Sampling

Population vs. Sample Population – The entire group you want to study Sample – The portion of the population you select to study Parameter – Fact about a population Statistic – Fact about the sample Parameter : Population :: Statistic : Sample The theory of sampling is the statistic should be the same or at least close to the parameter

Bad Sampling Read Example 5.1 on page 202 The design of a statistical study is biased if it systematically favors certain outcomes Voluntary response sampling is when you have people contact you to answer your survey. It’s biased because people with strong opinions for change are the most likely to go out of their way to contact you. Convenience sampling is when you pick individuals that are easy to reach. It is biased because they often have many lurking variables in common that made them easy to reach.

Bad Sampling Who likes going to the mall? Read example 5.2 on page 204 Who doesn’t want kids? Read example 5.3 on page 204

Good Sampling A simple random sample (SRS) means everyone in the population has an equal chance of being selected. The best way to be fair is to be random. Assign everyone in the population a number, then randomly draw numbers and interview the people whose number was drawn.

Is it random? Pick a random number. Was it really random or are there some numbers you’re more likely to pick than others? Dangers of physical mixing: Read Application 5.1 on page 215 In Excel, =rand() creates a random number between 0 and 1 – How would you have excel generate a random number between 0 and 100? =100*rand()

Population vs. Sample Ideally Ideally the statistic sample is the same as the population parameter Parameter =Percent =Statistic Population100%Sample

Population vs. Sample Actually In reality the statistic is a close approximation to the parameter, but doesn’t equal it. Assuming the sample isn’t biased, we can use the following equation to calculate a 95% confidence interval – p is the percent result from the statistic Be consistent on the decimal or percentage versions – n is the sample size

95% Confidence Interval Add and Subtract to the statistic, p This creates a range that you are 95% confident contains the true population parameter – There is a 95% chance that the true value is within that range

Class Survey: Dominant Hand Sample Size = 123 Left = 11%, Right = 85%, Ambidextrous = 5% Why does it add up to 101%? Round off Error We are 95% confident that between 5% and 17% of Saint Joe students are left handed.

Probabilistic Language You are never 100% sure of anything Assuming the sample wasn’t biased, we are 95% confident that the handedness of St. Joe students falls in these ranges.

Confidence Interval Example If you calculate your 95% confidence interval to be 1%, your actual error could be larger. That 1% is what we call a confidence interval. You are 95% confident that the error between your measured result and the actual result is 1%. If the results from your study show that the percent of Americans that believe in Heaven is %, what that means is you are 95% confident that between 83% and 93% of the population believes in Heaven.

2012 Iowa Caucus StatisticParameter – Santorum:16.3%24.6% – Romney:22.8%24.5% – Paul:21.5%21.4% – Gingrich:13.7%13.3% – Perry:11.5%10.3% – Bachmann6.8%5.0% – Huntsman:2.3%0.6%

Indiana Poll vs. Actual President StatisticObama 42.0%Romney 51.5% ParameterObama 44.8%Romney 54.3% US Senate StatisticDonnelly 46%Mourdock 39% ParameterDonnelly 50%Mourdock 44% Governor StatisticGregg 40%Pence 47% ParameterGregg 46%Pence 50%