Home Work 1

Problem 1: Provide summary statistics of the demographic variables (Age,
Height, Gender) using numerical and/or graphical presentations as
appropriate. Indicate the reason(s) for your choice of summary
statistics/graphics for each variable.

Problem 2: Show how height varies among the three treatment groups
using side-by-side boxplots.

Problem 3: Use a paired t-test to compare PLUC.pre and PLUC.post. Why is
it OK to use a paired t-test for this comparison?

Problem 4: Test the Null Hypothesis that boys and girls are equally above
average on the LWAS measure. Draw a graph to show the results of this
test.

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R Cheat Sheet

The following is an annotated recipe for doing the above homework with R.
These instructions assume that you have saved the default dataset (default.csv)
on your computer desktop:

1.) Start R graphical user interface (GUI) - you will have a window for 
    entering commands. In the window, the '>' symbol is the command prompt
    where you type your commands.

2.) Use the R change directory command to set your default directory to
    your desktop. On Windows R the change dir option is in the Files menu.
    On Mac, it's in the Misc menu. (This is the step I keep forgetting!!)

3.) Type the command: df = read.csv(file="default.csv") and press return.
    This command calls a function (named read.csv) to open a file in the
    current working directory (your Desktop after step 2) and read its
    contents. The contents are interpreted and stored in an object called
    a "data frame" (in this case called 'df'). The '=' tells R to assign the
    output of the read.csv function to 'df' and because read.csv creates a
    data frame, df will be a data frame.

    A data frame is sort of analagous to a spread sheet. It has a set of
    elements that correspond to the columns of the spread sheet and each
    element has a name, like a column header. Each element contains all the
    numbers (or other things like words) that would be stored in the rows
    of the spread sheet within each column. In R, each of these column-like
    elements are called vectors. A vector is simply a list of numbers or
    characters. To refer to an individual element of a data frame, us the
    syntax df$name (assuming 'df' is the name of the data frame, and 'name'
    is the name of the element (or column)).

4.) A good way to see what the read.csv function did is to ask for a 
    summary of the contents of 'df'. This is done with the command:
    summary(df). That is, type 'summary(df)' -- without the quotes --
    at the '>' prompt and press return. R will give you a summary of
    each element in 'df'. You'll see somthing like the following (and more):

      sid          age         sex         hgt             grp   
 s01    : 1   Min.   : 48.00   f:30   Min.   :38.99   Min.   :1  
 s02    : 1   1st Qu.: 64.75   m:30   1st Qu.:43.57   1st Qu.:1  
 s03    : 1   Median : 84.00          Median :46.69   Median :2  
 s04    : 1   Mean   : 90.42          Mean   :47.99   Mean   :2  
 s05    : 1   3rd Qu.:115.25          3rd Qu.:53.18   3rd Qu.:3  
 s06    : 1   Max.   :143.00          Max.   :58.09   Max.   :3  
 (Other):54                                                      
 
    Note that for non-numeric elements (like sid and sex above) you get a
    frequency count of up to six items. For numeric elements (like age
    hgt and grp) you get a parametric summary including mean, median, min,
    max, and the 1st & 3rd quartiles.

5.) Note that in step 4 some of the numeric elements like grp, shades, ped
    are treated like interval or ratio data even though they are really
    intended to be category designations. For instance, children belong to
    one of three groups; group 1, group 2, or group 3. Here, although we
    used numbers to indicate the groups, the numbers are really nothing more
    than names for the different groups. R does not know that is how we
    intended to use the numbers 1, 2, and 3 for grp. Fortunately, we can
    tell R to treat the grp element as a categorical vector (analagous
    to the way 'sex' was treated) and not a numerical vector. We do this
    by telling R that the element grp in data frame df is a 'factor' using
    a command of the form:

    > df$grp = factor(df$grp)

    This command passed the grp element of df (i.e., df$grp) to the factor
    function which converts the numerical data to categorical data. The
    'df$grp = ' part of the command causes the result of the factor function
    to be reassigned to the grp element of df. If we did not reassign it 
    that way, the factor function would just print its result in the 
    window and leave the element df$grp unchanged.

    There are two other elements (df$Shades and df$Ped) that will need to
    be redefined in the same way so that R functions will know how to handle
    them correctly.

    As an alternative to using typed commands to do this, we can also use
    Rcmdr. In Rcmdr, first make sure the data frame is loaded by clicking the
    "<No Active Dataset>" button and selecting "df" from the list. Then,
    select "Data->Manage variables in active dataset->Convert numeric variables 
    to factors". In the list on the left labeled "Variables (pick one or more)",
    select a variable (say, grp) and click OK. You will get a warning dialog
    that says the variable already exists and asks if it's OK to overwrite it.
    Click the Yes button. You will then get another dialog listing each numerical
    value for 'grp' and giving you a place to enter the name for that factor
    level. Enter a name for each group (e.g., Placebo, SupplA, SupplB). Note
    names should not contain spaces or special characters. This tells R we have
    a factor called "grp" with levels "Placebo, SupplA, and SupplB". You can
    repeat this process to convert Shades and Ped to factors and assign names
    to them.

    Note that when we used the command line approach, we did not assign names
    to each level of 'grp', but we could have. The command to do that will be
    displayed in the Rcmdr Script Window. For the example above, the command 
    would be similar to:

    > df$grp = factor(df$grp, labels=c("Placebo", "SupplA", "SupplB"))


6.) The summary(df) command already answered homework question 1 in large
    part. You might want to additionally describe age and hgt in terms of
    their distribution using histograms. In Rcmdr, select Graphs->Histograms..
    then choose the variable you want to plot as a histogram from the list.
    Note that you can set the number of histogram bins explicitly, or let
    R choose (leave the number of bins set to "<auto>"). You can also choose
    to view Frequency counts, Percentages, or Densities. We recommend using
    Frequency counts.

    Here's how you would do this using commands in R for age (hgt works 
    the same way):

    > hist(df$age)

    Pretty easy compared to Excel! This is the simplest form of the hist
    command. For something a little nicer, try:

    > hist(df$age, main="Histogram of Age", xlab="Age in months")

    If you want to learn about all the additional 'niceties' that you can
    add to the hist command, try the R command ?hist (i.e., type '?hist' at 
    a command prompt and press return).

    If you would like to save a graph, in either Windows or Mac, you can click
    on the title bar of the graph window (to be sure it's the active window)
    and select Edit->Copy to copy the graph to the clipboard. In Windows, the
    graph will be a windows metafile graph that you can paste directly into a
    word document and resize without any loss in quality. In Mac OS X, you need
    start the Preview program, and select "File->New from clipboard" to get a
    PDF copy of the R image file. Preview will then let you save the file as a
    PDF and Word can import the pdf, but resizing does not work as well.

7.) For homework question 2, in Rcmdr, select Graphs->Boxplot... then click
    on 'age' in the list of variables and click the button labeled 'Plot by
    groups'. In the dialog box that appears, select 'grp' and click OK then
    click OK in the Boxplot dialog as well. The data will be plotted.

    You can do the same in the regular R command window (not using Rcmdr)
    with the following command (note that a similar command is shown in
    the Rcmdr Script Window if you followed the steps above):

    > boxplot(age ~ grp, data=df)

    In R, a statement like "age ~ grp" translates loosely to "age separated
    by, or predicted by, grp". The command tells the boxplot function to
    look for elements called age and grp in a data frame called df. As with
    the hist function, there are may additional tweaks you can apply to make
    a more elaborate graph with labels and so forth. Read about them using
    the ?boxplot command.

8.) For homework question 3, in Rcmdr, select Statistics->Means->Paired t-test.
    In the dialog box that pops up, select PLUC.pre as the "First variable" and
    select PLUC.post as the "Second variable". Leave the "Two-sided" button
    selected and .95 Confidence level and click OK.

    Note the command that Rcmdr generated in the "Script Window" after you clicked
    OK. You can experiment with this and variants of it in the regular R command
    window if you wish to experiment with doing a t.test by hand.

9.) For homework question 4, see if you can figure this one out yourself!