Unformatted text preview: 4/15/11 Announcements Exam Monday Scanton will be PROVIDED ZTable will be PROVIDED Can have two pages (8.5x11) of notes, both sides, typed or hand wriOen ANY calculator is fine As long as it can not communicate with anyone else (e.g. a cell phone or laptop calculator is not okay) Be on Ume/early! Exam passed out at 11:00 Announcements Homework 3 Grading All computaUon quesUons; grading is instant. view your submission a/er you have clicked "Finish" to see correct answers and grade Book quesUons are useful pracUce. Odd numbered quesUons in book have answers in Appendix C 1 4/15/11 Last Ume FR BE OM FO RE Probability of Event A Number of A outcomes p(A) = Number of possible outcomes Probability The Normal DistribuUon p(A) = Area of A outcomes Total Area of DistribuUon 0 p(A) 1 F M RO BE FO RE F BE M RO FO RE p(Card > 5) 2 4/15/11 FR OM FO BE RE FR BE OM FO RE 36 52 F M RO BE FO RE Random SelecUon F BE M RO FO RE Each individual in the populaUon has an equal chance of being selected p(X > 60) 3 4/15/11 FR OM FO BE RE FR BE OM FO RE F M RO BE FO RE F BE M RO FO RE 5 + 11 + 7 + 2 35 25 35 4 4/15/11 FR OM FO BE RE ~ 0.71 F M RO BE FO RE F BE M RO FO RE p(X > 110)? 5 4/15/11 FR OM FO BE RE FR BE OM FO RE p(X > 110)? p(X > 110)? F M RO BE FO RE F BE M RO FO RE 1+1+0+2+1+3+8+21+42+62+96+157+239+385+546+78 6+1013+1523+1979+2370+3015+3575+4557+4909 100,000 25,291 100,000 6 4/15/11 FR OM FO BE RE FR BE OM FO RE p(X > 110)? = 100 = 15 62.5 70 77.5 85 92.5 =100 107.5 115 122.5 130 137.5 p(X > 110) = .253 F M RO BE FO RE p(X > 110)? = 100 = 15 F BE M RO FO RE p(X > 110)? p(z > ?)? = 100 = 15 62.5 70 77.5 85 92.5 =100 107.5 115 122.5 130 137.5 62.5 2.5 70 2 77.5 1.5 85 1 92.5 =100 .5 0 107.5 .5 115 1 122.5 1.5 130 2 137.5 2.5 7 4/15/11 FR OM FO BE RE p(X > 110)? p(z > .667)? = 100 = 15 FR BE OM FO RE 62.5 2.5 70 2 77.5 1.5 85 1 92.5 =100 .5 0 107.5 .5 115 1 122.5 1.5 130 2 137.5 2.5 F M RO BE FO RE p(X > 110)? p(z > .667)? 25.3% 62.5 2.5 70 2 77.5 1.5 85 1 92.5 =100 .5 0 .5 1 1.5 107.5 115 122.5 = 100 = 15 F BE M RO FO RE = 0 = 1 130 2 137.5 2.5 2.5 2 1.5 1 .5 .5 1 1.5 2 2.5 p(z > .667) = .253 (aka Unit Normal DistribuUon) The Z DistribuUon 8 4/15/11 FR OM FO BE RE = 0 = 1 FR BE OM FO RE Unit Normal Table 34% 14% 1.5 1 .5 34% 14% .5 1 1.5 2.5 2% 2 2 2% 2.5 (aka Unit Normal DistribuUon) The Z DistribuUon Area Under The Curve F M RO BE FO RE F BE M RO FO RE 9 4/15/11 FR OM FO BE RE FR BE OM FO RE Finding Area Under the Normal Curve Sketch distribuUon Shade in area to be found Restate problem in terms of z Use proporUons from Unit Normal Table to find area in shaded region 1. 2. 3. 4. F M RO BE FO RE Finding Scores from Area F BE M RO FO RE 1. Sketch distribuUon 2. Shade in area to be found 3. Use proporUons from Unit Normal Table to find z  boundaries 4. Restate problem in terms of X ProporUons are correct only for normally distributed data! 10 4/15/11 Quiz 1 TOM Quiz 1 FR OM FO BE RE = 10.5 = 3 FR BE OM FO RE = 10.5 = 3 TOM 2.5 2.5 1.5 1 .5 0 .5 1 1.5 Quiz 2 TOM Quiz 2 = 13.5 = 1.5 = 13.5 = 1.5 TOM 5 4 3 2 1 0 1 Quiz 1 F M RO BE FO RE = 10.5 = 3 F BE M RO FO RE TOM 2.5 1.5 1 .5 0 .5 1 1.5 ProporUons are correct only for normally distributed data! Quiz 2 = 13.5 = 1.5 TOM 5 4 3 2 1 0 1 11 4/15/11 FR OM FO BE RE Most physical characterisUcs of plants and animals Height and Weight of people Performance of stock Errors in measurement Most physical characterisUcs of plants and animals Height and Weight of people Performance of stock Errors in measurement F M RO BE FO RE Sampling Error The discrepancy (or amount of error) that exists between a sample staUsUc and the corresponding populaUon parameter F BE M RO FO RE PopulaUon All UCSD Students No Caffeine Group Group 2 StaIsIcs N = 50 82, 77 79, Average test score: 79 64, 81, 92, 74, 88, 91, 81, 79, 70... Caffeine Group N = 50 86, 76, 89, 91, 78, 89, 67, 54, 67, 88, 75, 90... Group 1 StaIsIcs Average test score: 75 12 4/15/11 FR OM FO BE RE PopulaUon All UCSD Students Two Possible Explana0ons: 1. There is no effect of caffeine on test scores and the 4point difference is due to sampling error 2. There is a real effect of caffeine on test performance No Caffeine Group Group 2 StaIsIcs N = 50 82, 77 79, Average test score: 79 64, 81, 92, 74, 88, 91, 81, 79, 70... Caffeine Group N = 50 86, 76, 89, 91, 78, 89, 67, 54, 67, 88, 75, 90... Sampling Error Group 1 StaIsIcs Average test score: 75 Single Sample Experiment PopulaUon 0, 0 5 4 3 2 1 1 2 3 4 5 Sampling Error n Treatment Sample X 13 4/15/11 Two Independent Samples PopulaUon n1 Random Assignment Treatment 1 Single Sample, Repeated Measures PopulaUon Sample 1 n2 X1 2 s1 X2 2 s2 n Treatment 1 Measure Treatment 2 Measure Treatment 2 Sample Sample 2 Measurement Philosophy of Science Research Methods in Psychology Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon 14 4/15/11 Measurement OperaUonal DefiniUon A procedure for measuring an external behavior so that those measurements may be used to infer about the status of the underlying construct The process of assigning numbers or labels to physical phenomena according to a rule Discrete vs. ConUnuous Measurement Types Discrete vs. ConInuous Discrete variables consists of separate categories where no values exist between neighboring categories (e.g. gender, number of children, wholenumber age in years) ConUnuous variables have a (theoreUcally) infinite number of values falling between any two observed values (e.g. actual age in years, distance, Ume) 15 4/15/11 Check Your Understanding Which of the following is an example of a conUnuous variable? Check Your Understanding Which of the following is an example of a conUnuous variable? A B C D the gender of each student in a psychology class the number of males in each class offered by the college the amount of Ume to solve a problem number of children in a family A B C D the gender of each student in a psychology class the number of males in each class offered by the college the amount of Ume to solve a problem number of children in a family Nominal Ordinal Interval/RaUo Measurement Scales a nominal scale consists of a set of categories that have different names. an ordinal scale consists of a set of categories that are organized in an ordered sequence e.g. gender, poliIcal ideology e.g. finishing place in race, Clothing sizes (S,M,L,XL) Olympic medals interval and raIo scales consists of a series of ordered categories where the categories form intervals of the same size. RaIo scales have a meaningful zero point e.g. distance, weight, temperature* 16 4/15/11 Check Your Understanding Using leOer grades (A, B, C, D, and F) to classify student performance on an exam is an example of what scale of measurement? Check Your Understanding Using leOer grades (A, B, C, D, and F) to classify student performance on an exam is an example of what scale of measurement? A B C D Nominal Ordinal Interval RaUo A B C D Nominal Ordinal Interval RaUo Measurement Philosophy of Science Research Methods in Psychology Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon 17 4/15/11 Measurement Philosophy of Science Psychological theories can be refuted by observaUon Psychological science is methodologically empirical Visual Displays of Data Measures of Central Tendency Research Methods in Psychology Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Empirical Research Methodologies Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability CorrelaUonal Method Experimental Method Describing the LocaUon of Scores Probability The Normal DistribuUon 18 4/15/11 CorrelaUonal Method Causality and the CorrelaUonal Method "Cum hoc ergo propter hoc" "CorrelaUon does not imply causaUon" Two or more variables are observed to determine if there is a relaIonship between them CharacterisUcs of a True Experiment ManipulaUon: the experimenter has manipulated some independent variable to see the effect it has on the dependent variable Control: extraneous variables are held constant across the levels of the independent variable Random Assignment: chance alone dictates what treatment each individual receives Check Your Understanding True or false: The use of random assignment in an experiment assures us that there are no differences between groups before the start of an experiment A B True False 19 4/15/11 Check Your Understanding True or false: The use of random assignment in an experiment ensures that there are no differences between groups before the start of an experiment Random Assignment The process of assigning treatments (levels of the IV) to subjects so that only chance is responsible for which treatment each subject receives Ensures that there are no systemaIc differences across groups before treatment (groups will only differ due to chance) A B True False Measurement Philosophy of Science Research Methods in Psychology Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon 20 4/15/11 Frequency DistribuUon Table Bar Chart Line Chart Frequency DistribuUons Types of Frequency Frequency DistribuUons DistribuUons Frequency DistribuUon Graph Grouped Frequency DistribuUon Table Grouped Frequency DistribuUon Graph ScaOer plots Frequency DistribuUon Table Cups of Coffee Consumed Each Day N = 10 Individuals Types of Frequency Frequency DistribuUons DistribuUons Frequency DistribuUon Graph Grouped Frequency DistribuUon Table Grouped Frequency DistribuUon Graph 2, 4, 3, 4, 2, 3, 1, 0, 2, 1 21 4/15/11 Frequency DistribuUon Graph 4 3 Popula0on of ci0es in thousands N = 100 ci0es f 2 1 0 0 1 2 3 4 220, 430, 301, 40, 290, 3000, 1230, 647, 356, 910, 22, 37, 483, 273, 84, 912, 378, 374, 12, 0.4, 2, 121, 54, 72, 145, 8, 376, 5, 981, 43, 777, 35, 427, 35, 467, 19, 23, 456, 37, 45, 366, 298... Cups of Coffee Grouped Frequency DistribuUon Graph 45 40 35 30 25 20 15 10 5 0 0  3 40 99 0 80 799 0 12 119 00 9  16 159 00 9  20 199 00 9  24 239 00 9  28 279 00 9  32 319 00 9  36 359 00 9  40 399 00 9 4 39 9 Describing the Shape of DistribuUons Symmetry Symmetric Asymmetric f Skew PosiUve Skew (skewed to the right) NegaUve Skew (skewed to the lex) PopulaUon of City (thousands) 22 4/15/11 Measurement Philosophy of Science Research Methods in Psychology Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon When to Use Each Measure Mean 1. When data are interval/raUo scale 2. Use unless there is a substanUal reason not to PopulaUon Sample Median 1. When Data are ordinal 2. When interval/ raUo data is highly skewed or there are extreme scores (outliers) Mode 1. When data are nominal. 2. When most common score is the most meaningful way to describe the data "mew" M
"M" X
"X bar" 23 4/15/11 PopulaUon Sample Check Your Understanding A teacher gave a reading test to a class of 5thgrade students and computed the mean, median, and mode for the test scores. Which of the following statements cannot be an accurate descripUon of the scores? !Xi = N !Xi X= n A B C The majority of the students had scores above the mean. The majority of the students had scores above the median. The majority of the students had scores above the mode. Check Your Understanding A teacher gave a reading test to a class of 5thgrade students and computed the mean, median, and mode for the test scores. Which of the following statements cannot be an accurate descripUon of the scores? Measurement Philosophy of Science Research Methods in Psychology A B C The majority of the students had scores above the mean. The majority of the students had scores above the median. The majority of the students had scores above the mode. Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon 24 4/15/11 Measurement Philosophy of Science Research Methods in Psychology PopulaUon Sample Visual Displays of Data Measures of Central Tendency Measures of Variability !
"sigma" s
"s" Describing the LocaUon of Scores Probability The Normal DistribuUon CalculaUng the Standard DeviaUon PopulaIon SS = !(Xi " )2 Parameters and StaUsUcs != SS N PopulaUon Sample Sample SS = !(Xi " X)
2 SS s= n !1 ? ? A ESTIM TION X s STATISTICS (ESTIMATES) PARAMETERS 25 4/15/11 POPULATION N = 20,000 ProperUes of EsUmators Consistency: "Does it get beOer with more data?" (RelaUve) Efficiency: "Does it err less than other esUmators?" Sufficiency: "Does it use all the data?" Bias: "Does it over or underesUmate the true value on average?" = 100 = 15 Standard deviaUons for 10 samples calculated using PopulaUon Formula (formula for ) Sample 01: = 13.43 Sample 02: = 11.86 Sample 03: = 11.87 Sample 04: = 13.12 Sample 05: = 13.96 Sample 06: = 11.97 Sample 07: = 13.05 Sample 08: = 9.65 Sample 09: = 15.25 Sample 10: = 12.34 Standard deviaUons for 10 samples calculated using corrected Formula (formula for s) Sample 01: s = 16.12 Sample 02: s = 14.23 Sample 03: s = 14.24 Sample 04: s = 15.75 Average s Sample 05: s = 16.75 = 151.83 / 10 Sample 06: s = 14.39 Sample 07: s = 15.66 = 15.18 Sample 08: s = 11.58 Sample 09: s = 18.30 Sample 10: s = 14.81 Average = 126.5 / 10 = 12.65 CalculaUng the Standard DeviaUon PopulaIon SS = !(Xi " )2 Check Your Understanding For a populaUon of N = 10 scores, you first measure the distance between each score and the mean, then square each distance and find the sum of the squared distances. What value have you calculated? != SS N Sample SS = !(Xi " X)2 A SS The populaUon variance The populaUon standard deviaUon s= SS n !1 B C 26 4/15/11 Check Your Understanding For a populaUon of N = 10 scores, you first measure the distance between each score and the mean, then square each distance and find the sum of the squared distances. What value have you calculated? Measurement Philosophy of Science Research Methods in Psychology A B C SS The populaUon variance The populaUon standard deviaUon Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon ZScore Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability The number of standard deviaUons a parUcular score deviates from its corresponding mean Describing the LocaUon of Scores Probability The Normal DistribuUon 27 4/15/11 ConverUng between Raw and Zscores Raw score to ZScore Check Your Understanding Which of the following zscore values represents the locaUon closest to the mean? X ! zi = i "
ZScore to Raw Score A B C D z = +0.50 z = +1.00 z = 1.00 z = 2.00 X i = + zi! Check Your Understanding Which of the following zscore values represents the locaUon closest to the mean? Check Your Understanding True or false: One reason for transforming X values into zscores is that the set of zscores will form a normal distribuUon. A B C D z = +0.50 z = +1.00 z = 1.00 z = 2.00 A B True False 28 4/15/11 Check Your Understanding Measurement Philosophy of Science True or false: One reason for transforming X values into zscores is that the set of zscores will form a normal distribuUon.
Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability A B True False Describing the LocaUon of Scores Probability The Normal DistribuUon Probability of Event A Measurement Philosophy of Science Research Methods in Psychology Number of A outcomes p(A) = Number of possible outcomes Visual Displays of Data Measures of Central Tendency Measures of Variability p(A) = Area of A outcomes Total Area of DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon 0 p(A) 1 29 4/15/11 Measurement Philosophy of Science Research Methods in Psychology Measurement Philosophy of Science Research Methods in Psychology Visual Displays of Data Measures of Central Tendency Measures of Variability Visual Displays of Data Measures of Central Tendency Measures of Variability Describing the LocaUon of Scores Probability The Normal DistribuUon Describing the LocaUon of Scores Probability The Normal DistribuUon = 0 = 1 Unit Normal Table 34% 14% 1.5 1 .5 34% 14% .5 1 1.5 2.5 2% 2 2 2% 2.5 (aka Unit Normal DistribuUon) The Z DistribuUon Area Under The Curve 30 4/15/11 Check Your Understanding Check Your Understanding What proporUon of a normal distribuUon is located between the mean and z = 0.67? A B C 0.7486 0.2514 0.2486 What proporUon of a normal distribuUon is located between the mean and z = 0.67? A B C 0.7486 0.2514 0.2486 Check Your Understanding Check Your Understanding What proporUon of a normal distribuUon is less than 0.65 standard deviaUons from the mean? A B C 0.2422 0.4844 0.2578 What proporUon of a normal distribuUon is less than 0.65 standard deviaUons from the mean? A B C 0.2422 0.4844 0.2578 31 4/15/11 2.5 2 1.5 1 .5 .5 1 1.5 2 2.5 2.5 2 1.5 1 .5 .5 1 1.5 2 2.5 0.4844 0.2422 0.2422 0.2422 0.2422 2.5 2 1.5 1 .5 .5 1 1.5 2 2.5 2.5 2 1.5 1 .5 .5 1 1.5 2 2.5 32 4/15/11 For Next Time Rewiew: Chapters 16 Do Homework 3, review answers once submiOed Review Homework 2 SoluUons Prepare for Midterm 1 Have a calculator Have notes for midterm (Two 8.5"x11" pages, both sides, any content desired) Exam covers Chapters 1 6 , Study Guide on WebCT 33 ...
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 Standard Deviation, Probability theory, distribuuon

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