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Statistical Analysis of Data ______________ statistics – summarize data Proportion of Responses 0.4 Histogram – (Frequency distribution) Used for continuous measures 0.3 0.2 0.1 0.0 <.51 .51-.55 .56-.60 .61-.65 .66-.70 .71-.75 >.75 Inter-response time Lect 10b 1 Bar Graph: Used for ______________ measures Mean Number Correct 80 60 40 20 0 A B C Condition Lect 10b 2 Descriptive statistics Central tendency- _____ score ______, ______, _____ 2, 2, 3, 5, 5, 7, 8 Mean = _____ Median = ____ Mode = _____ 2, 3, 3, 4, 6, 7 Mean = _____ Median = _____ Mode = ____ Lect 10b 3 Descriptive statistics Central tendency- typical score mean, median, mode 2, 2, 3, 5, 5, 7, 8 Mean = 4.57 Median = 5 Mode = 2, 5 2, 3, 3, 4, 6, 7 Mean = 4.33 Median = 3.5 Mode = 3 Lect 10b 4 Measure of variability – how spread out are the scores 1. Range – difference between ________ and _______ score 1, 2, 9, 6, 9 Range? 2. ______________________ - square root of the variance (average squared deviation from the mean). Lect 10b 5 1 Standard deviation = 68% scores 2 Standard deviations = 95% scores 3 Standard deviations = 99.7% scores e.g., if the SD of scores on a test was 6.9 we can conclude that ____% of the class fell within plus or minus 6.9 points of the mean. 12 Little variability – _____ convinced of effect Group 1 Group 2 Test Outcome 10 8 6 4 2 0 0 1 2 3 2 3 Group 16 Group 1 Group 2 14 Test Outcome 12 Large amount of variability – _____ convinced of effect 10 8 6 4 2 0 0 1 Group Lect 10b Measures of central tendency presented without measures of variability can be _______________! 7 Inferential Statistics Most common method for analyzing data in studies using ______________ (Single-subject designs use _______ only) ________ used to evaluate whether or not there is a functional relationship. p<_____ = suggests a functional relation Statistical significance never _____ a hypothesis, only shows that it isn’t _____ Lect 10b 8 Inferential Statistics Imagine you are doing a study with two groups. One gets treatment and one doesn’t. There are differences across groups due to the IV (hopefully not a confound) – _______________________ Even if the IV had no effect, we would expect variability across groups due to sampling error and chance factors and variability within a group due to chance factors (_______ ___________) Lect 10b 9 Rats in maze are given food for going the right way either immediately or after a delay. Rat # Immediate Food Rat # Delayed Food 1 12 6 19 2 13 7 20 3 16 8 16 4 11 9 18 5 14 10 15 M1 = 13.2 SD = 1.9 M2= 17.6 SD=2.1 How do tell whether this difference is a difference due to the IV or error? – Inferential statistics Inferential Statistics Inferential statistics give you the probability of obtaining the difference in means you observed if there really was ___________________ The difference is judged significant if the probability is below α (_______), usually set to 0.05 10b Image from Introductory Statistics: Concepts, Models,Lect and Applications David W. Stockburger 11 Null hypothesis _______________in population means Can either be _______ or ________ Rejecting the null means you support the ________________ hypothesis P value = calculated probability of obtaining these data given the null is true. (The _______ the p value the better) Obtain a p value of .05 means that there is a ___% chance that you would have obtained the results given that there really was ___ ____________ between the two groups Lect 10b 12 Inferential Statistics Statistics for calculating significance usually compare: Test statistic = Between-group variance (M1-M2) Error variance (standard error) Rat maze example: t = -6.4/1.55 = -4.13 (significant at the α =.01 level). Reject Null: Supports the hypothesis that reinforcer delay affects choice. Lect 10b 13 Errors in Hypothesis Testing ________ error - “False alarm” There is ____ difference (Null is true) but We conclude that there _____ a difference (We reject null) _________ error – “Miss” There ____ a difference (Null is false) but We conclude that there is ____ difference (We accept null) Lect 10b 14