In a research we sometimes find a statement such as "There is no significance difference between element A to element B", the statement is called Null Hyphotesis (Ho). To prove or reject the Null Hypothesis we use a Chi Square formula.
Chi Square:
Some steps need to be done before we can get the Chi Square value result. Here are some steps how to calculate Chi Square:
- Determine the expected frequency for each category
- Calculate according to x2 formula:
- Substract expexted from observed values
- Square each of the result
- Divide each result by the expected values
- Sum all results: add them all up
- Calculate the degree of freedom (check it on your table list of df)
- Using the x2 the df
- Make significance decision
Example
Police officer’s question on reading case studies of domestic violence: is there a significant tendency for extreme violence to be charged more often than milder violence? The data is:
Extreme violence Milder violenc
Charge 27 47
Not charge 4 103
State the hypothesis:
Ho There is no significant tendency for extreme violence to be charged more often than milder violence.
Determine the expected frequency for each category.
a. Calculate the expected values
Extreme violence Milder violence Total
Charge 27 47 74
Not charge 4 103 107
------------------------------------------------------------------------
Total 31 150 181
Expected frequency = Column Frequency X (Row Frequency/Overall Frequency)
31 X (74/181) = 12.67e
31 X (107/181) = 18.33e
150 X (74/181) = 61.33e
150 X (107/181) = 88.67e
b. Substract expected from observed values
Extreme violence Milder violence Total
Charge 27 47 74
Not charge 4 103 107
--------------------------------------------------------------------------------
Total 31 150 181
(Charge) = 27o - 12.67e = 14.33 47o - 61.33e = -14.33
(Not charge) = 4o - 18.32e = - 14.33 103o - 88.67e = 14.33
c.Square each of the results
2 2 2 2
(14.33) (-14.33) (- 14.33) (14.33)
------ + -------- + -------- + ------- =
12.67 e 61.32 e 18.32e 88.67e
205.34/12.67 = 16.21
205.34/61.32 = 3.35
205.34/18.32 = 11.21
205.34/88.67 = 2.31
Summed = 33.07
d. Calculate the df
—Use this – df = (c – 1) x (r – 1) with 2 + variables
—With 1 variable – df = (c – 1).
Calculate the degrees of freedom
df = (2 – 1) x (2 – 1) = 1
—Chi-square = 33.07 with 1 df.
—This is significant at the 5% level (can also be 1% level, depend on the question).
—There is a significant tendency for extreme violence to be charged.
— According to the result above we can then reject the Null hypothesis.
DBLN, 21.35-230111
