**Unformatted text preview:**

Jaymie TicknorQuantitative Methods 2317 Sect. 0017 and 12 February 2014Lecture #5Chapter #5 : Hypothesis Testing :Hypothesis Tests with Means of Samples: in real research, samples almost always have several people; canβt compare the mean of sample with a distribution of scores; compare mean of comparison distributionDistribution of Means: can determine this by using characteristics of the population of individuals scores, and number of scores in each sampleThree rules for determining the distribution of means: mean of the distribution ofmeans is the same as the mean of the original population of individual scores; the spread of the distribution of means is less than the spread of thepopulation of individual scores; the shape of the distribution of means is approximately normalRule #1: Mean: each sample is randomly selected from the population of individuals; the mean of a sample might be higher or lower than the mean of the population of individuals; but it will balance out; mean of distribution of means = mean of population of individualsRule #2: Spread: the spread of a distribution of means will be less than the spread of the population of individual scores; the more individuals in each sample, the less spread out the distribution of means will be; Law of Large Numbers: larger the numbers, the less likely there will be outliersThe variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample π2M = π2/NThe standard deviation of the distribution of means is the square root of the variance of the distribution of means; also called standard error of the mean (SEM) β(π2M)= β(π2/N)Rule #3: Shape: shape of a distribution of means is approximately normal if either each sample has 30 or more individuals or the distribution of the population of individuals is normalIf the distribution of individuals is not normal, how can the distribution of means be normal? Extreme values balance each other out when you take the mean of a sample; middle values more likely; extreme values less likelyHypothesis Testing with a Distribution of Means: Z-test: 5 steps to do a null hypothesis significance testing; Z = (M-πM)/πMControversy: Marginal Significance: usually researchers use standard significance levels of 5% or 1%; what if you get p = .06? marginally significant? some hold fast to the .05 cutoff; but most view p = .05 as arbitraryThe Z-test: the z-test that we learned is used when you know the population mean andstandard deviation; is quite rare in real research; usually when we get a sample and conduct a study, we donβt know what the population parameters are; in subsequent chapters, we will learn about tests for situations when we donβt know the population parameters (mean and standard deviation)Estimation and Confidence Intervals: majority of the class focuses on hypothesis testing; there is another way to approach statistical questions: Estimation and Confidence IntervalsIf population mean is unknown: best estimate of population mean (πM) is the sample mean; look at the standard error of the mean (πM) or standard deviation of the comparison distributionEstimate the range of possible means that are likely to include the population mean; this range of possible means is called confidence intervalConfidence Intervals Steps:Step #1: determine the standard error of the mean: πM = β(π2M)= β(π2/N)Step #2: CI = πM +- (Z)πM; for 95% CI, determine raw scores for 1.96 standard errors above and below sample mean; for 99% CI, determine raw scores for 2.58 standard errors above and below sample

View Full Document