Determining Population Results from Sample Data: Hypothesis Testing & Inferential Stats, Exams of Psychology

Download Determining Population Results from Sample Data: Hypothesis Testing & Inferential Stats and more Exams Psychology in PDF only on Docsity! 1 Hypothesis Testing / Inferential Statistics STAT Chap 9 / METH Chap 13 PSYC 201 – Psychological Research I Samples and Populations Inferential statistics are used to determine whether researchers can make statements that the results reflect what would happen if the experiment were conducted again and again with multiple samples Can we infer results taken from a sample to the population? Inferential Statistics Importance of ensuring that the groups are equivalent Achieved by experimental control and/or randomization True score + random error Random error will be responsible for some correlation between the scores or difference in the means 2 Null and Research Hypotheses Null hypothesis H0 = no effect, or no relationship present, or the population means are equal Research or Alternative hypothesis H1 or Ha = effect occurred, or relationship present, or the population means are not equal The Null is always the opposite of what the researcher wishes to demonstrate is true (because one cannot prove something true, but one can show something to be false…) Null and Research Hypotheses (con’t) Null hypothesis is a very precise statement If we can determine that the null hypothesis is incorrect, then we can reject it and accept the research hypothesis Null hypothesis is rejected when there is a low probability that the results could be due to random error = statistical significance SOP for Psychologists is to use non-directional hypotheses (referred to as a two-tailed test), so that’s what we do in this class, always. Non-directional hypothesis examples: H0: r = 0 H1: r ≠ 0 H0: µ1 = µ2 H1: µ1 ≠ µ2 Directional hypothesis examples: H0: r = 0 or H0: r = 0 H1: r < 0 H1: r > 0 H0: µ1 = µ2 or H0: µ1 = µ2 H1: µ1 > µ2 H1: µ1 < µ2 5 Review: Hypothesis testing steps 1. Choose the appropriate test (statistical model) 2. Create the Null and Alternative Hypotheses 3. State the criteria for rejecting Null 4. Do the calculations 5. Make the decision: Reject Null or Not 6. Draw Conclusions and write the results up in an APA-style format (Steps 1, 2, & 3 constitute “Setting up the Hypothesis Test”) STEP 1: Selecting the Appropriate Statistical Test - Differences One IV – two groups only Nominal scale data = chi square Ordinal scale data - Independent groups = Mann-Whitney U test - Repeated measures = Wilcoxon’s T or the sign test Interval or ratio scale data - Independent groups = t-test for independent samples - Repeated measures = Correlated t-test Selecting the Appropriate Statistical Test – Differences (con’t) One IV – three groups or more Nominal scale data = chi square Ordinal scale data - Independent groups = Kruskal Wallace H test - Repeated measures = Friedman T test Interval or ratio scale data - One-way analysis of variance for independent - groups or repeated measures 6 Selecting the Appropriate Statistical Test – Differences (con’t) Two or more IV’s Nominal scale data = chi square Ordinal scale data = no appropriate test is available Interval or ratio data = two-way analysis of variance Selecting the Appropriate Statistical Test - RELATIONSHIPS Correlation Degree of relationship = Pearson’s r Correlation Prediction = Regression Example: The t and F Tests Distribution for n = 20 Mean = 0 Standard deviation =1 g r o u p d i f f e r e n c e w i t h - i n g r o u p v a r i a b i l i t y Degrees of freedom = the number of scores free to vary once the means are known 7 Example: The t and F Tests (con’t) F test Analysis of variance (F test) is an extension of the t- test - t – test and F test identical when there is one IV with two levels - F statistic is a ratio of two types of variance - Systematic variance (between groups) - Error variance (within groups) Example: Correlation Coefficients Correlation coefficient – a statistic that describes how strongly variables are related to one another Pearson Product-Moment correlation coefficient Interval or ratio scale data r Values range from 0.00 to +1.00 and 0.00 to – 1.00 STEP 2 (Hypothesis Testing) Null hypothesis H0 = no effect, or no relationship present, or the population means are equal Research or Alternative hypothesis H1 or Ha = effect occurred, or relationship present, or the population means are not equal H0: r = 0 H1: r ≠ 0 10 STEP 6 (Hypothesis Testing) Draw conclusions and write those in APA- style Example: A Pearson’s r correlation between the self- esteem rating and the person’s intelligence quotient or I.Q. was calculated. There was a significant, positive correlation between self- esteem and I.Q., r(28) = .42, p = .02. The higher a person’s I.Q. score, the higher the level of self-esteem. Very Important Because inferential statistics are based on probability, and depend upon good sampling, and good control while conducting the research, etc.: Your decision may be correct or it may be wrong Outcomes of Decision Making Type II Error p = β Correct Decision p = 1 - α Do not reject Null Correct Decision p = 1 - β = power Type I Error p = α Reject Null Null is FalseNull is TrueTrue state of affairs Your decision ↓ 11 Psychologists generally consider the Type I error more serious (you assume that there is an effect in the population when in fact there is not) How do you decrease the risk of a Type I error? We’ll get into this a bit later when we talk about Statistical Power In a nutshell: Increase the number of subjects Increase the effect size Interpreting Nonsignificant Results Research is designed to show that a relationship between variables does exist Results of a single study may be nonsignificant when a relationship does exist Type II error 1. Procedures used 2. Sample size 3. Small effect size APA-style When you write up the results in an APA-style paper you must include the following information for each analysis conducted: Describe the data analyzed Describe the statistical test used State whether or not the results were significant Report the STAT statement (r(28) = .42, p = .02) Report the descriptive statistics Provide a conclusion 12 An example taken from a 1991 article in Newsweek by Crowley The amount of solar radiation (sunshine) was correlated with the incidence of deaths from breast cancer using Pearson’s r. There was a significant, negative correlation between solar radiation and the rate of breast cancer, r(253) = -.76, p < .05. As the amount of solar radiation increased, the incidence of deaths from breast cancer decreased, which may be due to a higher level of vitamin D.