2Purpose of this Section of the Research Support Lab Purpose of This RSL Part:Make statistics fun!Make you into a statistician!Introduce you to basic concepts and procedures in descriptive and inferential statisticsPrepare you for subsequent statistical coursesOverview of These RSL Parts:Begins with methods for describing and summarizing single-variable (frequency) distributions followed by methods for describing relationships between two (or more) variables.Then introduce probability theory as background for understanding inferential statistics.Methods are then presented for drawing inferences from research samples to populations from which the samples were drawn.Statistical tests covered include z-tests, t-tests, analysis of variance(F-tests), and nonparametric tests
3Textbook Credits Textbook Shavelson, R.J. (1996). Statistical reasoning for the behavioral sciences (3rd Ed.). Boston: Allyn & Bacon.Supplemental MaterialRuiz-Primo, M.A., Mitchell, M., & Shavelson, R.J. (1996). Student guide for Shavelson statistical reasoning for the behavioral sciences (3rd Ed.). Boston: Allyn & Bacon.
5Research DefinedResearch is doing one’s damnedest to answer perplexing questions…Or research is a systematic approach to finding answers to questionsScientific research, our focus, seeks answers to questions empirically and by inference, ruling out counter-interpretations to the one justified by the dataWith the scientific method, problems are formulated, hypotheses are identified, data are collected, inferences are drawn about which hypothesis is more credibleThe purpose of empirical research, therefore, is to provide answers to questions about behavior using the scientific method
6Statistics DefinedStatistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.Descriptive statistics consists of:the collectionOrganizationSummarizationpresentation of dataInferential statistics consists of:generalizing from samples to populationsperforming estimationshypothesis testingdetermining relationships among variablesmaking predictions
7Research Questions/Steps in Conducting Research What is happening?Is there a systematic (causal) effect?Why or how is it happening (“mechanism”)?Steps in Conducting ResearchIdentify and define a research problemFormulate hypothesis based on theory, research, or bothDesign the researchConduct the researchAnalyze the dataInterpret the data as they bear on the research question
8Data Collection and Sampling Techniques Surveys are the most common method of collecting data. Three methods of surveying are:Telephone surveysMailed questionnaire surveysPersonal interviewsOther methods include historical data gathering (empirical data)
9Some TerminologyVariable: is a characteristic or attribute that can assume different values(height, ability)Data are the values that variables can assume.Random variables have values that are determined by chance.A population consists of all subjects that are being studied.A sample is a group of subjects selected from a population.Random samples are selected using chance methods or random methods.Independent Variable(Factor/Treatment): A variable that is measured , manipulated (type of instruction), or selected (e.g., sex) to determine its relationship to some other observed variable.Control Variable: A variable which is held constant (or is “controlled”) to neutralize its effect on the dependent variable because it is not the focus of the study (e.g., control on sex in a reading study)Intervening Variable: A conceptual or theoretical variable that accounts for the relation between independent and dependent variable; an explanation for the relation or a hypothesized mechanism that accounts for the relation.Dependent Variable(Response): A variable that is observed and measured to determine its response to the independent variable (i.e., dependent on the independent variable)
10Measurement ScalesNominal—classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data.Ordinal—classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.Interval—ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero.Ratio—possesses all the characteristics of interval measurement, and there exists a true zero.
12Some Terminology: Summation Notation Summation notation is mathematical notation commonlyused in statisticsIt’s really simple if you pause, take a deep breath, relax andenjoy it… a little patience goes a long ways
14Research Designs Pre-experimental Designs Experimental Designs One-shot Case Study (Treatment group only)One Group Pretest to Posttest Design—measures of changeIntact Group Comparison at posttestExperimental DesignsRandom assignment to “treatment” & control groupPosttest Only Control GroupPretest-Posttest Control GroupFactorialQuasi-experimental DesignsNon-random assignment to “treatment” & control group observedNonequivalent-Control Group DesignTime-Series DesignEx-Post Facto DesignsStatistical controls for comparing alternative “treatments”Correlational DesignCriterion-Group Design
15Pre-experimental Designs One-shot Case Study (Treatment group only)Example:“X” is a new personnel policy, a job satisfaction measurement is taken, and then a response is observedOne Group Pretest to Posttest Design—measures changeA job satisfaction measurement is taken before and after treatment “X” is appliedIntact Group Comparison at posttestG1 receives the treatment, G2 does not; then a job satisfaction measurement is taken and observed(in this case G1 and G2 may represent two different business units)OXXO2O1XControlOG1G2
16Random assignment to “treatment” & control group Experimental DesignsRandom assignment to “treatment” & control groupPosttest Only Control Group • Pretest-Posttest Control GroupFactorialXControlOXControlO2O1X2X1OControlExample:A job satisfaction measurement is taken after treatment “X1” is applied or not and graveyard shift “X2” is implemented
17Quasi-experimental Designs Non-random assignment to “treatment” & control group observed.Include one or more control groups.Nonequivalent-Control Group DesignSubjects receive a pretest (O1) treatment or non-treatment and then receive a posttest (O2)Time-Series DesignMultiple observations are taken before and after a treatment is administered. Pretreatment observations establish a control group baseline. Post-treatment observations establish a consistent change in response.XControlO2G1G2O1XO2O1…
18Ex-Post Facto DesignsStatistical controls for comparing “treatment” and “control” (relationships between two variables). Called ex-facto because the researcher arrives after the treatment has been administered.Correlational DesignSAT scores (O1) and GPA (O2) are collected.Criterion-Group DesignGroup 2 is compared to Group 1O1O2OG1G2
19Threats to Internal Validity History:- something co-occurring with the treatment caused the outcomeMaturation- maturation, not the treatment, caused the outcome“Mortality”- loss of poorly performing subjects from a group caused the outcomeStatistical Regression- extreme groups are likely to improve on retestingSelection bias- the differences in outcomes existed before the treatments were givenInstrumentation- outcome measure not reliable, valid, or bothTesting- pretest cued subjects to outcome measureStability- Type I Error
20History ThreatOccurrence of events other than the independent variable.Treatment (X)Control
21Maturity ThreatTreatment (X)There may be developmental (physical or mental) changes occurring to the subjects during the time of the experiment
22Mortality Threat Treatment (X) Some subjects drop out the study and they have something in common, say, low achievement.
23Regression Threat Treatment (X) The groups were selected on the basis of extreme score. (Regression effect: low-extreme tends to increase, high-extreme tends to drop)
24Selection Threat Treatment (X) Initial difference exist in groups Control
25Instrumentation Threat Treatment (X)The measuring instruments is not reliable or not valid, therefore, the score obtained by subjects could not be accurate.?
26Testing Threat Pretest Treatment (X) The subject learns from the pretest, therefore, scores better on the posttestPretest
27Testing Threat Type I Error Type II Error Correct Decision H0 True H0 FalseType I Errorproducers risk (a)Type II Errorconsumers risk(b)Correct DecisionReject H0Do not reject H0A type I error occurs if one rejects the null hypothesis when it is true.A type II error occurs if one does not reject the null hypothesis when it is false.
28Ideal Model Experimental Design (Control Group + Random Assignment) Treatment (X)ControlRandomly Assigned
29Practice Exercises Select two out of the four major Research Designs. Support your two selected research designs with original hypothetical examples as outlined in this presentation.Compare and contrast them with one another.Indicate all threads to validity that you can document.