5.3.1. Histogram

This procedure allows the choice of ungrouped data, data with frequency counts or grouped data (see 5.0.2. One-Sample Data Types). It is possible to draw frequency and cumulative histograms for string variables and histograms with irregular class widths.

You can choose to display on the X-axis either the mid points or the lower and upper limits for each class using the Edit → Bars dialogue.

5.3.1.1. Regular and Irregular Class Intervals

After variable selection, a second dialogue will allow you to edit the number of classes suggested by the program and choose between regular and irregular class intervals. At this stage, the program would already have calculated the default values for the lower and upper bounds and the class interval.

Regular Class Intervals: If this (default) option is selected then the program will proceed with drawing the graph. The lower and upper bound and the class interval values can be edited subsequently, by opening the Edit → Axes dialogue. If the lower limit is higher than the minimum observation or the upper limit is lower than the maximum observation or more than 200 classes are generated, then a warning will be issued. In such cases the program will still proceed with plotting a histogram. If a wider class interval is entered, then the program will not rescale the Y-axis to cater for higher bars. This can be done manually.

Irregular Class Intervals: If this option is selected then the program will open a new dialogue to allow you to edit the suggested class intervals.

The dialogue contains a vertical scroll bar to edit up to 200 lower limits and the upper limit for the last class. Changes to the number of classes should be made before entering these values. The program will not proceed until a valid selection is made for all classes.

5.3.1.2. Histogram Output Options

With this version of UNISTAT, an Output Options Dialogue is introduced for Histogram and 3D Histogram procedures. The Summary Information option will produce three tables for frequencies, statistics and fitted distribution parameters (if any). As in other output options (see 2.1.5. Output Options Dialogue), when you click on the [Finish] button, the summary information and the histogram will be sent to the Output Medium with default options. If you want to edit the properties of the histogram, you can send it to Graphics Editor by clicking on the [Opt] button situated to the left of the Draw Chart check box.

The Summary Information option will produce output in the following format:

Histogram

Frequency Table

Room Averages	Frequency
440 - 520	7
520 - 600	28
600 - 680	36
680 - 760	39
760 - 840	30
840 - 920	11
920 - 1000	8
1000 - 1080	6
1080 - 1160	3
Total	168

 

Descriptive Statistics

	Room Averages
Mean	722.2976
Median	709.5000
Mode	720.0000
Lower Quartile	612.0000
Upper Quartile	805.5000

 

Distribution Fitting

	Parameter 1	Parameter 2	Parameter 3
Normal	722.2976	142.6569
Student's t	722.2976	142.6569	2.0001
Gamma	25.6358	0.0355
Erlang	26.0000	0.0360
Discrete Uniform	168.0000	0.0000
Negative Binomial	722.2976	26.5791

 

If the Class intervals box is unchecked in the Edit → Bars dialogue (i.e. if the midpoints will be displayed), then the Frequency Table will look as follows:

Frequency Table

Room Averages	Frequency
480	7
560	28
640	36
720	39
800	30
880	11
960	8
1040	6
1120	3
Total	168

5.3.1.3. Fitting Distribution Functions

When a histogram is displayed with default options, the program will already have fitted eighteen Distribution Functions (except for the negative binomial distribution) on the data. Any six of these can be displayed simultaneously by selecting the Edit → Distributions dialogue. The type, parameters and appearance of these Distribution Functions can be controlled by the user.

The Edit → Distributions dialogue features a Distribution and Parameters group at the bottom containing a drop-down list for all distributions supported. When a distribution is selected from this list, up to three more text fields are displayed immediately to the right of the list. These fields contain the estimated parameters for each distribution function (see Appendix). For instance, while for the normal distribution two fields will display the estimated mean and standard deviation, for t-distribution a third field will display the estimated degrees of freedom. A parameter which cannot be estimated is assigned the value ‑99. You can edit the values in each parameter field. For each distribution function you can also select the line style, thickness, colour, symbols, etc.

Any combination of continuous and discrete distribution functions can be selected for up to six distributions. The same distribution can be selected more than once. This may be useful for displaying one or more theoretical curves of the same distribution with different parameters against the fitted parameters.

Distributions in the drop-down list are in the same order as they are in the Distribution Functions dialogue (see 5.2.1. Cumulative Probability). Hypergeometric distribution ‑ for which the estimated frequencies procedure is not implemented ‑ is excluded. It is also possible to plot Distribution Functions without having to fit them on a frequency histogram by means of the Plot of Distribution Functions procedure.

Colour: This controls the colour of the fitted curves.

Symbol: The usual symbol selection group can be used to display Symbols for discrete distributions. When a selection is made other than None for a discrete distribution, a symbol will be drawn on the line at each distinct value of the X-axis variable.

Plot Frequency: This control determines the resolution of fitted distribution curves. The default value of 10 means that the functions will be evaluated at every 10^th pixel. This field can have a minimum value of 1, in which case the functions will be evaluated at every pixel. This will take 10 times longer to compute and it may be more difficult to distinguish various curves.

5.3.1.4. Bars

This dialogue provides controls for editing aspects of the histogram bars.

Function: The available options are (i) Frequency and (ii) Cumulative. Distributions can be fitted in either case.

Bar Fill Style: Bars can be filled with solid colours or with one of the six cross-hatch patterns provided.

Bar Colour: This controls the colour of the histogram bars.

Mean / Median / Mode: For numeric variables, this will draw a vertical line for each statistic along the X-axis. For string variables only the mode is drawn.

Quartiles: For numeric variables, a vertical line for 25% and 75% quantiles will be drawn along the X-axis.

Class Intervals: X-axis tick marks and their corresponding value labels can be drawn either in the middle of a class, or at the lower and upper boundaries. This option is available only for histograms with regular class intervals. Irregular histograms will always display class intervals. If the selected column contains String Data, tick marks will always be drawn at mid points.