# Statistics

## Statistics

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...