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How to Calculate Confidence Intervals for Crosstabs with Numeric Variable Sets

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In Displayr, you can create custom rules to add custom statistics or calculations to the table (using the statistics available). This article describes how to create a custom rule to show the upper and lower confidence intervals on crosstabs that use categorical variable sets (if using categorical data click here).  More specifically, this articles goes from a basic crosstab with a numeric variable set...

...to a table that displays the upper and lower confidence intervals:

Requirements

Method

1. Select your table.

2. In the object inspector, go to Data > Rules + > New Custom Rule.

3. Click Edit JavaScript and paste the below into the editor that opens:

// Choose which stats to replace based on those available for numeric data
var upper_statistic_to_replace = "Maximum";
var lower_statistic_to_replace = "Minimum";

// Confirm table has numeric data
if (table.availableStatistics.indexOf("Average") == -1) {
form.ruleNotApplicable('it only applies to tables containing the Average in the Statistics - Cells');
}

// Confirm table has standard error statistic that is needed
if (table.availableStatistics.indexOf("Standard Error") == -1){
table.suppressOutput('Confidence intervals not computed - the table should have the Average and Standard Error statistic available.');
form.ruleNotApplicable('it only applies to tables where the Standard Error is available in the Statistics - Cells');
}

//confirm table has a categorical variable in the columns
if (["Pick One", "Pick Any"].indexOf(table.brownQuestion.questionType) == -1){
table.suppressOutput('Confidence intervals not computed - the table should have a Nominal or Binary-Multi variable set selected in columns.');
form.ruleNotApplicable('the table should have a Nominal or Binary-Multi variable set selected in columns.');
}

//add titles to rule
form.setSummary('Calculate confidence intervals on crosstabs of means');
form.setHeading('Calculate confidence intervals on crosstabs of means');

// Set up controls for user to input significance level
var label = form.newLabel('Significance level:');
var p_level = form.newNumericUpDown('Lower'); // create numeric control
p_level.setIncrement(0.01);
p_level.setDefault(0.05);
p_level.setMaximum(1);
p_level.setMinimum(0);
form.setInputControls([label, p_level]); //add controls to the settings shown

//get the value from the input form above to set as the cutoff variable
var p_cutoff = p_level.getValue();


// Get relevant table stats
var means = table.get("Average");
var standard_errors = table.get("Standard Error");
var ns = table.get('Column n');
var upper_values = table.get(upper_statistic_to_replace);
var lower_values = table.get(lower_statistic_to_replace);


// Do the calculations
// Work out quantile of Student's T Distribution
for (var row = 0; row < table.numberRows; row++) {
for (var col = 0; col < table.numberColumns; col++) {
var t_quantile = jStat.studentt.inv(p_cutoff / 2, ns[row][col]);
var increment = t_quantile * standard_errors[row][col];
lower_values[row][col] = means[row][col] - increment;
upper_values[row][col] = means[row][col] + increment;
}
}

//set the values of the statistics we're overwriting to the new values on the table
table.set(lower_statistic_to_replace, lower_values);
table.set(upper_statistic_to_replace, upper_values);

//see if statistics for upper and lower CI are showing on table and if not, add them
var stats = table.statistics;
if(stats.indexOf(upper_statistic_to_replace) == -1) stats.push(upper_statistic_to_replace);
if(stats.indexOf(lower_statistic_to_replace) == -1) stats.push(lower_statistic_to_replace);
table.statistics = stats;

//rename the statistics we're overwriting to upper and lower CI
form.setTranslation(upper_statistic_to_replace, "Upper Confidence Interval");
form.setTranslation(lower_statistic_to_replace, "Lower Confidence Interval");

4. OPTIONAL: Change the statistics to replace from Minimum and Maximum at the top of the code, if desired.

5. Press the blue Play button > Close.

6. Choose your Significance level. By default, this is 0.05 to match Displayr's default Overall Significance Level setting, but if you are testing at a different level then change this number.

6. Press OK.

Additional details

  • This Rule applies the formula from the Default Confidence Intervals section of Confidence Interval which uses the quantiles of the Student's t-distribution. The rule uses the Average, Standard Error, and Column Sample Size statistics on your table.
  • Numbers may differ slightly (5th decimal place) from equivalent intervals computed on SUMMARY tables in Q due to different algorithms used to compute the quantiles of the t-Distribution.
  • This Rule uses the jStat JavaScript library to compute the quantiles of the Student's t-distribution.

Next

How to Customize a Rule

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