Self-Esteem
High Low
First
74
26
100
Birth
Second
56
19
75
Order
Third
38
22
60
168
67
235
A researcher is interested in determining if there is an association between birth
order and self-esteem. She collects data from participants who were either born first,
second, or third in relation to their siblings. These participants complete a self-
esteem questionnaire, and the researcher categorizes them as having high or low
self-esteem based on the results. She then decides to test the association between
these two variables. Using the collected (observed) data above and the expected
frequencies (you will need to calculate them all - one for each cell in the matrix) and
the chi-squared formula below, what is the calculated chi-squared value for this
data? Round your answer to two decimal places.
$$X^2 = \sum \frac{(f_o - f_e)^2}{f_e}$$