Chi Square Test of Statistical Significance
Chi Square is the test of statistical significance to use when the dependent variable
we want to analyze is nominal level measurement. The independent variable should be a
nominal level measure, or it can be an ordinal, interval or ratio level measure that has
been recoded into grouped categories.
In the practice example, we will compute a chi square test of statistical significance
to analyze the relationship between the parents belief that a child receives better
care through use of the same doctor and that child having participated in Headstart
screening, insurance screening, free screening, or screening in some other setting.
- In the survey2000 data file, select (highlight) the variables MEDAT and BETCARE. The
variables are not adjacent to each other. To highlight both variables, first select the
data values for the variable MEDAT. Then use the mouse to move the cursor to the variable
BETCARE. Hold down the Ctrl key and then select the data values for the variable BETCARE.
In the edit menu, click on Copy.
- Click on or insert a new worksheet. In the new worksheet, click in cell G5. Go to the
Edit menu and click on Paste Special, then select Values. The data values for MEDAT and
BETCARE should be pasted into the new worksheet. Click in cell A1 and type Steps in the
Computation of Chi Square. Press Enter. Click in cell A2 and type Observed Frequencies.
Press Enter. We are now ready to carry out the data analysis.
- Remove any missing data from the analysis by using the sort function. Sort the data by
MEDAT. Remove any cases with missing or duplicate data for MEDAT (including the
corresponding cases for BETCARE). Then sort the data by BETCARE to find and remove any
other cases with missing data.
- Using Pivot Table Wizard, create a table of frequencies showing the relationship between
MEDAT and BETCARE. MEDAT, the independent variable, will be the column variable in the
table. BETCARE, the dependent variable, will be the row variable and the data variable.
Tell Pivot Table Wizard to place the pivot table in cell A3 of the worksheet. Then edit
the Pivot Table to add labels for the values of each variable. For MEDAT, change 1 to
Headstart Screening, change 2 to Insurance Screening, and so forth for each category of
the variable. For BETCARE, change 1 to yes and change 2 to No.
- After producing the Pivot Table, click in cell A10 and type Expected Frequencies (Column
Total * Row Total / Grand Total) We are going to set up a table format for Expected
Frequencies and then compute the expected frequencies for each cell of the table. In cell
B11, type MEDAT. Then type the following information in each of these cells: Cell A12 type
BETCARE, Cell A13 type Yes, Cell A14 type No, Cell A15 type Column Total, Cell B12 type
Headstart, Cell C12 type Insurance, Cell D12 type Clinic, cell E13 type Row Total, Cell
B115 type 31, Cell C15 type 8, Cell D15 type 7, Cell E13 type 38, Cell E14 type 8, and
cell E15 type 46. Note that we have simply replicated the Pivot Table with empty cells for
the expected frequencies (the center of the table).
- Now we will compute an expected frequency for each cell. Click in cell B13. Type
=B$15*$E13/$E$15 The formula will compute an expected frequency (Column Total*Row
Total/Grand Total) for cell B13. Make sure you put the $ signs in the right places. Press
enter. A value for the expected frequency will appear. Place the cursor in the lower right
hand corner of cell B13. When a black cross appears, click and drag the formula to each of
the other cells for expected frequencies. When you have finished, the table of expected
frequencies should be complete.
- In cell A17 type Computation of Chi Square. In cell B18 type MEDAT. Then type the
following information in each of these cells: Cell A19 type BETCARE, cell A20 type Yes
agency, cell A21 type No, cell B19 type Headstart, cell C19 type Insurance, and cell D19
type Clinic. We are now ready to compute Chi Square.
- Click in cell B20. In this cell we will place a formula to compute the cell values used
in the computation of Chi Square. (See Page 179 of Weinbach and Grinnell for a good
explanation of how the formula is computed). Type =(B5-B13)^2/B13 Press Enter. Place the
cursor in the lower right hand corner of cell B20. When a black cross appears, click and
drag the formula to the other cells of the table.
- Having computed the cell values, we can now compute a value for Chi square. In cell A23
type Chi square = and press Enter. In cell B23 type the formula =SUM(B20:D21) and press
Enter. A value for Chi square should appear.
- Now compute degrees of freedom (r-1)*(c-1) for the table. In cell A25 type d.f. = and
press Enter. In cell B25 type =(2-1)*(3-1) and press Enter.
- Now we will compute a probability value for the Chi Square. In cell A27 type p value
(two-tailed) = and press Enter. Click in cell B27 and insert a statistical function by
clicking on the function icon beneath the menu bar at the top of you worksheet (¦ x). Clicking on this icon will open a Paste
function dialogue box. Select statistical from the "function category" and
select CHIDIST from the "function name" side of the menu. Click on Okay. A
second dialogue box should open, requesting several values. With the cursor in the area
titled "X," click on the cell containing your Chi square value (B23). Insert
your cursor into the area titled "Deg_freedom" and then click in the cell where
youve entered the value (B25). Click on Okay. A probability value should appear.
Steps in the Computation of Lambda
(A Measure of Association for Variables Measured at the Nominal Level)
- First, in cell A29 type Computation of Lambda. Press Enter.
- In cell A30, type E1. Press Enter. In cell B30, enter the following equation:
=E7-E5. This value reflects the "error" that would be made by predicting
placement of all cases while ignoring the independent variable.
- In cell A31, type E2 and press Enter. In cell B31, enter the following equation:
=(B7-B5)+(C7-C6)+(D7-D5). This formula reflects the "prediction" of our
values based on taking the independent variable into account.
- We are now ready to compute lambda. Lambda is based on the following equation:
In cell A32, type Lambda =. In cell B32 enter the following equation: =(B30-B31)/B30
A value for lambda should appear in the cell, ranging from 0 to 1. Our interpretation
of lambda could be that we would make 25% fewer errors in predicting a parents
beliefs about their child received better healthcare by always seeing the same doctor
through the knowledge of that child having participated in the various screening programs.