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Implement the chi-squared test

Lisa Wong
Updated

You can add the chi-squared test to your visualization to highlight whether there is a significant association between two categorical variables.

Note: The chi-squared test can be used with a maximum of two values of a pivoted field, such as Wave 1 and Wave 2. Use filters to exclude any additional values included in your data (e.g. Wave 3).
  1. In the Field Picker, select the Count measure to include it in the Data panel.

    The following step creates a table calculation for use in subsequent table calculations. After you create this table calculation you can hide the fields for these measures in the Data panel.

  2. Create a table calculation for Count:
    1. In the Field Picker, select Add > Table Calculation.
    2. Enter ${ and then select the Count measure from the drop-down list.
    3. In the Name text box, enter Count as the field name.
    4. Click Save.
  3. Create a table calculation for CountA:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy the appropriate table calculation template into the Expression text box. 
      # Convert NULLS to 0s to enable proper calculation
if(is_null(${sample1_count}),0,${sample1_count})
    3. Replace all instances of ${sample1_count} with the ${count} table calculation.
    4. In the Name text box, enter the field name.
      For example: CountA
    5. Click Save.
  4. Create a table calculation for Column total count:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy the appropriate table calculation template into the Expression text box. 
      sum(${sample1_count})
    3. Replace ${sample1_count} with the ${counta} table calculation.
    4. In the Name text box, enter the field name.
      For example: Column Total Count
    5. Click Save.
  5. Create a table calculation for Proportion%:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy the appropriate table calculation template into the Expression text box. 
      ${counta}/${column_total_count}
    3. In the Name text box, enter the field name.
      For example: Proportion %
    4. Click Save.
  6. Create a table calculation for Period over period change (PoP%):
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy the table calculation template into the Expression text box. 
      if(${period/sample_group}=1 # 1 is equal to the period number
# This can alternatively be equal to a sample_group name
# ----- Begin second pivot section ----------------------------------
OR ${second_pivot}!=pivot_offset(${second_pivot}, -1) 
# what the previous line of code is doing is that given the current column 
# like "Canada", return true if the column before's value is not "Canada"
# ----- End second pivot section   ----------------------------------
,null,
((${proportion}-pivot_offset(${proportion}, -1)))) 
# the -1 arguments above are taking the previous value
    3. Replace ${period/sample_group} in the first line with the period, sample group or wave dimension in your data, and if you are using a second pivot, replace ${second_pivot} with the second field you are pivoting on.
    4. In the Format drop-down list, select Percent.
    5. In the Decimals text box, enter 0.
    6. In the Name text box, enter the field name.
      For example: PoP%
    7. Click Save.
  7. Create a custom row total table calculation named Row total count:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy the appropriate table calculation template into the Expression text box. 
      if(${period/sample_group}="1" # 1 is equal to the period number
# This can alternatively be equal to a sample_group name
# ----- Begin second pivot section ----------------------------------
# Remove this section if you aren't including a second pivoted field
OR ${second_pivot}!=pivot_offset(${second_pivot}, -1)
# what the previous line of code is doing is that given the current column 
# like "Canada", return true if the column before's value is not "Canada"
# ----- End second pivot section   ----------------------------------
,null,
${sample1_count}+if(is_null(pivot_offset(${sample2_count},-1)),0,pivot_offset(${sample2_count},-1)))
# the -1 arguments above are taking the previous value
    3. Replace ${period/sample_group} in the first line with the period, sample group or wave dimension in your data, and replace ${second_pivot} with the second field you are pivoting on.
    4. Replace all instances of ${sample1_count} and ${sample2_count} with the ${count} table calculation.
    5. In the Name text box, enter the field name.
      For example: Row Total Count
    6. Click Save.
  8. Create a Max number of unique row values per 2 quarters table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation template into the Expression text box: 
      if(${period/sample_group}="1" # 1 is equal to the period number
# This can alternatively be equal to a sample_group name
# ----- Begin second pivot section ----------------------------------
# Remove this section if you aren't including a second pivoted field
OR ${second_pivot}!=pivot_offset(${second_pivot}, -1)
# what the previous line of code is doing is that given the current column 
# like "Canada", return true if the column before's value is not "Canada"
# ----- End second pivot section   ---------------------------------- 
,null,
max(list(sum(if(${counta}>=1,1,0)),sum(if(pivot_offset(${counta},-1)>=1,1,0)))))
    3. Replace ${period/sample_group} in the first line with the period, sample group or wave dimension in your data, and replace ${second_pivot} with the second field you are pivoting on.
    4. In the Name text box, enter the field name.
      For example: Max # of Unique Row Values per 2 Quarters
    5. Click Save.
  9. Create a Degrees of freedom table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation template into the Expression text box: 
      # Assuming only comparing max 2 waves at a time
# Thus, the degrees of freedom will always be
# (2-1) '(# of waves -1)' x (n-1) '# of choices -1'

(2-1)*(${max_number_of_unique_row_values_per_2_quarters}-1)
    3. In the Name text box, enter the field name.
      For example: Degrees of Freedom
    4. Click Save.
  10. Create an Expected frequency table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation template into the Expression text box: 
      if(is_null(
    (pivot_offset(${row_total_count},1)*${column_total_count})
/
sum(pivot_offset(${row_total_count},1))
),
#True, This marks the last period of the pivot table
${row_total_count}*${column_total_count}
/
sum(${row_total_count}),
#False
(pivot_offset(${row_total_count},1)*${column_total_count})
/
sum(pivot_offset(${row_total_count},1))
)
    3. In the Format drop-down list, select Decimals.
    4. In the Decimals text box, enter 2.
    5. In the Name text box, enter the field name.
      For example: Expected Frequency
    6. Click Save.
  11. Create a Chi-Squared table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation into the Expression text box: 
      #χ2 = (observed value - expected value)² / expected value

power(${counta}-${expected_frequency},2) / ${expected_frequency}
    3. In the Name text box, enter the field name.
      For example: Chi-Squared
    4. Click Save.
  12. Create a Final Chi-Squared table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation template into the Expression text box: 
      if(${period/sample_group}="1" # 1 is equal to the period number
# This can alternatively be equal to a sample_group name
# ----- Begin second pivot section ----------------------------------
# Remove this section if you aren't including a second pivoted field
OR ${second_pivot}!=pivot_offset(${second_pivot}, -1)
# what the previous line of code is doing is that given the current column 
# like "Canada", return true if the column before's value is not "Canada"
# ----- End second pivot section   ----------------------------------
OR ${row_total_count}=0
,null, 
  sum(${chi_squared})+sum(pivot_offset(${chi_squared},-1)))
    3. Replace ${period/sample_group} in the first line with the period, sample group or wave dimension in your data, and replace ${second_pivot} with the second field you are pivoting on.
    4. In the Name text box, enter the field name.
      For example: Final Chi-Squared
    5. Click Save.
  13. Create a Chi-Squared Significant table calculation:
    1. In the Field Picker, select Add > Table Calculation.
    2. Copy this table calculation template into the Expression text box: 
      if(${period/sample_group}="1" # 1 is equal to the period number
# This can alternatively be equal to a sample_group name
# ----- Begin second pivot section ----------------------------------
# Remove this section if you aren't including a second pivoted field
OR ${second_pivot}!=pivot_offset(${second_pivot}, -1)
# what the previous line of code is doing is that given the current column 
# like "Canada", return true if the column before's value is not "Canada"
# ----- End second pivot section   ----------------------------------
,null,

# If the max expected_frequency of the current period or the max expected_frequency
# of the previous period is less than 5, than null (minimum rule of thumb expected_frequency is 5)
if(max(${expected_frequency_1})<5 OR 
  max(pivot_offset(${expected_frequency_2},-1)) < 5,null,

# If chisq_dist is greater than 95% signficance level, return 1(true) else 0(false)
if(
  chisq_dist(${final_chi_squared},${degrees_of_freedom},yes) # Significance %
  >0.95,1,0)))
    3. Replace ${period/sample_group} in the first line with the period, sample group or wave dimension in your data, and replace ${second_pivot} with the second field you are pivoting on.
    4. Replace ${expected_frequency_1} and ${expected_frequency_1} with the ${expected_frequency} table calculation.
    5. In the Name text box, enter the field name.
      For example: Chi-Squared Significant
    6. Click Save.
Parent topic: Statistical analysis using table calculations
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