School

University of GuelphDepartment

Sociology and AnthropologyCourse Code

SOAN 2120Professor

Scott SchauThis

**preview**shows pages 1-2. to view the full**7 pages of the document.**Lecture Mon Apr. 1 2013

Parameter vs. Statistic

-parameter: the summary description of a given variable in a population (the parameter is

constant, it will not change)

-statistic: the summary description of a variable in a sample (variable that you use to

estimate)

-through statistics we try to infer the true value of a population parameter

The Sampling Distribution

-if many independent random samples are selected from a population and a statistic

calculated in each of them the sample statistics provided by those samples will be

distributed around the population parameter in a bell-shaped fashion

-this bell (or normal) curve is called the sampling distribution

Standard and Sampling Error

-when we move into calculating the average value of this error for a whole sampling

distribution we then have a measure called the standard error (s.e.)

-i.e. the average difference between a group of sample statistics and the true population

parameter

-more simply: the standard error is the average dispersion in a sampling distribution

Calculating (estimating) the s.e. from A Sample Binomial Statistic

-page 195 in text

-s.e. = √ (P x Q / n)

-P is the population parameter we want to calculate (e.g. the proportion of sociology

students who were born in Canada)

-Q = 1-P

-n is the number of cases in each sample

-the standard error indicates how tightly sample estimates will be distributed around a

population parameter

-if small the sample statistics most closely resemble the population parameter

-e.g. if you increase n, you will get a smaller standard error

Factors Affecting the Standard Error

(you always want the standard error to be as small as possible)

-how can the standard error become smaller?

-the standard error will increase as a function of P x Q – highest number when there is a

total split between the two

i.e. both P and Q = 0.5 higher heterogeneity

homogeneous populations render a smaller s.e.

-the standard error is also a function of the sample size n, and will decrease as th sample

size gets larger

-this is what the CENTRAL LIMIT THEOREM is all about

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

S.E In The Normal Distribution

-certain proportions of the sample statistics will often fall within a specified number of

standard error from the population parameter

-approx. 68% of sample stats will fall within 1 and -1 s.e. of the population

parameter

-95% of sample stats will fall within 2 and -2 s.e. of the population parameter

-99% of sample stats will fall within 3 and -3 s.e. of the population parameter

Level of Confidence

-we can express the accuracy of a sample stat in terms of the level of confidence that the

stat falls within a specified interval from the parameter

-CONFIDENCE INTERVAL: a range in which we expect a sample stat to lie for a given

percentage of the time (confidence level)

-e.g. 95% or 68% of the time we expect a sample stat to fall between a range of

numbers (the confidence interval)

Calculating Confidence Intervals

Example:

-prof J Benhaim want to estimate the proportion of Mcgill students who voted I the past

Candian ferdal election. To do so (instead of asking every mcgill student if they voted or

not) she collects a random sample of 100 students. She finds that 35% of thos estudents

voted in the past federal election.

How would she go about getting a 95% confidence interval of Mcgill students who voted

in the past federal election?

ANSWER

-assign your values…

- n = 100

- 35% = P (a stat that estimates the parameter)

-the middle part of our curve is at 35%

-next calculate standard error

s.e. = √ (P x Q / n)

P= 0.35 Q= (1=0.35)=0.65 n=100

-plug in the values to get the answer:

s.e. = 0.048

-next calculate the confidence interval

95% c.i. = P ± 2 x s.e.

= 0.35 ± 2 x 0.048

= (0.254, 0.446) or between 25.4% and 44.6%

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