Descriptive and Inferential Statistics: Analyzing Independent Groups - Prof. Eric Amsel, Study notes of Psychology

Download Descriptive and Inferential Statistics: Analyzing Independent Groups - Prof. Eric Amsel and more Study notes Psychology in PDF only on Docsity! 1 Lecture 6: Analysis of Independent Groups Design III ANALYSIS A. Descriptive Statistics § Analysis of Independent Groups Design involves two types of statistical concepts and procedures. § Descriptive statistics are used to summarize a data set, to estimate population parameters, and to reduce a large body of raw information (observations) to a smaller body of summarized information § Inferential statistics are used to make some judgments about the population of interest based upon the sample statistics. III ANALYSIS A. Descriptive Statistics § Let’s discuss a particular study § College students are told of Jane and Bob who were resting by a tree on campus. § They were told how Bob climbed the tree and played on one of the branches while Jane was watching. Also how Bob sidled up to Jane and she scampered away. § Students were then asked to judge whether “Bob was romantically interested in Jane” on a 7-point Likert scale § “ Very Strong Agree” to “ Strongly Disagree” III ANALYSIS A. Descriptive Statistics § There was one IV and one DV. § Fifteen students were randomly assigned to the “student” condition, where Bob and Jane were described as students who lived on campus. § Another fifteen students were randomly assigned to the “squirrel” condition, where Bob and Jane were described as squirrels who lived on campus. § It was hypothesized that the explanation would be judged more acceptable in the Human than the Squirrel condition. 2 III ANALYSIS A. Descriptive Statistics LIKERT SCALE § LIKERT SCALE Frequency § 1. I very strongly agree with the explanation. 1 § 2. I strongly agree with the explanation. 3 § 3. I agree with the explanation. 5 § 4. I neither agree nor disagree with the explanation. 12 § 5. I disagree with the explanation. 5 § 6. I strongly disagree with the explanation. 3 § 7. I very strongly disagree with the explanation. 1 § Compute the mean of the sample § A measure of central tendency found by computing the average observation. § M=Σ X/n § 120/30 = 4 III ANALYSIS A. Descriptive Statistics § Compute the Standard Deviation of the sample: § A measure of variability found by computing the average distance from the mean of the observations. § pΣ(X-M)2/ (n−1) § p52/29 = 1.34 § sd2 = s (variance) = 1.342 = 1.80 III ANALYSIS A. Descriptive Statistics § Having a mean (M) and a standard deviation (sd) of a sample is a powerful combination of numbers with which you can figure out a lot! § You can figure out properties of the sampled distributions (Descriptive statistics) III ANALYSIS A. Descriptive Statistics 5 § B.2.ii Significance Testing § To test whether samples agree on population estimates, we have to do significance testing § Significance testing asks the question, Do group means differ from each other more than we would expect from chance? § If so, then the difference between groups is not just a difference that may be expected by sampling two random samples from the same population. § Rather, the two groups differ because they can not be said to come from the same population! III ANALYSIS B. Inferential Statistics § B.2.ii Significance Testing § Growing Plants: § You want to find out whether or not the fertilizer you use is cost -effective in growing tomatoes. § Randomly assign plots of land to be treated or untreated by the fertilizer § Grow tomato plants on both plots and find that the fertilized plots have 1.65 more tomatoes per plant. § Is it worth using the fertilizer? § Yes, if you expect little variability in the number of tomatoes per plant. No, if you expect much more. III ANALYSIS B. Inferential Statistics § B.2.ii Significance Testing § We just outlined the basic procedure of t-test. § t-Statistic: Compares the difference between the means to an estimate of the extent to which randomly selected sample means will vary. § t = Difference between means / SEMs M1 - M2 p (SD1/pn1)2 + (SD2/pn2)2 III ANALYSIS B. Inferential Statistics § B.2.ii Significance Testing § If the t-value ratio is above roughly 2, then we say that the difference between groups is real, not due to chance. § Why “2” is a long story, but basically because 2 standard deviations from the mean represents a very unlikely event (p < .05), so a critical ratio of 2 is also considered very unlikely to occur by chance alone. § Actually, the critical t value is determined as a function of the DEGREES OF FREEDOM (n-2) and checked on a “critical values of t” table. III ANALYSIS B. Inferential Statistics 6 § B.2.ii Statistical Conclusion § The critical value of t further depends on whether your test is one-tailed or two-tailed. § A two-tailed test assumes no directionality to the hypothesis. The prediction is that one group is different than the other, without specifying which one. § A one-tailed test assumes directionality to the hypothesis. The prediction specifies that one particular group (Students) scores higher than the other (Squirrels). III ANALYSIS B. Inferential Statistics § B.3. Other Concepts § 1. Type 1 and Type II Error § When the observed value of t is greater than the critical value of t, we conclude that the difference is significant! § It doesn’t mean it ’s an important or valuable difference, only one which is greater than what we would expect by chance. § Statistically significant doesn’t even mean not unlikely, only that the difference would happen 5 times or less out of 100. III ANALYSIS B. Inferential Statistics § We may be wrong in our inferential conclusion! § Type I Inference Error: Reject null hypothesis when it’s true § CONSEQUENCE: You earn a bad reputation because you will publish data which looks significant but can’t be replicated. § Type II Inference Error : Fail to reject null hypothesis when it’s false § CONSEQUENCE: Lost chance at finding significance. It was there, but you missed it! III ANALYSIS B. Inferential Statistics § B.3. Other Concepts § 2. Parametric and Non-Parametric Statistics § A t-test is a parametric statistic because it requires making estimates of populations. § Such estimates are central in null hypothesis testing. § But sometime such estimates make no sense. § Consider a distribution of 10 boys and 10 girls, what is the population estimate of gender? 1.5? § Only Interval and Ratio scaled variables can be assumed to offer meaningful population estimates. III ANALYSIS B. Inferential Statistics 7 § B.3. Other Concepts § 2. Parametric and Non-Parametric Statistics § Non-parametric statistics (e.g., chi-square) do not require making population estimates. § Non-parametric statistical methods can be used to perform statistical significance testing on Nominal or Ordinal variables. III ANALYSIS B. Inferential Statistics § 2. Experiments as the production of variance. § Science as the production and understanding of variance can now understood not only at the level of design (IV è DV), but also at the level of statistical analysis. § A t-test is an examination of two types of variability (difference between means and variability of groups) and computing a ratio between them. § Think variability. III ANALYSIS C. Chance and the t distribution § 1. Research with Statistics in mind. What is the consequence on the significance of the t - value of… 1. Lowering alpha level (p<.05) to (p.<01)? 2. Increasing sample size? 3. 2-tail vs.1-tail testing? 4. Increasing effect size (M1-M2)/sd (pooled) III ANALYSIS C. Chance and the t distribution Significance is … 1. harder to find 2. easier to find 3. depends 4. easer to find M1 - M2 p (SD1/pn1)2 + (SD2/pn2)2 § 1. ANOVA § ANOVAs analyze the variance which appears in the data. § The Variance is divided (or partitioned) into sources responsible for producing the variation (e.g., those associated with IVs) § In a simple ANOVA, variance is portioned into. § Between Group Variation: Variability in scores associated with IV but also with individual differences and error. Contains both Error and Systematic Variance § Within Group Variation: Variability in scores associated with individual differences and measurement error. Contains only Error Variance. III ANALYSIS D. F and X2 Tests