1.StatsIntro GE

Statistics for Psychology: An Introduction Gravetter and Wallanau (G&W) Chapter 1 You should be able to . . . Define statistics and tell the difference between descriptive and inferential statistics Tell the difference between populations and samples parameters and statistics Define data and tell the difference between qualitative and quantitative data and tell the difference between discrete and continuous data You should be able to . . . Understand key components of experiment designs variables and constants independent and dependent variables control and experimental conditions experimental and correlational studies Define the four scales of measurement and tell the difference among them: 1. nominal 2. ordinal 3. interval 4. ratio What’s a Statistic? A set of tools used to organize, describe, and analyze numerical observations Why are they important? These tools are used to describe and analyze numerical observations derived from populations and samples Lying with Statistics Inappropriate Averages (e.g., tax refunds) Small Sample sizes Biased Samples (e.g., CNN/Fox News viewer polls) Illusory Correlations Populations and Samples Population The set of all individuals of interest depressed humans Sample A subset of a population those individuals in our research study Populations and Samples We use different terms to refer to the statistics used for populations and samples Parameter A numerical description of a characteristic of a population average # of hours of sleep for entire population of depressed individuals Statistic A numerical description of a characteristic of a sample average # of hours of sleep for those in our study Parameters and Statistics The term statistics is used to refer to the whole set of tools we use to describe and analyze numerical observations A statistic refers to a specific tool applied to samples E.g., an average for a sample A parameter refers to a specific tool applied to populations E.g., an average for a population Statistic Sample Parameter Population describes describes Descriptive vs Inferential Statistics Descriptive statistics Statistical procedures used to summarize, organize, and simplify the data Examples: Arithmetic Average (statistical mean), standard deviation, Quartiles, etc Inferential statistics Techniques to study samples and make use of generalizations about the population from which they were selected T-statistic, F-Statistic, Chi-Square, correlation coefficient (r) Inferential Statistics Tools for making inferences from observations Tools for generalizing beyond the available observations Allows for inferences about populations based on samples Population Select (draw sample) Sample infer Sampling Error There may be discrepancies between the sample and the population A sample is not a perfect picture of a population The discrepancy between the sample statistic and the population parameter is sampling error For example: Average # of hours depressed people sleep For sample = 12 hrs/per night population 11.25 hrs/per night The .75 difference can be attributed to sampling error Another Example of Sampling Error Sample #1 Sample Statistics Nelly 4413 Lil’ Kim 4474 Nicki Minaj 4162 Lupe Fiasco 4439 Jay-Z 4506 Average = 4398.8 40% Female, 60% Male Sample #2 Sample Statistics Drake 3522 Missy Elliott 3874 Redman 5331 ICP 4149 Wiz Khalifa 3707 Average = 4116.6 20% Female, 80 % Male Population of 85 Hip Hop Artists Number of unique words used in their lyrics Parameters Average = 4604.5 4% Female, 96% Male Wu-Tang Clan Sample Statistics Method Man 4951 Raekwon 5001 Ghostface Killah 5774 RZA 5905 GZA 6426 Average = 5611.4 100% Male Data extracted from: http://rappers.mdaniels.com.s3-website-us-east-1.amazonaws.com/ Data Collection of numerical observations from a survey or experiment a single datum is a raw score Qualitative versus Quantitative Data Qualitative data A single observation which represents a class or category (sometimes referred to as categorical data) Marital status, religious affiliation, etc. Quantitative Data A single observation is an amount or a count Reaction time, height, performance accuracy, etc. Quantitative OR Qualitative? Political Party Amount of Coffee Body Temperature Biological Sex Finishing position in World Cup Discrete versus Continuous Data Discrete data consist of a countable number of possible values e.g., number of cars in a parking lot countable with integers Continuous data consist of an infinite number of possible values on a scale in which there are no gaps or interruptions heights: 72.5 inches, 72.55 inches, 72.575 inches . . . . weights: 160.00 pounds, 160.5 pounds . . . number of hours of sleep: 8.6 hours, 6.4 hours, 10.2 hours . . . Discrete versus Continuous Data Qualitative data are always discrete there’s no gray area with categories But, Quantitative data are not always continuous: number of cars in parking lot is discrete and quantitative Experimental Design and Other Considerations Experimental Design Variable A characteristic or property of organisms, events, or objects that can take on different values height, weight, IQ, mood, degree of anxiety, personality type, etc. Can be identified by letters such as X, Y, or Z Experimental Design Constant A characteristic or property that does not change ? is a constant : 3.1416 . . . to convert proportions to percentages, you multiply by a constant: .5 X 100 = 50% Experimental Design Independent Variable (IV) a variable that is manipulated by the investigator Dependent Variable (DV) a variable that is measured by the investigator Experimental Design We conduct an experiment to determine if a new antidepressant drug is effective We have two groups of depressed participants Importance of Random Assignment in controlling for extraneous variables We give one group an antidepressant drug Experimental or treatment condition We give the other group a placebo Control condition (i.e., no treatment) We measure symptoms of depression over the course of a month for both groups Why Random Assignment? Random Assignment SAMPLE Control Group Experimental Group Test for Differences Control Group Experimental Group Why Random Assignment? Confounding Variables SAMPLE Are differences due to manipulation or confounding variable? Why Random Assignment? No Confounding Variables SAMPLE Control Group Experimental Group Differences are due to manipulation, not an extraneous variable, because mood is randomly determined. Independent and Dependent Variables: Example What is the independent variable? Drug: antidepressant vs. placebo What is the dependent variable? symptoms of depression Importance of Operational Definitions A highly specific definition of a construct of interest Different Example : Want to know alcohol consumption affects memorization of word lists. Experimental Design overview Other Relevant Study Designs Independent Measures Sometimes known as Between-Subjects {5C22544A-7EE6-4342-B048-85BDC9FD1C3A}Cond 1 (Sub #) Cond 2 (Sub #) Cond 3 (Sub #) Cond 4 (Sub #) 80 (1) 36 (5) 43 (10) 81 (14) 25 (2) 49 (7) 45 (11) 79 (15) 39 (3) 27 (8) 78 (12) 66 (16) 17 (4) 89 (9) 56 (13) 68 (17) {93296810-A885-4BE3-A3E7-6D5BEEA58F35}Subject # Cond 1 Cond 2 Cond 3 Cond 4 1 77 87 88 67 2 55 56 45 56 3 32 12 46 65 4 44 65 76 40 Repeated Measures Sometimes known as Within-Subjects NOTE: These are all different participants NOTE: These are the same participants Other Relevant Study Designs Quasi-Experimental (“non-experimental”) Cases where researcher has no control of group assignment Used when you cannot manipulate IV yourself Example, when comparing pre-existing , categorical groups Gender, trauma/abuse, relationship status, etc. Inability to rigorously control for extraneous variables Example: Pre- and Post-Test studies Changes observed in DV may be a product of the passage of time. Non-Equivalent Groups Inability to control assignment to group due to previously established membership Other Relevant Study Designs Correlational study Investigator measures two DVs and looks for a relationship Is there a relationship between vocabulary size and age? Key limitation: CORRELATION DOES NOT DETERMINE CAUSATION Concept Check Correct Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list. What kind of research design is this? Concept Check Correct Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list.. In this experiment, exposure to Red Bull is the _____. Concept Check Correct Alphonso wants to test the prediction that drinking “red bull” enhances memory. He has one group of students drink a can of “red bull” while reading a list of words. Another group reads the same list without drinking the energy drink. Afterwards, all participants complete a memory test for the list.. In this experiment, the memory test is the _____. Scales of Measurement The answers to the following three questions appear to be the same: What number did you wear in the drinking contest? 10 What place did you finish? 10 How many minutes did it take you to finish? 10 Are these answers equivalent? No, because each answer of piece of data represents a different scale of measurement Scales of Measurement are . . . The methods of assigning numbers to objects or events There are four scales of measurement: Nominal Ordinal Interval Ratio Nominal Measurement Scale Refers to data that consist of names, labels, or categories “nominal” from Latin for “name” Numeric associations with labels are arbitrary and are used only to identify an object or event Data cannot be meaningfully arranged in order NAME Nominal Measurement Scale There is nothing in particular that requires use of numbers -- any label would suffice Examples Clothing brands/designs: Supreme, Obey . . . Rat strains: Long-Evans, Sprague-Dawley The number you wore in the drinking contest 10 Ordinal Measurement Scale Refers to data or scores that can be arranged in some order Numbers are used to identify an object or event (nominal) and to tell us the rank order of each object or event ORDER Ordinal Measurement Scale Examples Ranks in high school graduating class: 1st, 20th, 100th . . . Tests of elementary students: Below average, average, above average, gifted Place of finish in drinking contest: 10 10th Interval Measurement Scale Refers to data that have meaningful differences between scores Numbers are used to identify an object or event (nominal) and to tell us the rank order of each object or event (ordinal) NAME + ORDER + INTERVALS Two defining principles: 1.) Equidistant scale 2.) no true zero (AKA absolute zero) Interval Measurement Scale Equidistant Scales Those values whose intervals are distributed in equal units The differences or distances (intervals) between the scores are meaningful, unlike nominal or ordinal data If someone concluded: “Satsifaction ratings were three-times greater among man than women” wouldn’t be appropriate Interval Measurement Scale However, a zero point may be lacking or it may be arbitrary 0? 0 1 2 -2 -1 Average Very Good Poor Interval Measurement Scale Celsius and Fahrenheit temperature scales are both interval scales Zero degrees in both is determined “arbitrarily” That is, zero does not mean the absence of heat Another example: Personality Interval Measurement Scale: Example A difference can be determined between 25 and 50 degrees Fahrenheit . . . but 50 degrees is not twice as hot as 25 What about the Kelvin scale? There is an absolute zero 0 degrees K is the temperature at which movement ceases Ratio Measurement Scale Refers to data on a scale with a true zero point Has all properties of nominal, ordinal, and interval scale Is an interval scale with a true zero True zero point: Complete absence of data being measured 0! Ratio Measurement Scale NAME + ORDER + INTERVALS + TRUE ZERO Ratio Measurement Scale Examples Height Weight The time it takes to finish the drinking contest Blood Alcohol Concentration (BAC) Concept Check Correct Name the Measurement scale for … Military Title: Lieutenant, Captain, Major Concept Check Name the Measurement scale for … Number of Errors committed on Exam Correct Because you can have zero errors and zero is meaningful Concept Check Name the Measurement scale for … Class Rank (Freshman, Sophomore, Junior, Senior, Super-Senior) Correct Because it indicates order/direction (high versus low) Concept Check Name the Measurement scale for … Time as measured using a 12 hour clock Correct Moves along a continuous measure (milliseconds, seconds, minutes, hours, etc) without a zero point in time and with equal intervals Concept Check Name the Measurement scale for … Social Security Number Correct Because it represents who you are, the number themselves are arbitrary Note on Statistical Notation summation sign (? “sigma”) Summation Sign (? “sigma”) ? read as “the sum of” ?X means to add all the scores for variable X Summation Sign (? “sigma”) ?X2 means first square each value of X, then add all of those squared values ?(X+1) means first add 1 to each value of X, then add all of those new values Summation Sign (? “sigma”) ?(X+1)2 means (1) add 1 to each value of X, (2) square each of those new values, (3) add all of those squared values In G&W textbook, see section 1.5 (p. 25) for more on statistical notation and order of operations. Example (Ch.1, Problem 19) Find... X 4 a. ?X 6 0 3 2 = 15 Example (Ch.1, Problem 19) Find... X 4 a. ?X = 15 6 0 b. ?(X2) 3 2 Example (Ch.1, Problem 19) X Find... 4 => 16 a. ?X = 15 6 => 36 0 => 0 b. ?(X2) 3 => 9 2 => 4 Example (Ch.1, Problem 19) X Find... 4 => 16 a. ?X = 15 6 => 36 0 => 0 b. ?(X2) = 65 3 => 9 2 => 4 Example (Ch.1, Problem 19) X Find... 4 a. ?X = 15 6 0 b. ?(X2) = 65 3 2 c. ?(X+1) Example (Ch.1, Problem 19) X Find... 4 => 5 a. ?X = 15 6 => 7 0 => 1 b. ?X2 = 65 3 => 4 2 => 3 c. ?(X+1) Example (Ch.1, Problem 19) X Find... 4 => 5 a. ?X = 15 6 => 7 0 => 1 b. ?X2 = 65 3 => 4 2 => 3 c. ?(X+1) = 20 Example (Ch.1, Problem 19) X Find... 4 a. ?X = 15 6 0 b. ?X2 = 65 3 2 c. ?(X+1) = 20 d. ?(X+1)2 Example (Ch.1, Problem 19) X Find... 4 => 5 a. ?X = 15 6 => 7 0 => 1 b. ?X2 = 65 3 => 4 2 => 3 c. ?(X+1) = 20 d. ?(X+1)2 Example (Ch.1, Problem 19) X Find... 4 => 5 => 25 a. ?X = 15 6 => 7 => 49 0 => 1 => 1 b. ?X2 = 65 3 => 4 => 16 2 => 3 => 9 c. ?(X+1) = 20 d. ?(X+1)2 Example (Ch.1, Problem 19) X Find... 4 => 5 => 25 a. ?X = 15 6 => 7 => 49 0 => 1 => 1 b. ?X2 = 65 3 => 4 => 16 2 => 3 => 9 c. ?(X+1) = 20 d. ?(X+1)2 = 100 More examples… Variable x = [1 2 3 4] ?x = _________ (?x) + 10 = _______ ?(x + 10) = _________ (?x) 2 = _______ ?(x 2) = _________