In this section we review sampling distributions, especially properties of the mean and standard deviation of a sample, viewed as random variables. We look at hypothesis testing of these parameters, as well as the related topics of confidence intervals, effect size and statistical power. For samples that are sufficiently large it turns out that the mean of the sample is normally distributed (the Central Limit Theorem), and so the techniques described for the normal distribution can be used.

Topics:

- Basic Concepts
- One Sample Hypothesis Testing
- Standardized Effect Size
- Confidence Intervals
- Central Limit Theorem
- Hypothesis Testing using the Central Limit Theorem
- Comparing Means with Known Variances
- Simulation
- Sampling
- Statistical Power and Sample Size
- Power and Sample Size using Real Statistics
- Identifying Outliers and Missing Data

I need help with the following problem:

after conducting a survey to a specific group (n=75) it turned that many groups are over or under represenative. for example: 13 females, 60 males, and 2 other.

I am trying to find the relationship between gender and responses, how can I undersize or oversize my sample? any advice please.

Thank you

For many of the tests that you might use, it is acceptable to have different sized samples.

For tests where this is a problem, you have three main choices:

1. eliminate elements from the larger sample at random (the at random part is essential)

2. impute values for missing elements from the smaller sample (this is not such a great choice unless the smaller sample is almost the same size as the larger sample)

3. choose a different test which accepts unequal sample sizes

Charles