Presentation on theme: "Chapter 1: Introduction to Statistics"— Presentation transcript:
1 Chapter 1: Introduction to Statistics PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Eighth Edition by Frederick J Gravetter and Larry B. Wallnau
2 Learning Outcomes 1 Know key statistical terms 2 Know key measurement terms3Know key research terms4Know the place of statistics in science5Understand summation notation
3 Math Skills Assessment Statistics requires basic math skillsInadequate basic math skills puts you at risk in this courseAppendix A Math Skills Assessment helps you determine if you need a skills reviewAppendix A Math Skills Review provides a quick refresher course on those areas.The final Math Skills Assessment identifies your basic math skills competenceSome instructors may prefer to put this slide at the end of the lecture.
4 1.1 Statistics, Science and Observations “Statistics” means “statistical procedures”Uses of StatisticsOrganize and summarize informationDetermine exactly what conclusions are justified based on the results that were obtainedGoals of statistical proceduresAccurate and meaningful interpretationProvide standardized evaluation proceduresInstructors may wish to note that there are many different meanings of the term “statistics” so students should be certain they understand which meaning is being referenced in this course.
5 1.2 Populations and Samples The set of all the individuals of interest in a particular studyVary in size; often quite largeSampleA set of individuals selected from a populationUsually intended to represent the population in a research studyPopulation vs. sample is a critical distinction that will be the basis for understanding many others aspects of applying statistical procedures in this course. Instructors may wish to emphasize some of the subtle clues the text authors used to remind tem of the differences, e.g., greek letters for population parameters, italicized sample statistic symbols, and N vs. n.
6 Figure 1.1 Relationship between population and sample FIGURE 1.1 The relationship between a population and a sample.
7 Variables and Data Variable Data (plural) Data set A datum (singular) Characteristic or condition that changes or has different values for different individualsData (plural)Measurements or observations of a variableData setA collection of measurements or observationsA datum (singular)A single measurement or observationCommonly called a score or raw score
8 Parameters and Statistics A value, usually a numerical value, that describes a populationDerived from measurements of the individuals in the populationStatisticA value, usually a numerical value, that describes a sampleDerived from measurements of the individuals in the sample
9 Descriptive & Inferential Statistics Descriptive statisticsSummarize dataOrganize dataSimplify dataFamiliar examplesTablesGraphsAveragesInferential statisticsStudy samples to make generalizations about the populationInterpret experimental dataCommon terminology“Margin of error”“Statistically significant”
10 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 parameterExample: 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)Students sometimes associate “error” with being wrong. Although that is not a completely incorrect understanding, it tends to prevent them from being able to accept that a quantifiable degree of imprecision is much better than a random guess.
11 Figure 1.2 A demonstration of sampling error FIGURE 1.2 A demonstration of sampling error. Two samples are selected from the same population. Notice that the sample statistics are different from one sample to another, and all of the sample statistics are different from the corresponding population parameters. The natural differences that exist, by chance, between a sample statistic and a population parameter are called sampling error.
12 Figure 1.3 Role of statistics in experimental research FIGURE 1.3 The role of statistics in research.
13 Learning Check A statistic A variable A parameter 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…AA statisticBA variableCA parameterDA sample
14 Learning Check - Answer 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…AA statisticBA variableCA parameterDA sample
15 Learning CheckDecide if each of the following statements is True or False.T/FMost research studies use data from samplesWhen sample differs from the population there is a systematic difference between groups
16 Learning Check - Answer TrueSamples used because it is not feasible or possible to measure all individuals in the populationFalseSampling error due to random influences may produce unsystematic group differences
17 1.3 Data Structures, Research Methods, and Statistics Individual VariablesA variable is observed“Statistics” describe the observed variableCategory and/or numerical variablesRelationships between variablesTwo variables observed and measuredOne of two possible data structures used to determine what type of relationship exists
18 Relationships Between Variables Data Structure I: The Correlational MethodOne group of participantsMeasurement of two variables for each participantGoal is to describe type and magnitude of the relationshipPatterns in the data reveal relationshipsNon-experimental method of study
19 Figure 1.4 Data structures for studies evaluating the relationship between variables Figure 1.4 One of two data structures for studies evaluating the relationship between variables. Note that there are two separate measurements for each individual (wake-up time and academic performance). The same scores are shown in table (a) and graph (b).
20 Correlational Method Limitations Can demonstrate the existence of a relationshipDoes not provide an explanation for the relationshipMost importantly, does not demonstrate a cause-and-effect relationship between the two variables
21 Relationships Between Variables Data Structure II: Comparing two (or more) groups of ScoresOne variable defines the groupsScores are measured on second variableBoth experimental and non-experimental studies use this structureInstructors may wish to introduce the term “quasi-experimental” in this section.
22 Figure 1.5 Data structure for studies comparing groups FIGURE 1.5 The second data structure for studies evaluating the relationship between variables. Note that one variable is used to define the groups and the second variable is measured to obtain scores within each group.
23 Experimental Method Goal of Experimental Method Manipulation To demonstrate a cause-and-effect relationshipManipulationThe level of one variable is determined by the experimenterControl rules out influence of other variablesParticipant variablesEnvironmental variables
24 Figure 1.6 The structure of an experiment FIGURE 1.6 The structure of an experiment. Participants are randomly assigned to one of two treatment condition: counting money or counting blank pieces of paper. Later, each participant is tested by placing one hand in a bowl of hot (122° F) water and rating the level of pain. A difference between the ratings for the two groups is attributed to the treatment (paper versus money).
25 Independent/Dependent Variables Independent Variable is the variable manipulated by the researcherIndependent because no other variable in the study influences its valueDependent Variable is the one observed to assess the effect of treatmentDependent because its value is thought to depend on the value of the independent variable
26 Experimental Method: Control Methods of controlRandom assignment of subjectsMatching of subjectsHolding level of some potentially influential variables constantControl conditionIndividuals do not receive the experimental treatment.They either receive no treatment or they receive a neutral, placebo treatmentPurpose: to provide a baseline for comparison with the experimental conditionExperimental conditionIndividuals do receive the experimental treatment
27 Non-experimental Methods Non-equivalent GroupsResearcher compares groupsResearcher cannot control who goes into which groupPre-test / Post-testIndividuals measured at two points in timeResearcher cannot control influence of the passage of timeIndependent variable is quasi-independent
28 Figure 1.7 Two examples of non-experimental studies Insert NEW Figure 1.7FIGURE 1.7 Two examples of nonexperimental studies that involve comparing two groups of scores. In (a), a participant variable (gender) is used to create groups, and then the dependent variable (verbal score) is measured in each group. In (b), time is the variable used to define the two groups, and the dependent variable (depression) is measured at each of the two times.
29 Learning CheckResearchers observed that students exam scores were higher the more sleep they had the night before. This study is …ADescriptiveBExperimental comparison of groupsCNon-experimental group comparisonDCorrelational
30 Learning Check - Answer Researchers observed that students exam scores were higher the more sleep they had the night before. This study is …ADescriptiveBExperimental comparison of groupsCNon-experimental group comparisonDCorrelational
31 Learning CheckDecide if each of the following statements is True or False.T/FAll research methods have an independent variableAll research methods can show cause-and-effect relationships
32 Learning Check - Answer FalseCorrelational methods do not need an independent variableOnly experiments control the influence of participants and environmental variables
33 1.4 Variables and Measurement Scores are obtained by observing and measuring variables that scientists use to help define and explain external behaviorsThe process of measurement consists of applying carefully defined measurement procedures for each variable
34 Constructs & Operational Definitions Internal attributes or characteristics that cannot be directly observedUseful for describing and explaining behaviorOperational DefinitionIdentifies the set of operations required to measure an external (observable) behaviorUses the resulting measurements as both a definition and a measurement of a hypothetical constructInstructors may with to flag operational definition as a principle so important to behavioral science that it will re-appear in other courses such as research methods and experimental design.
35 Discrete and Continuous Variables Discrete variableHas separate, indivisible categoriesNo values can exist between two neighboring categoriesContinuous variableHave an infinite number of possible values between any two observed valuesEvery interval is divisible into an infinite number of equal partsDiscussing government statistics which report a fractional number of children in an “average” family is a humorous yet useful way of illustrating how discrete variables are fundamentally different from continuous variables.
36 Figure 1.8 Example: Continuous Measurement FIGURE 1.8 When measuring weight to the nearest whole pound, and are assigned the value 150 (top). Any value in the interval between and is given the value of 150.
37 Real Limits of Continuous Variables Real Limits are the boundaries of each interval representing scores measured on a continuous number lineThe real limit separating two adjacent scores is exactly halfway between the two scoresEach score has two real limitsThe upper real limit marks the top of the intervalThe lower real limit marks the bottom of the intervalSome students struggle with real limits. Instructors may wish to insert an example with the measurement scale in 10ths (or 100ths) to help reinforce the importance of ½ score unit above and below the scale value of the measurement unit.
38 Scales of MeasurementMeasurement assigns individuals or events to categoriesThe categories can simply be names such as male/female or employed/unemployedThey can be numerical values such as 68 inches or 175 poundsThe complete set of categories makes up a scale of measurementRelationships between the categories determine different types of scales
39 Scales of Measurement Nominal Ordinal Interval Ratio Scale CharacteristicsExamplesNominalLabel and categorizeNo quantitative distinctionsGenderDiagnosisExperimental or ControlOrdinalCategorizes observationsCategories organized by size or magnitudeRank in classClothing sizes (S,M,L,XL)Olympic medalsIntervalOrdered categoriesInterval between categories of equal sizeArbitrary or absent zero pointTemperatureIQGolf scores (above/below par)RatioEqual interval between categoriesAbsolute zero pointNumber of correct answersTime to complete taskGain in height since last yearThis material is arguably in the “Top Ten Most Important” concepts the students will encounter in the study of statistics and may merit identifying it as such.
40 Learning Check Continuous and ordinal Discrete and interval A study assesses the optimal size (number of other members) for study groups. The variable “Size of group” is …ADiscrete and intervalBContinuous and ordinalCDiscrete and ratioDContinuous and interval
41 Learning Check - Answer A study assesses the optimal size (number of other members) for study groups. The variable “Size of group” is …ADiscrete and intervalBContinuous and ordinalCDiscrete and ratioDContinuous and interval
42 Learning CheckDecide if each of the following statements is True or False.T/FVariables that cannot be measured directly cannot be studied scientificallyResearch measurements are made using specific procedures that define constructs
43 Learning Check - Answer FalseConstructs (internal states) can only be observed indirectly, but can be operationally measuredTrueOperational definitions assure consistent measurement and provide construct definitions
44 1.5 Statistical NotationStatistics uses operations and notation you have already learnedAppendix A has a Mathematical ReviewStatistics also uses some specific notationScores are referred to as X (and Y)N is the number of scores in a populationn is the number of scores in a sampleStudents’ eyes often glaze over in this section. Remind them how difficult it is to make yourself understood if you do not speak the language in use by everyone else, and point out that they will experience the same difficulty and frustration in this course if they do not understand the “language” and symbols of statistics.
45 Summation NotationMany statistical procedures sum (add up) a set of scoresThe summation sign Σ stands for summationThe Σ is followed by a symbol or equation that defines what is to be summedSummation is done after operations in parentheses, squaring, and multiplication or division.Summation is done before other addition or subtraction
46 Learning Check instructs you to … Square each score and add 47 to it, then sum those numbersBSquare each score, add up the squared scores, then add 47 to that sumCAdd 47 to each score, square the result, and sum those numbersDAdd up the scores, square that sum, and add 47 to it
47 Learning Check - Answer instructs you to …ASquare each score and add 47 to it, then sum those numbersBSquare each score, add up the squared scores, then add 47 to that sumCAdd 47 to each score, square the result, and sum those numbersDAdd up the scores, square that sum, and add 47 to it
48 Learning CheckDecide if each of the following equations is True or False.T/F
49 Learning Check - Answer FalseWhen the operations are performed in a different order, the results will be differentTrueThis is the definition of (ΣX)2