Chapter 1 Introduction to Statistics PDF

Chapter 1 Introduction to Statistics Essentials of Statistics for the Behavioral Sciences Ninth Edition by Frederick J Gravetter, Larry B. Wallnau, and Lori-Ann B. Forzano  Learning Objectives Define basic statistical terms, describe the relationships between them, and identify examples of...

Chapter 1 Introduction to Statistics Essentials of Statistics for the Behavioral Sciences Ninth Edition by Frederick J Gravetter, Larry B. Wallnau, and Lori-Ann B. Forzano  Learning Objectives Define basic statistical terms, describe the relationships between them, and identify examples of each Define two general categories of statistics, descriptive and inferential, and how they are used in a typical research study Describe the concept of sampling error and explain how sampling error creates the fundamental problem that inferential statistics must address Describe, compare and contrast descriptive, correlational, and experimental, and nonexperimental research, and identify the data structures associated with each Define independent, dependent, and quasi-experimental variables and recognize examples of each  Statistics allow Psychologists to: ► Organize data ► Statistics allow psychologists to present data in ways that are easier to comprehend. ► Describe data ► Descriptive statistics provide a way to summarize facts ► Make inferences based on data ► Using statistical analysis, researchers can determine the likelihood that a phenomenon is true or otherwise  Basic Statistical Terms Figure 1.1 Relationship between population and sample A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. The entire group of American adolescents is an example of a _________. a. Population b. Sample  A researcher is interested in the eating behavior of rats and selects a group of 25 rats to be tested in a research study. The group of 25 rats is an example of a ______. a. Population b. Sample A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. Based on the set of 356 surveys that were completed and returned, the researcher finds that these students spend an average of 3.1 hours each day watching television. For this study, the set of 356 students who returned surveys is an example of a _______. a. Population b. Sample Population Parameter Sample Statistic A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. The goal of the research is to determine the average number of hours each day that American adolescents spend watching television. The researcher is trying to determine a number that is an example of a _____. A. Parameter B. Statistic A researcher records the change in weight (gained or lost) during the first semester of college for each individual in a group of 25 freshmen, then calculates the average change in weight. The average weight of the 25 freshmen is an example of a _______. A. Parameter B. Statistic ► A researcher is interested in the effect of amount of sleep on high school students’ exam scores. A group of 75 high school boys agree to participate in the study. The group of 75 high school boys are…  Variables and Data ► A Variable is a Characteristic or condition that changes or has different values for different individuals ► Ex. Stress Levels, Gender, Intelligence ► Values are every possible number or category that a score can have ► Ex. 0-20 in a Stress Scale, Male or Female  Variables and Data ► A datum (singular) ► A single measurement or observation ► Commonly called a score or raw score ► Data (plural) ► Measurements or observations of a variable ► Data set ► A collection of measurements or observations  Descriptive & Inferential Statistics ► Descriptive statistics ► Inferential statistics ► Summarize data ► Study samples to make generalizations about ► Organize data the population ► Simplify data ► Interpret experimental ► Familiar examples data ► Common terminology ► Tables ► “Margin of error” ► Graphs ► “Statistically ► Averages significant”  Sampling Error ► Sample is never identical to population ► Sampling error ► The discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter ► Example: Margin of error in polls ► “This poll was taken from a sample of registered voters and has a margin of error of plus-or-minus 4 percentage points.” ► Decide if each of the following statements is True or False. Statistics in the context of research  Data Structures, Research Methods, and Statistics  One (or more) variables measured per individual Data Structure I: “Statistics” describe the observed variable Descriptive May use category and/or numerical variables research (individual variables)  One group of participants Data Measurement of two variables for each Structure II: participant Correlational Goal is to describe type and magnitude of the research relationship (individual Patterns in the data reveal relationships variables) Non-experimental method of study Correlational Method Limitations ► Can demonstrate the existence of a relationship ► Does not provide an explanation for the relationship ► Most importantly, does not demonstrate a cause-and-effect relationship between the two variables  One variable defines the groups Data Structure Scores are measured on second variable III: Comparing Both experimental and non-experimental studies use this structure two (or more) groups of scores  Data structure for studies comparing groups Independent variable Group A Group B Dependent variable Researchers conducted an experiment in which What is the participants were able independent to tolerate more pain variable? when they were shouting their favorite swear words rather What is the than when they were dependent shouting neutral words. variable? In this study,  Experimental Method ► Goal of experimental method ► To demonstrate a cause-and-effect relationship ► Manipulation ► The level of one variable is determined by the experimenter ► Control rules out influence of other variables ► Participant variables ► Environmental variables  Non-Experimental Methods ► Non-equivalent groups ► Researcher compares groups ► Researcher cannot control who goes into which group ► Pre-test / Post-test ► Individuals measured at two points in time ► Researcher cannot control influence of the passage of time ► Independent variable is quasi-independent ► Researchers observed that students’ exam scores were higher the more sleep they had the night before. This study is … ► Researchers observed that students exam scores were higher the more sleep they had the night before. This study is … ► Decide if each of the following statements is True or False.  In a correlational study, how many variables are measured for each individuals and how many groups of individuals are in the study? a. One variable, one group b. One variable, two groups c. Two variables, one group d. Two variables, two groups A recent study comparing alcohol use for college students in a. Correlational the United States and b. Experimental in Canada reports that c. Non-experimental many Canadian d. Non-correlational students drink but American students drink more Researchers asked waitresses to wear different colored tshirts on different days for a six-week period and recorded the tips left by male customers. The results show that male customers gave bigger tips to waitresses when they were wearing red. For this study, What is the dependent variable? What is the independent variable? For a research study comparing attitude scores for males and females, participant gender is an example of what kind of variable? a. An independent variable b. A dependent variable c. A quasi-independent variable d. A quasi-dependent variable  Chapter 1 Introduction to Statistics Part 2 Variables and Measurement Statistical Notations Essentials of Statistics for the Behavioral Sciences Ninth Edition by Frederick J Gravetter, Larry B. Wallnau, and Lori-Ann B. Forzano Learning Outcomes Describe discrete and continuous variables and identify examples of each Define real limits and explain why they are needed to measure continuous variables Compare and contrast the four scales of measurement (nominal, ordinal, interval and ratio) and identify examples of each Identify what is represented by the following symbols: X, Y, N, n and ∑ Perform calculations using the summation notation and other mathematical operations following the correct order of operations Variables and Measurement  Discrete and Continuous Variables ► Discrete variable ► Has separate, indivisible categories ► No values can exist between two neighboring categories ► Continuous variable ► Has an infinite number of possible values between any two observed values ► Every interval is divisible into an infinite number of fractional parts  Real Limits of Continuous Variables ► Real limits are the boundaries of each interval representing scores measured on a continuous number line ► The real limit separating two adjacent scores is exactly halfway between the two scores ► Each score has two real limits ► The upper real limit marks the top of the interval ► The lower real limit marks the bottom of the interval Real Limits of a Continuous Measurement Identify whether continuous or discrete variable How many times you went to a dentist? – Is it quarter to 7 in the evening? – How old are you? – How many boys are there in your class? – What is your religious affiliation? – ► What are the real limits of a score X= 32? ► What are the real limits of a score X= 45? Dichotomous Variable ► one that takes on one of only two possible values when observed or measured. ► Artificial Dichotomous (Passed/Failed) – derived from scores ► True Dichotomous (Male/Female, Yes/No, True/False, Heads/Tails)  SCALES OF MEASUREMENT  Levels of Measurement Nominal scale ► consists of a set of categories that have different names. ► Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations. ► also known as categorical variables ► E.g. (Gender, Nationality, Currency)  Levels of Measurement Ordinal Scale ► Numeric variable in which the values are ranks. ► also known as rank-order variable ► E.g. (Job position, Position in Race, IQ Level)  Levels of Measurement Interval ► variable that contains equal interval between numbers ► contains no absolute zero point. ► E.g. GPA  Levels of Measurement Ratio ► an interval scale with the additional feature of an absolute zero point. ► E.g. Time, Weight, Age  Scales of Measurement Scale Characteristics Examples Nominal Label and categorize Gender No quantitative distinctions Diagnosis Experimental or Control Ordinal Categorizes observations Rank in class Categories organized by size or Clothing sizes (S,M,L,XL) magnitude Olympic medals Interval Ordered categories Temperature Interval between categories IQ of equal size Golf scores (above/below par) Arbitrary or absent zero point Ratio Ordered categories Number of correct answers Equal interval between categories Time to complete task Absolute zero point Gain in height since last year Which of the following is not an example of ordinal scale? a. Job position b. Position in race c. Satisfaction scale d. Marital Status Statistical Notations  Quiz Height Weight Scores ►Scores are referred to as X (and Y) ►N is the number of scores in a population ►n is the number of scores in a sample X= 35 n=7 N= 7  Summation Notation ► Many statistical procedures involve summing (adding up) a set of scores ► summation sign “Σ” ► “the sum of” ► ΣX reads “the sum of the scores” ► 10, 6, 7, 4 ► ΣX = ? N=?  Summation Notation ► The Σ is followed by a symbol or equation that defines what is to be summed ► Order of Mathematical Operations 1. P - Any calculation contained within parentheses is done first. 2. E - Squaring (or raising to other exponents) is done second. 3. M D - Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right. 4. S - Summation using the Σ notation is done next. 5. A S - Any other addition and/or subtraction is done. “P E M D S A S”  PEMDSAS ΣX = ? ΣX2 = ? (ΣX)2 = ?  PEMDSAS ► PEMDSAS ΣXY = ?  PEMDSAS ► Use summation notation to express each of the following. a. Add 4 points to each score and then add the resulting values. Σ(X+4) b. Add the scores and then square the total. c. Square each score, then add the squared values. PEMDSAS PEMDSAS  PEMDSAS 4. 5. PEMDSAS Σ(X+1)  PEMDSAS What is the first step to be performed when computing Σ (X + 2)2 a. Square each value b. Add 2 points to each score c. Sum the squared values d. Sum the (X + 2) values  PEMDSAS ► What is the final step to be performed when computing Σ(X – 2)2? a. Square each value b. Subtract 2 points from each score c. Sum the squared values d. Subtract 22 from each X2 value