is greater than the critical value, we reject the null hypothesis:

abs(example_test$statistic) > qt(0.975,9)

```

Easy!