Quant1_Week6_ProbTesting

Quant1_Week6_ProbTesting - Confindence Intervals and...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Confindence Intervals and Probability Testing PO7001: Quantitative Methods I Kenneth Benoit 28 October 2009 Using probability distributions to assess sample likelihoods I Recall that using the and from a normal curve, we can then assess the probability of finding specific scores along this distribution (as we did last week) I The question: If we assume equals some specific value, then how likely was it to have drawn a given sample mean X? I A variation would be: If we draw two sample means, what is the probability that they have identical population means? Confidence intervals I Recall that a confidence interval is the range of values within which our population mean is most likely to fall I Confidence intervals are expressed as a percentage of confidence: If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter I Confidence intervals can be: I parametric: based on either assumed probability distributions I nonparametric: obtained through simulation (e.g. bootstrapping) Confidence intervals for proportions I Often we may seek to estimate a population proportion on the basis of a random sample: e.g. proportion to vote Yes on the Lisbon Treaty referendum I We use a version of the standard error known as the standard error of the proportion : s p = r p (1- p ) N where I s p is the standard error of the proportion I p is the sample proportion I N is the total number of cases in the sample I Because proportions have only a single parameter of which p is an estimate, we can use the normal distribution and not t I So: 95% CI for proportions = p 1 . 96 s p Confidence intervals for proportions: example Say, we want to look at the voter support for Vladimir Putin. 66% of 1600 respondents in a survey say they will vote for Putin. SE ( p ) = p p (1- p ) / n = p ( . 66 . 34) / 1600 = . 012 CI 95% = [ p- 2 SE ( p ); p + 2 SE ( p )] = [ . 637; . 683] Confidence intervals for proportions: example 0.62 0.64 0.66 0.68 0.70 5 10 15 20 25 30 35 Support Putin Density Figure: Confidence interval of support for Putin Confidence intervals for proportions: example qnorm(c(.025, .975), .66, sqrt(.66 * .34 / 1600)) prop.test(.66 * 1600, 1600) Hypothesis testing I Hypothesis testing refers to a method of making statistical decisions using experimental data: a result is called statistically significant if it is unlikely to have occurred by chance I The null hypothesis ( H ) is the proposition that we will try to reject. It usually states the assumption that there is no effect or difference (depending on the research question) I The null hypothesis is stated as the opposite of what we would like to prove (more shortly) I The alternative hypothesis ( H 1 or H a ) states the research hypothesis which we will test assuming the null hypothesis . Steps in hypothesis testing...
View Full Document

Page1 / 63

Quant1_Week6_ProbTesting - Confindence Intervals and...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online