Download Descriptive Vs Inferential Statistics - Foundation of Inferential Statistics | PSYC 102 and more Study notes Psychology in PDF only on Docsity! 1 Foundations of Inferential Statistics Dr. Greg Hurtz Psychology 102 Slide FIS-2 Descriptive vs. Inferential Statistics Descriptive: Summarizing a distribution of scores. Inferential: Making generalizations (inferences) from a sample to a population. Confidence intervals (CIs) Null hypothesis significance testing (NHST) Slide FIS-3 Frequency Histogram of 30-Day Alcohol Use Projecting the theoretical normal distribution onto the sample distribution. •Is it a reasonably good fit? •Could we use our knowledge of the normal probability distribution to make statements about drinking in the population of Sac State students? 2 Slide FIS-4 The Standard Normal Probability Distribution -2.00 0.00 2.00 Normal 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% P er ce nt Standard scores (z-scores) along the x-axis Percents (or proportions) along the y-axis Interpreted as Probabilities under a Random Sampling Scheme Slide FIS-5 What’s the likelihood of randomly sampling a person with a score falling outside ±1.96 SD’s from the mean? -2.00 0.00 2.00 Normal 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% P er ce nt There’s a 5% chance that a randomly sampled population member would fall outside these boundaries. 2.5%2.5% Slide FIS-6 What does this have to do with our research decisions? Thus far we have framed this as if we’re sampling a person from a population. In inferential statistics we’re talking about sampling a “sample” of people from a population. Our research sample is but 1 of many, many samples that could be drawn from the population. 5 Slide FIS-13 Confidence Intervals 1X 2X 3X 4X 5X 6X CI #4 does not include For a 95% CI, 95 out of 100 X-bars will have CIs that include Thus, when we calculate our single CI, we’re 95% confident it includes Slide FIS-14 Sample Size and the Precision of Confidence Intervals Since larger samples contain less sampling error (i.e., narrower sampling distributions), Larger samples result in narrower confidence intervals Which means we have more precise estimates of the population parameter Slide FIS-15 The Inferential Question Addressed by Interval Estimation Given the sample data, our best estimate of the population value is ___ (our point estimate), and we are __% confident that the true value falls within the range of ± ___ (our confidence interval). 6 Slide FIS-16 The Null Hypothesis Significance Testing (NHST) Approach Assuming that the null hypothesis is true, what is the probability that we would get these sample data? If it is unlikely that we would get these data if the null hypothesis were true, then we assume the null hypothesis must therefore not be true, and we reject it Otherwise we do not reject the null hypothesis Slide FIS-17 Null Hypothesis Significance Testing 1X 2X 3X 4X 5X 6X Sample #4 is not likely to belong to the null distribution For an alpha level of .05, 5 out of 100 sample means in the red ranges belong to the population with our null-hypothesized (the “null distribution”). The rest belong to a different population. These samples are assumed to belong to the null distribution Slide FIS-18 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 P Score Group Distributions One possible “other” distribution What is this “Different” Population? The “null” distribution 7 Slide FIS-19 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 P Score Group Distributions Is this sample red or blue? One possible “other” distribution Q: How do we know which of these populations our sample was from? (A: We don’t know for sure!) The “null” distribution Slide FIS-20 Type I & II Errors The “Truth” in the Population H0 is True H0 is False Decision From Null Hypothesis Statistical Test (NHST) Reject H0 Type I error (Probability = ) Correct Decision (Probability = 1 - ) Do not Reject H0 Correct Decision (Probability = 1 - ) Type II error (Probability = )