# Means with Error Plots - Advanced Tab

Graphical Analytic Techniques

The Advanced tab of the Means with Error Plots Startup Panel contains various additional (to the Means with Error Plots - Quick tab) options for the Means with Error Plots. Use the options on this tab to specify the variables and select the type of graph you want to create. Some of the options on this tab are used  to add additional components, such as the fit of a predefined function, the outliers and extremes, and certain test statistics.

Graph type. Select the type of Mean with Error Plot to be plotted from the Graph type list. Click the desired plot link listed below for a brief description of that type of graph. Whiskers High-Low Close

Together with the Graph type selected above, you can also choose between two types of graph formats. Click the desired graph format listed below to learn more about it. Regular Multiple

The choice of the combination of the Graph type and format will depend on the objective you have in mind. For example, if you have selected more than one dependent variable and your aim is to compare their distributions, then you may select Whiskers with Multiple graph format.

Variables. Click the Variables button to display a standard variable selection dialog box in which you select the Dependent variable and the Grouping variable for creating the graph. The dependent variable values will be used in calculating the respective statistics that define the components of the graph (e.g., means, medians, standard deviations, etc.), while the grouping variable will be used to categorize the data, using the method of categorization as selected via the options in the Grouping intervals group box. Note that more than one dependent variable can be selected and selection of the Grouping variable is optional. If you select multiple dependent variables and the Regular graph type (see above), a sequence of Means with Error Plots (one for each dependent variable) will be produced in separate graphs. If the graph type is set to Multiple, the Means with Error Plots for all the selected dependent variables will be combined into a single graph. The selection of variables made will be displayed below the Variables button.

Grouping intervals. Use the options under Grouping intervals to specify a method  (Integer mode, Unique values, Categories, Boundaries, Codes, or Multiple subsets) to define the manner in which the values in the chosen grouping variable will be used to determine the categories for the graph. Note that separate means (medians, etc., as chosen by the user) will be computed for each group as defined by the values in the grouping variable. The methods for categorizing the values in the grouping variable are discussed in detail in Methods of Categorization.

Change Variable. Click this button to display a standard variable selection dialog box in which you can change the selection of the Dependent variable(s) and/or the Grouping variable. If you change the variable(s) using this button, display of the variable selection under the Variables button will change accordingly.

Fit. You can fit an equation to the points in the plots by selecting one of the predefined functions in this list. Linear Distance Weighted Least Squares Polynomial Negative Exponential Weighted Logarithmic Spline Exponential Lowess

Graph icon. The graph icon displayed represents the currently selected Graph type (Whiskers or High-Low Close) and the Middle point options (see below). It also previews the selected Value (Conf. Interval, Non-outlier range, Min-max, or Constant) that will define the Mean with Error Plot that you are about to create as specified in the Whisker group box.

Middle point. The options in the Middle point group box are used to specify the statistic that will be used as middle point in the Means with Error Plots.

Value. The middle point can be either the Mean, Median, Mean/Median (uses the Mean as the middle point, plus it has an added marker for the Median), or Median/Mean (uses the Median as the middle point, plus it has an added marker for the Mean) of the selected variable (variable and group).

Style. Use the Style drop-down list to specify how the middle point should be represented in the Whiskers or High-Low Close plot. You can choose the selected middle point to appear as a line (select Line) or as a point (select Point).

Pooled variance. The Pooled variance check box is available when you select Mean as the Middle point Value. The setting of this check box determines how the standard deviations and standard errors (for the means) are computed from grouped data. When the Pooled Variance check box is selected, STATISTICA computes the pooled within-group (category) variance for all groups (categories), and uses this value as an estimate of σ (Sigma) in computing the standard errors for the means (see, for example, Milliken and Johnson, 1984). Specifically, STATISTICA  computes the pooled within-group (category) variance as:

spooled2 = 1/(n-k) * [s12*(n1 -1) + ... + sk2 *(nk -1)]

In this equation, k refers to the k groups in the plot, s12, refers to the variance in the i'th category or group, n1 refers to number of valid observations in the i'th category or group, and n is the overall number of valid observations in the plot.

The standard error of the mean for the i'th group is then computed as:

s.e.(mean) = spooled / square root(ni)

Multiple box layout. The options in the Multiple box layout group box are used to control the display of the Means with Error Plots in your graph. Note that these options are applicable only when you have selected more than one dependent variable, and if you selected Multiple as the Graph type (see above).

Shifted. Select the Shifted option button to display a series of Means with Error Plots for the selected dependent variables in different colors, side by side.

Overlaid. Select the Overlaid option button to display a series of Means with Error Plots for the selected dependent variables in different colors, one on top of the other.

Trim distrib. extremes. Use the Trim distrib. extremes box to specify the percent of cases to be "trimmed" from the extremes (i.e., tails) of the distributions of cases for the selected dependent variables. For example, if you specify 10%, then for a variable with 100 cases, STATISTICA removes the 10 cases with the lowest values and the 10 cases with the highest values for the respective variable from the graph, and uses only the 80 remaining ("middle") cases. If you enter a value for Trim distrib. extremes for mean-based Means with Error Plots, then the so-called "trimmed means" will be used in the graph.

Whisker. Specify the options for computing the range of Whiskers or High-Low Close, i.e., to define the error ranges.

Value. Use the Value drop-down box to choose how the range of Whiskers or High-Low Close is computed (Conf. Interval, Non-outlier range, Min-max, or Constant). If you select Conf. Interval, the range will be displayed as the confidence interval around the mean value. If you select Non-outlier range, STATISTICA determines which points in the data are outliers (see Outliers and extremes), and then uses the highest and lowest data points that are closest to the outliers (but are not outliers) to determine the range in the plot. The option Min-Max uses the minimum and maximum values of the data to determine the range, without considering whether these values are outliers. If you choose Constant, the specified constant will be added/subtracted from the chosen center point (mean or median), to define the range around that center point.

Probability/Coefficient. If you specify Value (see above) as the Conf. Interval, you also need to specify a value between 0.15 and .99 in the Probability edit field. This value will be used to determine the length of the Whiskers or High-Low Close around the Mean value, based on the standard error for the respective means, and the standard normal (z) value associated with the chosen probability. When you select the Value as Non-outlier range or Min-max (see above), you also need to specify a value in the Coefficient edit field by which the selected Value will be multiplied to determine the range. In case of the Value option as Constant, the value of the Coefficient itself determines the range (no multiplier is used). By default the value of the Coefficient is 1.

Outliers. The options under Outliers are used to control the display of outliers and extremes. Select either Off, Outliers, Extreme, or Outl. & Extremes from the drop-down box. See Outliers and Extremes for additional details on these options.

Coefficient. If you select Outliers, Extreme, or Outl. & Extremes in the above drop-down box, specify a coefficient in the Coefficient edit field to be used to determine the outlier or extreme value range; see Outliers and Extremes for additional details.

Statistics. You can choose to include a variety of statistics as a footnote in the graph by selecting one or more of the statistics listed in the Statistics group box.

Kruskal-Wallis test. Select the Kruskal-Wall test check box to include the Kruskal-Wallis test statistic as a footnote on the graph.

F test, p. Select the F test, p check box to include the F test and p statistics (analysis of variance results) as a footnote on the graph.

Connect middle points. Select the Connect middle points check box to connect the selected middle points (Means, Medians, trimmed Means, or trimmed Medians) of the Whiskers or High-Low Close.

Display raw data. Select this check box to display the raw data points.

Jitter. Use the options in this group box to jitter the data points, i.e., modify the original position of the data point from the center of the graph in order to more easily identify/brush overlapping points.

Off. If you select Off, no jitter is applied to the raw data points, outliers, and extremes.

Sequential. If you select Sequential, the jitter is applied sequentially to the raw data points, outliers, and extremes. The jitter is applied such that the first case in the data set is maximally shifted to the left and the last case is shifted maximally to the right.

Random. If you select Random, the data point is randomly shifted within the available range.

Width. With this option, you can specify the maximum jitter width defined as percentage of box width. Possible percentages range from 0 to 250.