How to Calculate Confidence Intervals for Crosstabs with Numeric Questions

Introduction

This article describes how to go from a crosstab which includes a numeric question...

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

Requirements

This example may be used to compute confidence intervals for crosstabs where there is a numeric question (Number, Number - Multi, or Number - Grid) selected in the Blue drop-down menu, and a Pick One or Pick Any question selected in the Brown drop-down menu. The rule borrows statistics from the table (by default it takes over the Index and Missing n statistics), and renames them to Upper Confidence Interval and Lower Confidence Interval respectively.

Method

1. Select your table.

2. Go to Automate > Custom Rule.

3. Paste the below into the dialog:

// Choose which stats to replace.
var upper_statistic_to_replace;
var lower_statistic_to_replace;
// Numeric results
if (table.availableStatistics.indexOf("Average") > -1) {
   var upper_statistic_to_replace = "Maximum";
   var lower_statistic_to_replace = "Minimum";
} else {
   form.ruleNotApplicable('it only applies to tables containing the Average in the Statistics - Cells');
}

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');
}

if (["Pick One", "Pick Any"].indexOf(table.brownQuestion.questionType) == -1){
  table.suppressOutput('Confidence intervals not computed - the table should have a Pick One or Pick Any question selected in the Brown drop-down menu.');
  form.ruleNotApplicable('the table should have a Pick One or Pick Any question selected in the Brown drop-down menu.');
}

// Set up controls for user input.
form.setSummary('Calculate confidence intervals on crosstabs of means'); 
form.setHeading('Calculate confidence intervals on crosstabs of means');

var label = form.newLabel('Significance level:');
var p_level = form.newNumericUpDown('Lower');
p_level.setIncrement(0.01);
p_level.setDefault(0.05);
p_level.setMaximum(1);
p_level.setMinimum(0);
form.setInputControls([label, p_level]);

// Work out quantile of Student's T Distribution
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
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;
 } 
}

table.set(lower_statistic_to_replace, lower_values);
table.set(upper_statistic_to_replace, upper_values);
form.setTranslation("Maximum", "Upper Confidence Interval");
form.setTranslation("Minimum", "Lower Confidence Interval");

3. OPTIONAL: Change the statistics to replace from Minimum and Maximum, if desired.

4. Press the blue Play button > Close.

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

6. Press OK > OK.

Note the following:

• 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 n 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 quatiles of the Student's t-distribution.

Next

How to Calculate Confidence Intervals for Crosstabs with Categorical Questions

How to Use Rules in Q

How to Customize a Rule