Hypothesis Testing & Data Analysis. Statistics. Descriptive Statistics. What is the difference between descriptive and inferential statistics?

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1 2 Hypothesis Testing & Data Analysis 5 What is the difference between descriptive and inferential statistics? Statistics 8 Tools to help us understand our data. Makes a complicated mess simple to understand. Descriptive Statistics: Sums up the data. Describe basic characteristics of the data. Inferential Statistics: Use to infer relationships or to make predictions. 9 Descriptive Statistics

2 10 Describe our data Central tendency Mean, median, mode Spread/Variability Range, variance, standard deviation Shape Skewness 11 Inferential Statistics Hypothesis testing 12 The process of determining an answer to a question through probability estimation. Let s say you think that science majors are smarter than English majors. How would you test this hypothesis? John is a science major with an IQ score of 115. Jack is an English major with an IQ score of 105. Science majors are smarter than English majors. What about means? 13 Suppose we give IQ tests to 5 Science majors and 5 English majors and obtain the following IQ scores: Science majors: 110, 105, 98, 120, 115 English majors: 100, 95, 101, 113, 99 The mean is higher for science majors (109.6) than for English majors (101.6) Science majors are smarter than English majors.

3 Why means are not enough 14 How would we decide if a difference is real? 109 vs vs vs Real differences cannot be proven with certainty. Impossible to sample every Science and English major. Statistical tests can tell us how probable it is that the difference is real. Null Hypothesis Testing 15 How does science prove something? Prove that the opposite is false -- the foundation of null hypothesis testing. The null hypothesis (Ho) suggests that there is no difference between 2 or more conditions -- the IV has no effect on the DV. Reject the null to support your alternative hypothesis (H1). Formulating your hypothesis 16 Question: Are science majors smarter than English majors? What is the Ho & H1? Ho: Science majors and English majors have the same level of intelligence. H1: Science majors and English majors have different levels of intelligence. The all-important p-value 17 Are science majors smarter than English majors? Science majors: 110, 105, 98, 120, 115 English majors: 100, 95, 101, 113, 99 MScience = , SD = 8.56 MEnglish = 101.6,0 SD = 6.77 t(8) = 1.64, p =.14 What does this p-value mean?

4 18 What does p =.14 mean? 1. If H 1 is true, the chance of obtaining these data is 14%. 2. If H 0 is true, the chance of obtaining these data is 14%. 3. If the same study is conducted again with a different sample of the same size, the likelihood of replication is 14%. 4. Based on these data, there is an 86% chance that the H1 is true. 5. Based on these data, there is an 86% chance that the H0 is true. 6. There is a 14% probability that the data you obtained are due to chance What does it mean when you perform a statistical analysis and your p-value is.03? 27 Given these data, the probability that the null is true is 3%. Given that the null is true, the probability of obtaining these data is 3%.

5 How to reject the null? 28 Ho: µscience = µenglish H1: µscience µenglish Null hypothesis testing tells you the probability that you will obtain the pattern of results in your sample if the null is true. If this likelihood is very small, then we abandon the assumption that the null is true -- reject null. A significant result 29 A result is significant if its likelihood of occurrence is less than α when we assume Ho is true. What is α? The probability that you deem acceptable to make an error while rejecting the null. The conventional value of α is.05. Statistical Decision Making 30 Ho is true Ho is false Reject Ho Type I Error Correct Fail to Reject Ho Correct Type II Error Steps for hypothesis testing 36 Identify the IV and DV Identify the scales for IV and DV Categorical Continuous State the H0 and H1 Choose the appropriate test

6 What type of statistical test? 37 chi-square test of proportions t-test ANOVA Correlation Regression Chi-square 38 Compare proportions data from two or more groups E.g., are people more likely to agree to partake in a survey on a sunny day than on a cloudy day? Collect data from 40 individuals, 20 on a sunny day and 20 on a cloudy day. Count proportions willing to do the survey. Compare actual with expected proportions Sample data: Data for Chi Sq.sav Instructional video: SPSS - chi sq test of proportions t-test 39 Compare two means or compare 1 mean with a number. Suitable for comparing continuous DV with categorical IV. 1. One sample t-test 2. Independent samples t-test 3. Paired samples t-test One sample t-test 40 Compare one mean with a number. E.g., collected IQ score data from 10 individuals. Does my sample have IQ score higher or lower than 100? Sample data: Data for Chi Sq.sav Instructional video: SPSS - One sample t-test

7 Independent samples t-test 41 Compare means from 2 different groups. Compare IQ scores between Americans and Canadians. Sample data: Data with IQ Scores Science & English majors.sav Instructional video: SPSS - Independent Samples t-test Paired Samples t-test 42 Compare 2 means from the same group or from 2 matched groups. E.g., Compare IQ score before and after drinking coffee. Sample data: Data with IQ Scores Science & English majors.sav Instructional video: SPSS - Paired Samples t-test Analysis of Variance (ANOVA) 43 Compare 3 or more means. Suitable for comparing continuous DV with categorical IV. E.g., compare IQ scores between Americans, Canadians, and Mexicans. Between subjects ANOVA 44 Compare means between 2 or more groups. Instructional video: SPSS - Univariate ANOVA Repeated measures ANOVA Compare 2 or more means from the same group. Instructional video: SPSS - Repeated Measures ANOVA

8 Correlation 45 Measure the strength of relation between two or more variables. Suitable for data on a continuous scale. E.g., how strong is the relationship between height and weight? Instructional video: SPSS - Correlation Multiple Regression 46 Allows one to predict a value on the DV based on the value(s) on the IV(s). Suitable for data on a continuous or categorical scale. ANOVA is a special case of regression. E.g., what are the effects of gender and GPA on SAT scores? Effect Size 48 Goes beyond statistical significance testing. A measure of the size of the difference between the distributions. Cohen s d for two means comparison. Partial eta squared for multiple-group comparison. r 2 for multiple regression. Understanding your Results 49 Main Effects Interactions How to identify each

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