How to calculate this problem
Message posted by Dr.Sankar (via 152.163.201.56) on November 9, 2001 at 3:38 AM (ET)

In a hospital during last year 394 patients were treated and 30 of them developed complications and during this year 192 patients were treated and 12 of them developed complications.How to compare this two and determine which is statistically significant and better.

1.By chi square analysis
2.How to calculate P-Value in this problem
3.Is there any other methods.

Please help me.

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Re: How to calculate this problem
Message posted by Tomi (via 154.32.142.194) on November 9, 2001 at 10:14 PM (ET)

Although Jack has given you another method, it is possible to use chi squared analysis.

What you do is create a contingency table:

[ ]#[Year1]#[Year2]#[Total]
[ Complications]#[ 30]#[ 12]#[ 42]
[No Complications]#[ 364]#[ 180]#[544]
[ Total]#[ 394]#[ 192]#[ 586]

The expected values for each cell in the table can be calculated from the row and column totals:
{Year1 Complications} = 42*394/586
{Year2 Complications} = 42*192/586
{Year1 No Complications} = 544*394/586
{Year1 Complications} = 544*192/586

to give the following values:

[ ]#[Year1]#[Year2]#[Total]
[ Complications]#[ 28.2]#[ 13.8]#[ 42]
[No Complications]#[365.7]#[178.2]#[544]
[ Total]#[ 394]#[ 192]#[ 586]

A quick glance at the expected values shows that they are very similar to the observed values, indicating that there is probably no difference between the years. However, we need to work out the X squared statistic:

X squared = sum {(observed - expected)^2} / expected = 0.110 + 0.225 + 0.008 + 0.017 = 0.361

2*2 contingency table has degrees of freedom df = 1.

p score can be calculated in Excel by {=CHIDIST(0.361,1)} which gives 0.548

This p value is much larger than the 0.05 = 5% usually taken as a significance level.

Oops! Should have stated at the beginning:

Null hypothesis: No of complications independent of Year.

Alternative hypothesis: No of complications dependent on Year.

Conclusion: No of complications is independent of Year.