Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

Raw or Observed Data Table

STUDENT GRADE IN RESEARCH METHODS

HEIGHT CBATOTAL

Ta l l 3 0 10 10 5 0

Medium 10 30 10 50

Short (^302050100)
Total 70 60 70 200
Expected Values Table
Expected value = (Column total  Row total)/Grand total). EXAMPLE (70  50)/200 = 17.5
STUDENT GRADE IN RESEARCH METHODS
HEIGHT CBATOTAL
Tall 17.5 15.0 17.5 50.0
Medium 17.5 15.0 17.5 50.0
Short 35.0 30.0 35.0 1 00.0
Total 70.0 60.0 70.0 200.0
Difference Table
Difference = (Observed – Expected). EXAMPLE (30 – 17.5) = 12.5
STUDENT GRADE IN RESEARCH METHODS
HEIGHT CBATOTAL
Tall 12.5 –5.0 –7.5 0.0
Medium –7.5 15.0 –7.5 0.0
Short –5.0 –10.0 1 5.0 0.0
Total 0.0 0.0 0.0 0.0
Chi-square = Sum of each difference squared, then divided by the expected value of
the cell. Example: 12.5 squared = 156.25, divided by 17.5 = 8.93.
Chi-square = 1st row (8.93 + 1.67 + 3.21) +
2nd row (3.21 + 15 + 3.21) +
3rd row (.71 + 3.33 + 6.43) = 45.7
Because chi-square is not zero, the data are not independent; there is an association.
The chi-square coefficient cannot tell us the direction (e.g., negative) of the association.
For inferential statistics, we need to use a chi-square table or computer program to eval-
uate the association (i.e., to see how likely such a large chi-square is to occur by chance
alone). Without going into all the details about the chi-square table, this association is rare;
it occurs by chance less than 1 in 1,000 times. For a table with nine cells, a chi-square of
45.7 is significant at the .001 level.

EXAMPLE BOX 5

(continued)