Analysis of Variance (ANOVA) Can compare the effects of different treatments Can make population level inferences based on sample population.

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Presentation transcript:

Analysis of Variance (ANOVA) Can compare the effects of different treatments Can make population level inferences based on sample population

Population: a data set representing the entire entity of interest Sample: a data set representing a portion of a population Population Sample

Population mean – the true mean for that population -a single number Sample mean – the estimated population mean -a range of values (estimate ± 95% confidence interval) Population Sample

As our sample size increases, we sample more and more of the population. Eventually, we will have sampled the entire population and our sample distribution will be the population distribution Increasing sample size

MEAN ± CONFIDENCE INTERVAL When a population is sampled, a mean value is determined and serves as the point-estimate for that population. However, we cannot expect our estimate to be the exact mean value for the population. Instead of relying on a single point-estimate, we estimate a range of values, centered around the point-estimate, that probably includes the true population mean. That range of values is called the confidence interval.

Confidence Interval Confidence Interval: consists of two numbers (high and low) computed from a sample that identifies the range for an interval estimate of a parameter. y ± (t  /0.05 )[(  ) / (  n)] 132 ±    145.8

Single Population Size Boudreaux tells everyone that his bass pond has bass that average 8 pounds His neighbor, Alphonse, doesn’t believe him. Who is right?

Single Sample t-test Used to compare the mean of a sample to a known number Assumes that subjects are randomly drawn from a population and the distribution of the mean being tested is normal Basically, does the confidence interval include the number of interest?

Simple as Creating a Confidence Interval N = 10 Range = 3.3 – 8.9 Mean = 5.79 Var(  )= t  /0.05 = 1.82 y ± (t  /0.05 )[(  ) / (  n)] 5.79 ± (1.82)(2.599)/(3.16)= 5.79 ± 1.497= 4.29  5.79  is not included in the range- Boudreaux is wrong!

Are Two Populations The Same? Boudreaux : ‘My pond is better than yours, cher’! Alphonse : ‘Mais non! I’ve got much bigger fish in my pond’! How can the truth be determined?

Two Sample t-test Simple comparison of a specific attribute between two populations If the attributes between the two populations are equal, then the difference between the two should be zero This is the underlying principle of a t- test

Analysis of Variance Can compare multiple means Compares means to determine if the population distributions are not similar Uses means and confidence intervals much like a t-test Test statistic used is called an F statistic (F-test), which is used to get the P value If P-value > 0.05 the means are not significantly different; If P< 0.05 the means are significantly different

Analysis of Variance – post hoc F test does not tell us what means are different

Analysis of Variance