PSYC 2260 Lecture Notes - Lecture 5: Point Estimation, Null Hypothesis, Statistical Hypothesis Testing
26 Jun 2018
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PSYC 2260 Introduction to Research Methods in Psychology
Chapter 5 Hypothesis Tests with Means of Samples
The Distribution of Means
Distribution of means: distribution of means of samples of a given size from a population (also
called a sampling distribution of the mean); comparison distribution when testing hypothesis
involving a single sample of more than one individual
- Problem: we often do not know what the distribution of means is…. So we estimate it
Distribution of means can be derived, following 3 principles:
1. The mean of a distribution of means = mean of population µM= µ2
- Any given sample may have a mean lower/ higher
- But, if a large number of samples, the mean of the sample will average out
2. The spread of a distribution of means is less than the spread of the population
- In any sample, extremes tend to cancel out (thus, sample variance will be smaller than
population variance)
Formulas:
- Variance of a distribution of the means:
- Standard deviation of a distribution of means (standard error) :
How much the means would vary in samples taken from the same population
As N gets larger, standard error gets smaller
3. The shape of the distribution of means is normal
- With repeated sample, extremes cancel out: mean is “pulled” to the middle
- Normally achieved when samples are of 30 or more individuals
See handout
In real-life, often don’t know the population mean..
- However, sample mean is best estimate of population mean. Why?
- Logic of chance
More likely to get a sample mean from a population with the same mean that from
a population with a different mean
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Chapter 5 hypothesis tests with means of samples. Distribution of means: distribution of means of samples of a given size from a population (also called a sampling distribution of the mean); comparison distribution when testing hypothesis involving a single sample of more than one individual. Problem: we often do not know what the distribution of means is . Distribution of means can be derived, following 3 principles: the mean of a distribution of means = mean of population m= 2. Any given sample may have a mean lower/ higher. But, if a large number of samples, the mean of the sample will average out: the spread of a distribution of means is less than the spread of the population. In any sample, extremes tend to cancel out (thus, sample variance will be smaller than population variance) Standard deviation of a distribution of means (standard error) : How much the means would vary in samples taken from the same population.
