.. _SUMmath:

Summary
=======

Summary provides information integral to correctly analyzing data,
such as histograms and descriptive statistics for the variables in a
data set. The Summary page can be accessed after parsing your data
into .hex format by going to the drop down menu **Data** and
selecting **Summary**. 


Inputs
""""""

**Key**

   Enter the .hex key associated with the data set to be summarized. 


**X**

   Select the columns for which summary information is desired. If a
   header was not used in the original data set, the columns are indexed
   by number beginning at 0 on the left. 

**Max Column Display**

   An alternative to selecting specific X; Max Column Display allows
   users to define the maximum number of columns that summary information
   will be provided for. For example, if users specify Max Column Display
   to be 5, the first 5 columns of the original data set will be
   displayed, and all others will be omitted regardless of the subset of
   columns selected in the X field. 


Output
""""""

**Column Name** 

   The variable name as it was provided in the header when the data
   were parsed, or as assigned by H\ :sub:`2`\ O if no header was included. 

**Base Stats** for *Numerical Data*

  *NAs*
   Displays a count of the number of elements in the column that are
   interpreted as NA by H\ :sub:`2`\ O, either because the original element was
   given as NA, or because the original element was uninterpretable
   when the data were parsed

  *Average*: Abbreviated **avg** 
   The arithmetic mean of the data in the column, defined
   as the sum of the values in the column divided by the number of
   elements in the column. 

   :math:`Average\:(X_{i})=\frac{\sum_{k=1}^{N}X_{k}}{N}`


  *Standard Deviation*: Abbreviated **sd**
   The standard deviation of the data in the column, defined as the
   square root of the sum of the deviance of observed values from the
   mean divided by the number of elements in the column less one.
   For some columns of data a standard deviation of -0 may be produced. 
   This outcome is the special case where the standard deviation is a very, 
   very small negative number. The exact value has not been rounded, but the 
   number of digits displayed have been truncated. 


   
   :math:`Standard\:deviation\:(X_{i})=\sqrt{\frac{\sum_{k=1}^{N} (X_{k}-\bar X)^2}{N-1}}`

  *Zeros*: 
   The number of elements in the column that are 0. 


  *Min[ ] and Max[ ]* 
   Return a list of the minimum and maximum elements of the
   column respectively. The default is the lowest and highest five 
   numbers, but for binomial data (for example), the minimum are
   listed as 0,1 and the maximum as 1,0. 

**Percentiles** 
  a table displayed only for *Numeric Data* 
  A percentile of value X at P threshold is interpreted as 
  "X is greater than or equal to P percent of the values 
  in this column." For example, if 83 is given as the 
  value at threshold .75, we would say that 83 is greater 
  than 75% of the other elements in the column.
   

  *Threshold*
   Displays the percentile levels. For example .25 corresponds to the
   25th percentile, .5 corresponds to the median and .75 corresponds to
   the 75th percentile. 

  *Value*
   In H\ :sub:`2`\ O the values presented relative to thresholds as percentiles are 
   obtained through approximation relying on information derived from the 
   histogram.   


**Base Stats** for *Categorical Data*

  *NAs* 
   Displays a count of the number of elements in the column that are
   interpreted as NA by H\ :sub:`2`\ O, either because the original element was
   given as NA, or because the original element was uninterpretable
   when the data were parsed. 

  *Cardinality* 
   Displays the number of unique categories present in the data. For
   example, if a column of 100 elements gives information about the
   color of an object, and the possible values for color are red, green,
   and blue, cardinality is 3. 



**Histogram**

  *First Row (top)*
   Lists the unique values or categorical levels in the column. 

  *Second Row (middle)* 
   Lists a corresponding count of the number of observations of the
   value given in the top row. 

  *Third Row (bottom)* 
   Gives a percentage of the number of observations that are equal to
   the corresponding value. 

  *Users should note that the tables in Summary can become
  quite large. When the width of the table exceeds the width of the
  display users can view more information by hovering over the table
  with their mouse and scrolling left and right.*