Hypothesis Testing and T-tests

Question 1

What type of statistical test can you run on discrete data?

Answer 1

Chi-square test

Question 2

What do we know about samples?

Answer 2

• Samples help us estimate characteristics of the population
• Sample means are subject to some degree of error.

Question 3

What is the Central Limit Theorem?

Answer 3

• The central limit theorem specifies the shape, mean, and variance of the sampling distribution of the mean.
• Given a population with a mean μ and a variance σ2, the sampling
  distribution of the mean will have a mean equal to μ and a variance
  σ2/n. The shape of the sampling distribution approaches normal
  as the sample size (n) increases. (textbook)
• Each sample mean is an estimate of its relative population mean. But differs from the population mean by an amount indicated by the standard error.
• The larger the sample, the smaller the standard error.

Question 4

What is a t-test?

Answer 4

• A t-test allows us to compare the means for two distributions by taking into account the standard error.
• You can compare a sample mean to a population mean. Or compare to sample means.

Question 5

What is the t-test formula?

Answer 5

t=(x1-x2)/Serror

Question 6

What is the procedure for hypothesis testing?

Answer 6

1. Set up research hypothesis (H1: decide if directional or not)
2. Set up null hypothesis (H0)
3. Choose a significance level (alpha)
4. Measure particular outcome (t- sample statistic)
5. Calculate probability from hypothesis sampling distribution (p)
6. Decide if outcome is representative of hypothetical distribution.
   - If unlikely (p<a), reject assumed parameters(H0), it is reasonable to assume alternative parameters H1
   - Otherwise (p>a), the result is inconclusive.

Question 7

What do we know about confidence and decision making?

Answer 7

• Decision-making conventions in statistics help us determine where randomness ends, and an effect begins.
• Thus these conventions help us determine whether our observations are random (i.e. part of the hypothetical/null distribution) or the function of our independent variable (and therefore part of the alternative distribution)

Question 8

How do we decide what is random and what is an effect?

Answer 8

We use alpha

Question 9

What is alpha?

Answer 9

• Alpha is a confidence level
• It tells you the level of confidence you can have in your decision.
• At 95% confidence level, you accept a 5% chance of being wrong.
• At 99% confidence level, you accept a 1% chance of being wrong.