10_30_03 Quantitative

Estimation: Making educated guesses

Point estimation

Interval estimation

àHypothesis testing

Case Ia

Does a particular samplet of observations in this study come froma specified population or does it represent a different population?

"Known" population mean

"Known" population standard deviation

For all studies, two foci – one, the "mu" or population parameter, the second, the sample statistic.

The logic of hypothesis testing

Null hypotheses H₀ - a position of no difference m=100

Alternative hypotheses H₁ m¹100

In hypothesis testing we continue to believe in the null hypothesis until we have enough evidence to give up that belief. Innocent until proven guilty, essentially.

HOWEVER we are going to put it up against an alternative hypothesis. Why am I starting to think that hypothesis testing sounds a lot like Pokemon?

General model

· Identify the specific population and population parameter of interest

· Define the null hypothesis and alternative hypothesis

· Collect data on a random sample selected from population of interest

· Compute a sample statistics tat is an estimate of the parameter of interest

· Decide on a criteria for evaluating the sample evidence

· Make decision to retain the null hypothesis or discard the null hypothesis in favor of the alternative hypothesis

Decision	The True State of Reality
		The Null hypothesis is true	The Alternative hypothesis is True
	The Null hypothesis is true	Correct Decision Probability = 1 - a	Type II error (risk b)
	The Alternative hypothesis is True	Type I error (risk a)	Correct decision Probability = 1-b

"Even the end result is not going to tell us what the possible alternatives are. That is the tragedy of statistics."

A type 1 error is always a possibility, but we can control the risk of making that kind of error. We can create a decision rule that minimizes that risk and lets us know how big a risk we are taking.

We generally don’t' talk about type 1 error, we talk about significance – they're two of the same type of thing.

If level of significance is set at 5% you're saying I can live with the risk of not knowing if what I'm saying is significant 5% of the time. (alpha)µ= .05

Type II error can be controlled/minimized by size of sample.

Decision rule: The value of the sample statistic that keeps you believing H₀ and the value that leads you to reject H₀

I want to hide in a hole in the ground. This is a looooong day already.

This weekend I am going to do all my reading like a good little monkey.

The meaning of likely/unlikely. Within 2 sem (95%) is likely. Outside two s.e.m. (5%) is unlikely.

Sampling distribution of means: Two tailed (alpha = .05) – need to find z score that has only 2.5 above it

z score of mean has to be…