How to Reject The Null Hyphotesis (Chi Square)

Monday, January 24, 2011 JS Hanniffy 0 Comments

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

Blogger since 2008, writing with a fresh perspective.

Twitter Feeds