Descriptive Vs Inferential Statistics - Foundation of Inferential Statistics | PSYC 102, Study notes of Psychology

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 = )