MOSAIC PLOTS (AND BAR GRAPHS)

A mosaic plot shows the frequencies in an n-way table by nested rectangular regions whose area is proportional to the frequency in a cell or marginal subtable. The display uses color and shading to represent the sign and magnitude of standardized residuals from a specified model.  Blue means a positive residual. Red indicates a negative residual. 

The names of the categories, the value of the observed frequency and the value of the residual of the associated cell in the table data are shown when the pointer of the mouse is moved along the mosaic plot.

A mosaic plot is built using conditional probabilities. For a two-way table, with cell frequencies nij, and cell probabilities pij =nij/n++, a unit square is first divided into rectangles whose width is proportional to the observed marginal frequencies ni+ and hence to the marginal probabilities pi=ni+/n++. 

Each such rectangle is then subdivided horizontally in proportion to the conditional probabilities of the second variable given the first, pj/i=nij/ni+. 

The order that variables are added to the plot is important. The original rectangles in the first plot are split into smaller rectangles when a second variable is added. Then, these rectangles are subdivided into other rectangles, but the original shape remains recognizable.

BAR GRAPHS

A Bar Graph is used to portray the (grouped) frequency distribution of a variable at the Nominal level of measurement. Such variables are called Category Variables in ViSta. It consists of vertical bars drawn above categories such that

1.The height of the bar corresponds to the frequency 

2.The bars are separated by empty space since the nominal level of measurement has separate, discrete categories.

STACKED (SEGMENTED) BAR GRAPHS

While a bar graph represents the frequencies of categories of one variable, a stacked (segmented) bar graph represents the frequencies of combinations of categories of two variables. In a stacked (or segmented) bar graph: 

1.The horizontal axis still represents one variable, with each bar representing one of the catgories of the variable. 

2.Each bar is segmented according to the categories of the second variable. Alternatively, each bar can be seen as being made up of smaller bars stacked on top of each other.  

COMPARISON OF MOSAIC PLOTS AND BAR GRAPHS

A mosaic plot presents the same information as is presented by a stacked bar-graph: The frequencies of combinations of categories of two variables. 
 
1.A mosaic plot consists of rectangles laid out in a mosaic. The rectangles are like the sub-bars in a stacked bar-graph. 

2.In a mosaic plot, each column of rectangles represents a category of the variable on the horizontal axis. 

3.In a stacked bar-graph, each bar represents the overall frequency of a category of the variable plotted on the horizontal axis. In a mosaic, the several column of tiles are all the same height, representing 100%. Thus each tile in a mosaic represents a proportional frequency of a category combination.

4.Whereas a stacked bar-graph's sub-bars representing the joint frequency of a category of each of the two variables, in a mosaic plot each rectangle represents the joint probability of a category of each of the two variables. 
