# SOC202H1 Lecture Notes - Sample Size Determination, Statistical Parameter, Sampling Error

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Soc202 Readings notes 2

Chapter 7 － Using Probability Theory to Produce Sampling Distributions

(Focus on pages 206 - 215 (up to "Nominal Variables"); pages 219 – 222)

Point Estimates

Sampling error – the difference between the calculated value of a sample

statistic and the true value of a population parameter (unknown)

Point estimate – a statistic provided without indicating a range of error.

(mean of a population)

o There’s a variability in statistical outcomes from sample to sample

Predicting Sampling Error

Repeated sampling – drawing a sample and computing its statistics and then

drawing a second sample, a third, a fourth, and so on. (learned that sampling

is only a estimate)

Symbols to represent population parameter for interval/ratio variables

o UX = the mean of a population

o OX = the standard deviation of a population

Sampling error = Xbar – UX

Sampling error is patterned and systematic and therefore is predictable

o 1) The resulting sample means were similar in value and tended to

cluster around a particular value.

o 2) sampling variability was mathematically predictable form

probability curves

Sampling distribution

From repeated sampling, a mathematical description of all possible sampling

outcomes and the probability of each one

A raw score distribution is scores of each person in your sample

Sampling distribution for interval/ratio variables

Example: Physicians

o 48 years = mean of sample means

o UX = mean of a sampling distribution of means, will always equal to

population mean

o As with any normal curve, standard deviation is the distance to the

point of inflection of the curve

o Sampling distribution of means (X bar) describes all possible

sampling outcomes and the probability of each outcome.

Standard Error

Standard error – the standard deviation of a sampling distribution. The

standard error measures the spread of sampling error that occurs when a

population is sampled repeatedly

o Measures the spread

o Equation – the standard error of a sampling distribution of means is

the samples standard deviation divided by the square root of the

sample size (S(xbar) = sx/square root of N)

Law of large numbers

The larger the samples size, the smaller the standard error

Replacing n with higher number, sample error decreases

The central limit Theorem

Regardless of the shape of a raw score distribution of an interval/ratio

variable, its sampling distribution will be normal when the sample size, n, is

greater than 121 cases and will center on the true population mans.

Sampling distribution has a small range than the raw score distribution (not

a normal curve)

Distributions are rectangular in shape when the raw scores have equal

chances of getting picked

Bean Counting as a Way of Grasping the Statistical Imagination

Sampling distribution is a probability distribution, it tells us how frequently

to expect any and all sampling out comes when we draw random samples

The central limit theorem essentially states that random sampling results in

normal curves: symmetrical distributions that bunch in the middle and tail

out to the sides

As long as sample size is sufficiently large, the sample distribution of

proportions takes the bell shape of a normal curve

Distinguishing Among Populations, Samples, and Sampling Distributions

Sample = Statistics, Population = Parameter, Sampling distribution =

Hypothetical distribution of an infinite number of samples of size N.

Statistical Follies and Fallacies: Treating a point estimate as though it were

absolutely true

No single statistics is the last word on estimating a parameter of the

population