Hypothesis Testing Chapter 5 Lecture 5 Jaymie Ticknor Quantitative Methods 2317 Sect 001 7 and 12 February 2014 Hypothesis Tests with Means of Samples in real research samples almost always have several people can t compare the mean of sample with a distribution of scores compare mean of comparison distribution Distribution of Means can determine this by using characteristics of the population of individuals scores and number of scores in each sample Three rules for determining the distribution of means mean of the distribution of means 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 the population of individual scores the shape of the distribution of means is approximately normal Rule 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 individuals Rule 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 outliers The variance of a distribution of means is the variance of the population of individuals divided by the number of individuals in each sample 2 M 2 N The 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 2 M 2 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 normal If 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 likely Hypothesis Testing with a Distribution of Means Z test 5 steps to do a null hypothesis significance testing Z M M M Controversy 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 arbitrary The Z test the z test that we learned is used when you know the population mean and standard deviation is quite rare in real research usually when we get a sample and conduct a study we don t know what the population parameters are in subsequent chapters we will learn about tests for situations when we don t 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 Intervals If population mean is unknown best estimate of population mean M is the sample mean look at the standard error of the mean M or standard deviation of the comparison distribution Estimate the range of possible means that are likely to include the population mean this range of possible means is called confidence interval Confidence Intervals Steps Step 1 determine the standard error of the mean M 2 Step 2 CI M Z M 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 mean M 2 N