FANR 3000 1nd Edition Exam 2 Study Guide Lectures 7 10 Lecture 7 February 11 Data Interpretation I II Data Interpretation and T table a T distribution i More area in the tails and less in the center than z distribution ii As n increases though a t distribution will approach the standard normal distribution iii T values allows us to estimate uncertainty Alpha acceptable probability of error o As we want to be more confident in our analyses we decrease our alpha level o Alpha value is the acceptable probability of confidence the inferences you make from the data you collect is wrong Decrease in alpha levels more confidence levels Acceptable probability of error is the alpha value Ex For 95 confidence we are saying that we are willing to accept a 5 chance our range of possible means is wrong so alpha 05 Based on your degrees of freedom you can calculate t score from any alpha level interested o df degrees of freedom n 1 within the distribution there is a true population mean more samples results in less variability tighten cluster of t distribution less range of predicted values more confident more accurate numbers less samples more variability bad Confidence intervals A way to incorporate our sampling error in our population parameter estimate Range of values around a sample mean that has a probability of containing the true population mean Steps for determining confidence interval 1 Calculate mean of sample 2 Calculate variance SD and SE 3 Determine critical value from distribution table 4 Plug values into CI formula As CI increases the CI get wider Decrease variability add more samples Smaller sample sizes generate wider intervals Lecture 8 February 16 P Values III IV V Hypotheses Inferential Statistics o To estimate a population parameter o To test a hypothesis The assumption made about the population parameters 1 Determine null H0 and alternative hypotheses a H0 the belief that the mean of the population is or a specific value b H1 opposite of the null hypothesis holds true if H0 is found to be false c Results of test will either be i Reject null hypothesis ii Fail to reject null hypothesis Type I and Type II Errors 2 Specify level of significance a Type I Error a false positive rejection of H0 when in reality it is true b Type II Error a false negative failure to reject H0 when in reality it is not true Increasing the sample size will reduce both types of error 3 Select the test statistic that will be used 4 Collect the sample data and compute the value of the test statistic P values 5 Use value of the test statistic to make a decision using a p value a P values the smallest level of significance at which the H0 will be rejected assuming the H0 is true the probability that the observed statistic occurred by chance alone b To determine if the observed outcome is statistically significant compare p value to acceptable probability i If p value reject H0 ii If p value fail to reject H0 6 Interpret statistical results in real world terms Lesson 9 February 23 T Tests I II III Hypothesis Testing Comparing 2 populations 1 Determine null H0 and alternative H1 hypotheses 2 Specify level of significance probability of Type I error 3 Select the test statistic that will be used 4 Collect the sample data and compute the value of the test statistic 5 Use the value of the test statistic to make a decision using a rejection point Zc tc or a p value 6 Interpret statistical results in real world terms 1 Allowable error 2 The level of significance p value denotes significant results 3 Acceptable probability of a Type I Error 0 01 0 10 4 the location of the rejection boundary is a function of 5 The smaller the value of the more difficult it is to reject H0 6 Test results are stronger with a lower T Tests A 2 sample t test is appropriate ONLY if the samples meet the following criteria 1 2 samples one from each population are independent and random 2 Both populations are approximately normally distributed Compare 2 means using a new sampling distribution the sampling distribution for the difference in means o To determine if the samples come from the same population The larger the difference the larger the calculated t score so the further out in the tail the calculated t score will be 1 Determine Null and Alternative hypotheses a When testing differences between means the null hypothesis is that the difference between means is some specified value usually zero 2 Choose a significance level 3 Select the test statistic that will be used difference between sample means 4 Collect sample data from both populations 5 Execute the test statistic Types of T tests 1 One sample t test trying to determine if there is a difference in the population mean calculated from your samples against the hypothesized population mean 2 Two sample t test to determine if there is a difference in the population mean between the two groups you have sampled For equal or unequal variance 3 Paired sample t test to determine differences between populations when you have paired samples When you have similar sample individuals each receiving a different treatment or when the same sample individual is in the first treatment control and then is subjected to the second treatment For t values if we calculate a t value that is greater than our critical t value then the two populations are statistically different For p values if we calculate a p value less than our alpha value then we assume the two populations to be statistically different Lecture 10 March 2 Determining Sample Size I II Determining Sample Size Mean variance o Increase samples decrease variance Subject to time budget and ease of selection constraints o Task determine how large of a sample a good estimate of population parameter would require Determine how much error you are willing to accept in estimating the mean of a population o Sample size should be statistically and practically efficient Calculate Sample Size 1 Using the bound on the sampling mean a Based on the absolute amount of error acceptable based on the standard error of the mean b Bx 2Sx 2 Using the standard deviation and desired closeness or coefficient of variation CV and allowable acceptable error AE The formula used varies based on whether or not N in population is known Finite population when N is known o Using BOUND on the sampling mean n number of individuals you will need to sample N number of individuals in your population B your bound typically 2 times your Standard Error but doesn t have to be s