5.3.6. Box and Whisker and Dot Plots

Multisample data can be entered in the form of multiple columns or data columns classified by factor columns. If at least one factor is selected, then a further dialogue will pop up asking for the combination of the categories on the X-axis. Although an unlimited number of data series can be plotted, properties of only the first nine can be individually controlled from the Edit → Data Series dialogue. The rest of the series will repeat the properties of the first nine in a circular fashion. The Apply to all variables check box allows you to apply the current variable’s settings to all selected variables.

Symbol type, symbol size, colour and Point Labels can be controlled for outlying points on Box and Whisker Plot for each data series individually.

The Edit → Width / Notch / Dots dialogue can be used to control the statistical parameters represented on the graph. The three check boxes in the Type panel allows drawing any combination of Box and Whisker Plot, Dot Plot and Error Bar Plot on the same graph. The Confidence although it is also available in the Variable Selection Dialogue. When the Type is changed, the change will apply to all data series.

5.3.6.1. Box and Whisker Plot

A box and whisker plot conveys the following information:

Lower Quartile: Bottom line of the box.

Median: Middle line of the box.

Upper Quartile: Top line of the box.

Lower Whisker: Lower adjacent value. This is equal to the maximum of (i) lower quartile minus 1.5 times the inter-quartile range and (ii) the minimum observation. Any values below this are outliers and are plotted individually.

Upper Whisker: Upper adjacent value. This is equal to the minimum of (i) upper quartile plus 1.5 times the inter-quartile range and (ii) the maximum observation. Any values above this are outliers and are plotted individually.

Box Width: The variable box width conveys information about the size of the sample. See below.

Notch: When there is a notch, it conveys information about the dispersion of data about the median. See below.

On the Width / Notch / Dots dialogue, the first group of controls concerns the Box and Whisker plots.

Width: The width of boxes can be used to convey information about sample sizes:

      Fixed: No information is conveyed.

      Sqr(n): The widths are proportional to the square root of their sample size.

      Log(n): The widths are proportional to the 10 based logarithm of their sample size.

      n: The widths are proportional to their sample size.

Notch: The extent of notches represents the following dispersion measures:

      None: A notch is not drawn.

      t-interval:

          

           

      where is the critical value from t-distribution with n - 1 degrees of freedom.

      Z-interval:

          

           

      Standard Error:

          

           

      Standard Deviation: As above, but with sample standard deviation.

          

           

      Variance: As above, but with sample variance.

          

           

      Robust Confidence Interval: The robust standard error (SE*) is defined as:

          

where IQR is the inter-quartile range and n is the sample size. The robust confidence interval is then defined as:

          

           

      where  is the critical value from the standard normal distribution (see McGill, R., Tukey, J. W. and Larsen, W. A. 1978).

5.3.6.2. Dot Plot

The second group of controls concerns the Dot plots.

Number of Classes: The dot plot is essentially a histogram and this parameter controls the number of classes (the default is 20). The size of dots can be adjusted from the Edit → Data Series → Symbol panel to obtain the desired appearance.

Centre Dots: When this box is checked, dots will be centred. Otherwise they will be left-justified.

5.3.6.3. Error Bar Plot

Central Tendency and Confidence Interval: The following central tendency measures and their confidence limits can be drawn.

· Mean

·      t-interval

·      Z-interval

·      Standard Error

·      Standard Deviation

·      Variance

·  Geometric Mean

·      t-interval

·      Z-interval

·  Harmonic Mean

·      t-interval

·      Z-interval

·  Median

·      Quartiles

·      95% Quantile

·      Robust Confidence Interval

      When Central Tendency is Mean and one of Standard Error or Standard Deviation options is selected, a dialogue pops up asking for a multiplier.

      Error bars for standard error will then be calculated as:

          

          

      and for standard deviation:

          

           

      where k is the multiplier defined by the user.