- Submitted By: tars1021
- Date Submitted: 01/23/2014 3:31 PM
- Category: Miscellaneous
- Words: 3209
- Page: 13
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Chi-Square tests:

:set of statistical procedures that investigate differences in proportions orfrequencies in different populations.

Proportion as a mean:

n# of observed unit that possess the character of interestover the total observed units:

p = n1/n

p is a statistic estimator of thepopulation parameter П (“pi”).

If variable of interest isdichotomous,

where the characteristic of interest (psychotic patients) isscored 1 and

0 is given when characteristic of interest isnot present (non- psychotic patients)

Then, p estimates П as X estimates µ.

(Note: proportion in terms ofnominal variables is similar to the concept of means for continuous variables.

The proportion becomes...

the measure of central tendency.

Formula to find the variance of a proportion from a population

σ2 = ∑ (X-µ)2 = ∑(X – П)2 = П (1-П)

N N

Central Limit Theorem:

samplingdistribution of the mean of any shape frequency distribution (includingdichotomous) will approach normal distribution as the sample size increases

Distribution of many different values of p will become

normal with a mean proportion of pi.

Standard Error of p

SD of the distribution for a proportion

Intervals of p, + or - 2 standard errors will provide

confidence interval

Approximately _____% will include the parameter pi?

95%

3 influencing factors on SE of proportions:

1. the influence of n on SE

2. the influence of the sampling fraction (f) on standard error (true as long as the sample taps into less than 5% of the pop)

3. The influence of pi on standard error- pi at its max when it is .50 (the further away pi is from .50 the smaller the SE.

The closer p is to .50

the smaller the sample size needed for normal distribution

We use a z score distribution

to see if a sample proportion is the same as a population proportion

2 assumptions of the z-score distribution for proportions

1. Random sample size of n

2. The sampling distribution of p...