  ASP Statistical Software A STATISTICAL PACKAGE (ASP) For Business, Economics, And The Social Sciences

# Character Plots

## Nature Of Character Plots

Character plots are constructed from ASCII characters. These plots are present in all version of ASP and are the only plots included in the Student Version. Three of these plots, (Frequency Plots, Box And Whisker Plots, and Stem And Leaf Plots) allow you to examine data quite quickly in that you can input more than one variable at a time. They also generate summary statistics for each variable.  The standard version of ASP also allows you to generate high resolution versions of most of the character plots that are available in ASP.

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## Correlation Plots

ASP allows you to generate three kinds of character correlation plots:

• Autocorrelation Plots.
• Partial Correlation Plots.
• Cross Correlation Plots.

In creating the auto and partial correlation plots you are allowed to specify four parameters:

• Number of lags for which autocorrelations are to be calculated.
• Degree of differencing to apply to the series being examined.
• Number of seasonal periods in the series.
• Degree of seasonal differencing to apply to the series being examined.

In the large-lag standard error is listed to the left of the autocorrelation plot along with the autocorrelations being plotted. The box-pierce q statistic for the null hypothesis that all of the autocorrelations are zero is also listed at the top of the plot along with its degrees of freedom and p-value. Two standard error intervals above and below a zero correlation are indicated by parentheses.

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## Control Charts

ASP allows you to generate four kinds of character plot control charts :

 Variables Means Proportions Defects Ranges Moving Ranges

Estimates of the standard deviations from which the control limits for each chart are derived are based on the average variation within the subgroups.

In constructing each chart each value plotted is listed to the left of the plot. Also listed to the left of the plot is an indicator variable (REJECT) that indicates whether the plotted value is (0) or is not (1) within three standard deviations of the mean of the values being plotted.

The center vertical mark on the scale at the top of the plot indicates the mean of the values being plotted. The distance between the vertical marks represents one standard deviation of the values being plotted. The values of the mean and three standard deviations above and below the mean are listed on the scale at the top of the plot.

The control charts for Means, Proportions, Defects, and Ranges also generate tables of the sample values and statistics that are used to generate the chart.

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## Frequency Plots

ASP allows you to generate character frequency plots for a set of variables. You are also given the option of calculating a set of summary statistics for each variable. These statistics include the mean, median, sample standard deviation, interquartile range, first and third quartile, midpoint of the interquartile range, lower and upper adjacent values, number of valid cases and missing values, and the minor and major outliers, if any, in the variable being plotted.

In addition to the plot and summary statistics (if not suppressed), the output also lists the frequencies for each interval or value, the cumulative frequencies, frequencies as a percent of the total, and cumulative frequencies as a percent of the total.

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## Box And Whisker Plots

ASP allows you to generate character box and whisker plots for a set of variables using either an independent or a common scale. You are also given the option of calculating a set of summary statistics for each variable. These statistics include the mean, median, sample standard deviation, interquartile range, first and third quartile, midpoint of the interquartile range, lower and upper adjacent values, number of valid cases and missing values, and the minor and major outliers, if any, in the variable being plotted.

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## Stem And Leaf Plots

This option allows you to generate character stem and leaf plots for a set of variables. When this option is executed you are prompted to specify the:

• Number of digits in the stem.
• Number of lines in the stem.
• Number of digits in the leaf.

You are also given the option of calculating a set of summary statistics for each variable. These statistics include the mean, median, sample standard deviation, interquartile range, first and third quartile, midpoint of the interquartile range, lower and upper adjacent values, number of valid cases and missing values, and the minor and major outliers, if any, in the variable being plotted.

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## Quantile Plot

ASP allows you to generate one and two variable character quantile character plots. In constructing a two variable quantile plot the values for each quantile are calculated for each variable. In constructing a one variable quantile plot the values for each quantile are calculated for the given variable, and these values are then plotted against the quantiles to which they correspond.

If the number of quantiles selected is 4 then the value for each quartile is calculated and plotted against the quartile to which it corresponds. If the number of quantiles selected is 100 then the value for each percentile is calculated and plotted against the percentile rank to which it corresponds.

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## More Character Plots

There are five additional character plot options in ASP:

• Scatter Plot. This option allows you to plot one variable against another. When this option is executed you are prompted to select two variables for the plot and are given the option of breaking down the plot by a third variable.

• Overlay Plot. This option allows you to plot a set of variables on a single graph. Each variable in the plot is represented by a unique letter (a, b, etc.) and is plotted against its sequence number.

• Vertical Sequence Plot. This option allows you to generate a vertical sequence plot. In constructing this plot the center vertical mark on the scale at the top of the plot indicates the mean of the variable being plotted. The values for the mean and three standard deviations above and below the mean are listed on this scale.

• Normal Probability Plot. This option allows you to generate a normal probability plot of a variable against its expected value on the assumption that the values of the variable come from a normal distribution.

• Cumulative Plot. This option allows you to generate a cumulative plot of a variable. In constructing this plot the ith value of the variable being plotted is plotted against i/n where n is the number of observations in the variable.

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