1、Chapter 1: Introduction to StatisticsPowerPoint Lecture SlidesEssentials of Statistics for the Behavioral Sciences Eighth Editionby Frederick J Gravetter and Larry B. WallnauLearning Outcomes Know key statistical terms1 Know key measurement terms2 Know key research terms3 Know the place of statistic
2、s in science4 Understand summation notation5 Statistics requires basic math skills Inadequate basic math skills puts you at risk in this course Appendix A Math Skills Assessment helps you determine if you need a skills review Appendix A Math Skills Review provides a quick refresher course on those a
3、reas. The final Math Skills Assessment identifies your basic math skills competenceMath Skills Assessment1.1 Statistics, Science and Observations “Statistics” means “statistical procedures” Uses of Statistics Organize and summarize information Determine exactly what conclusions are justified based o
4、n the results that were obtained Goals of statistical procedures Accurate and meaningful interpretation Provide standardized evaluation procedures1.2 Populations and Samples Population The set of all the individuals of interest in a particular study Vary in size; often quite large Sample A set of in
5、dividuals selected from a population Usually intended to represent the population in a research studyFigure 1.1Relationship between population and sample Variables and Data Variable Characteristic or condition that changes or has different values for different individuals Data (plural) Measurements
6、or observations of a variable Data set A collection of measurements or observations A datum (singular) A single measurement or observation Commonly called a score or raw scoreParameters and Statistics Parameter A value, usually a numerical value, that describes a population Derived from measurements
7、 of the individuals in the population Statistic A value, usually a numerical value, that describes a sample Derived from measurements of the individuals in the sampleDescriptive & Inferential Statistics Descriptive statistics Summarize data Organize data Simplify data Familiar examples Tables Graphs
8、 Averages Inferential statistics Study samples to make generalizations about the population Interpret experimental data Common terminology “Margin of error” “Statistically significant”Sampling Error Sample is never identical to population Sampling Error The discrepancy, or amount of error, that exis
9、ts 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” (Box 1.1)Figure 1.2 A demonstration of sampling error Figure 1.3Role of s
10、tatistics in experimental research Learning Check 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 boys are A statisticA A variableB A parameterC A sampleDLearning Check - Answer A r
11、esearcher 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 boys are A statisticA A variableB A parameterC A sampleDLearning Check Decide if each of the following statements is True or False. Most
12、 research studies use data from samplesT/F When sample differs from the population there is a systematic difference between groupsT/FLearning Check - Answer Samples used because it is not feasible or possible to measure all individuals in the populationTrue Sampling error due to random influences ma
13、y produce unsystematic group differencesFalse1.3 Data Structures, Research Methods, and Statistics Individual Variables A variable is observed “Statistics” describe the observed variable Category and/or numerical variables Relationships between variables Two variables observed and measured One of tw
14、o possible data structures used to determine what type of relationship existsRelationships Between Variables Data Structure I: The Correlational Method One group of participants Measurement of two variables for each participant Goal is to describe type and magnitude of the relationship Patterns in t
15、he data reveal relationships Non-experimental method of studyFigure 1.4Data structures for studies evaluating the relationship between variables Correlational Method Limitations Can demonstrate the existence of a relationship Does not provide an explanation for the relationship Most importantly, doe
16、s not demonstrate a cause-and-effect relationship between the two variablesRelationships Between Variables Data Structure II: Comparing two (or more) groups of Scores One variable defines the groups Scores are measured on second variable Both experimental and non-experimental studies use this struct
17、ureFigure 1.5 Data structure for studies comparing groupsExperimental 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 Enviro
18、nmental variablesFigure 1.6 The structure of an experimentIndependent/Dependent Variables Independent Variable is the variable manipulated by the researcher Independent because no other variable in the study influences its value Dependent Variable is the one observed to assess the effect of treatmen
19、t Dependent because its value is thought to depend on the value of the independent variableExperimental Method: Control Methods of control Random assignment of subjects Matching of subjects Holding level of some potentially influential variables constant Control condition Individuals do not receive
20、the experimental treatment. They either receive no treatment or they receive a neutral, placebo treatment Purpose: to provide a baseline for comparison with the experimental condition Experimental condition Individuals do receive the experimental treatmentNon-experimental Methods Non-equivalent Grou
21、ps 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-independentFigure 1.7Two examples of non-experimental studies Ins
22、ert NEW Figure 1.7Learning Check Researchers observed that students exam scores were higher the more sleep they had the night before. This study is DescriptiveA Experimental comparison of groupsB Non-experimental group comparison C CorrelationalDLearning Check - Answer Researchers observed that stud
23、ents exam scores were higher the more sleep they had the night before. This study is DescriptiveA Experimental comparison of groupsB Non-experimental group comparisonC CorrelationalDLearning Check Decide if each of the following statements is True or False. All research methods have an independent v
24、ariableT/F All research methods can show cause-and-effect relationshipsT/FLearning Check - Answer Correlational methods do not need an independent variableFalse Only experiments control the influence of participants and environmental variablesFalse1.4 Variables and Measurement Scores are obtained by
25、 observing and measuring variables that scientists use to help define and explain external behaviors The process of measurement consists of applying carefully defined measurement procedures for each variableConstructs & Operational Definitions Constructs Internal attributes or characteristics that c
26、annot be directly observed Useful for describing and explaining behavior Operational Definition Identifies the set of operations required to measure an external (observable) behavior Uses the resulting measurements as both a definition and a measurement of a hypothetical constructDiscrete and Contin
27、uous Variables Discrete variable Has separate, indivisible categories No values can exist between two neighboring categories Continuous variable Have an infinite number of possible values between any two observed values Every interval is divisible into an infinite number of equal partsFigure 1.8Exam
28、ple: Continuous MeasurementReal 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 rea
29、l limit marks the top of the interval The lower real limit marks the bottom of the intervalScales of Measurement Measurement assigns individuals or events to categories The categories can simply be names such as male/female or employed/unemployed They can be numerical values such as 68 inches or 175
30、 pounds The complete set of categories makes up a scale of measurement Relationships between the categories determine different types of scalesScales of MeasurementScaleCharacteristicsExamplesNominalLabel and categorize No quantitative distinctionsGenderDiagnosisExperimental or ControlOrdinalCategor
31、izes observationsCategories organized by size or magnitudeRank in classClothing sizes (S,M,L,XL)Olympic medals IntervalOrdered categoriesInterval between categories of equal sizeArbitrary or absent zero pointTemperatureIQGolf scores (above/below par)RatioOrdered categoriesEqual interval between cate
32、goriesAbsolute zero pointNumber of correct answersTime to complete taskGain in height since last yearLearning Check A study assesses the optimal size (number of other members) for study groups. The variable “Size of group” is Discrete and intervalA Continuous and ordinalB Discrete and ratioC Continu
33、ous and intervalDLearning Check - Answer A study assesses the optimal size (number of other members) for study groups. The variable “Size of group” is Discrete and intervalA Continuous and ordinalB Discrete and ratioC Continuous and intervalDLearning Check Decide if each of the following statements
34、is True or False. Variables that cannot be measured directly cannot be studied scientificallyT/F Research measurements are made using specific procedures that define constructs T/FLearning Check - Answer Constructs (internal states) can only be observed indirectly, but can be operationally measuredF
35、alse Operational definitions assure consistent measurement and provide construct definitionsTrue1.5 Statistical Notation Statistics uses operations and notation you have already learned Appendix A has a Mathematical Review Statistics also uses some specific notation Scores are referred to as X (and
36、Y) N is the number of scores in a population n is the number of scores in a sampleSummation Notation Many statistical procedures sum (add up) a set of scores The summation sign stands for summation The is followed by a symbol or equation that defines what is to be summed Summation is done after oper
37、ations in parentheses, squaring, and multiplication or division. Summation is done before other addition or subtractionLearning Check instructs you to Square each score and add 47 to it, then sum those numbersA Square each score, add up the squared scores, then add 47 to that sumB Add 47 to each sco
38、re, square the result, and sum those numbersC Add up the scores, square that sum, and add 47 to itD472XLearning Check - Answer instructs you to Square each score and add 47 to it, then sum those numbersA Square each score, add up the squared scores, then add 47 to that sumB Add 47 to each score, squ
39、are the result, and sum those numbersC Add up the scores, square that sum, and add 47 to itD472XLearning Check Decide if each of the following equationsis True or False. T/FT/F22XX 2XXXLearning Check - Answer When the operations are performed in a different order, the results will be differentFalse This is the definition of (X)2TrueAnyQuestions?Concepts?Equations?
