Session 7 Session 7 Introduction to Research Introduction to Research

and Evaluation and Evaluation

Topic 1: Research Questions and Topic 1: Research Questions and Hypothesis Testing Hypothesis Testing

AndAnd

Topic 2: Introduction to StatisticsTopic 2: Introduction to Statistics

For TonightFor Tonight

TodayToday

Review the contents of the proposal Review the contents of the proposal Topics tonightTopics tonight

– Finish the research questionsFinish the research questions– Types of data reviewTypes of data review– Hypothesis Testing Hypothesis Testing – Intro to Stats Intro to Stats

The phases of a research projectThe phases of a research project

Problem statement Problem statement Purpose Purpose Hypothesis development / research Hypothesis development / research

question(s) question(s) Population / Sample typePopulation / Sample type Results reporting (data) Results reporting (data) Statistical testingStatistical testing Conclusions RecommendationsConclusions Recommendations

Parts of the Research ReportParts of the Research Report

Chapter 1Chapter 1 Chapter 2Chapter 2 Chapter 3Chapter 3 Chapter 4Chapter 4 Chapter 5Chapter 5 ReferencesReferences Appendix Appendix

Components of Chapter 1Components of Chapter 1 IntroductionIntroduction Background of the studyBackground of the study Problem statementProblem statement Significance of studySignificance of study Overview of methodologyOverview of methodology Delimitations of studyDelimitations of study Definitions of key termsDefinitions of key terms Conclusion (Conclusion (optionaloptional))

Characteristics of Characteristics of Components in Chapter 1Components in Chapter 1

Introduction – 1 paragraph – 3 pagesIntroduction – 1 paragraph – 3 pages– Gets attention - graduallyGets attention - gradually– Brief vs. reflective openingBrief vs. reflective opening

Background – 2-5 pagesBackground – 2-5 pages– History of problem, etc.History of problem, etc.– Professional vs. practical useProfessional vs. practical use– Be careful of personal intrusionsBe careful of personal intrusions

Characteristics of Components in Characteristics of Components in Chapter 1Chapter 1

Problem Statement – ½ pageProblem Statement – ½ page– States problem as clearly as possibleStates problem as clearly as possible

Significance of study – 1 pgh. to 1 pageSignificance of study – 1 pgh. to 1 page– Answers: “Why did you bother to conduct the Answers: “Why did you bother to conduct the

study?”study?”– Be careful of promising too muchBe careful of promising too much

Ways to Convey Ways to Convey SignificanceSignificance

Problem has intrinsic importance, affecting Problem has intrinsic importance, affecting organizations or peopleorganizations or people

Previous studies have produced mixed Previous studies have produced mixed resultsresults

Your study examines problem in different Your study examines problem in different settingsetting

Meaningful results can be used by Meaningful results can be used by practitionerspractitioners

Unique populationUnique population Different methods usedDifferent methods used

Characteristics of Characteristics of ComponentsComponents

Delimitations – as neededDelimitations – as needed– Not flawsNot flaws– Establishes the boundaries – can study be Establishes the boundaries – can study be

generalized?generalized?– Consider:Consider:

samplesample SettingSetting time periodtime period methodsmethods

Stating the ProblemStating the Problem Developing a hypothesisDeveloping a hypothesis::

– Methods: estimation and hypothesis testing.Methods: estimation and hypothesis testing. Estimation, the sample is used to estimate a Estimation, the sample is used to estimate a

parameterparameter and a and a confidence intervalconfidence interval about the about the estimate is constructed. estimate is constructed.

– Parameter: Parameter: numerical quantity measuring some numerical quantity measuring some aspect aspect

– Confidence Interval: Confidence Interval: range of values that estimates a range of values that estimates a parameter for a high proportion of the time parameter for a high proportion of the time

Hypothesis Testing: the most common useHypothesis Testing: the most common use– Hypothesis: an intelligent guess or assumption that guides Hypothesis: an intelligent guess or assumption that guides

the design of the studythe design of the study– Null hypothesis: there is no difference or there is no effectNull hypothesis: there is no difference or there is no effect– Alternative hypothesis: there is a difference or there is an Alternative hypothesis: there is a difference or there is an

effecteffect– Hypotheses: more than hypothesis, which are related to the Hypotheses: more than hypothesis, which are related to the

populationpopulation

TYPES OF DATA TYPES OF DATA

VariablesVariables Two categories:Two categories: IndependentIndependent

– Variables in an experiment or study which are Variables in an experiment or study which are not easily to be manipulated without changing not easily to be manipulated without changing the participants. the participants. Age, gender, year, classroom teacher, any Age, gender, year, classroom teacher, any

personal background data, etcpersonal background data, etc DependentDependent

– Variables which are changed in an experimentVariables which are changed in an experiment Hours of sleep, amount of food, time given to Hours of sleep, amount of food, time given to

complete an activity, curriculum, instructional complete an activity, curriculum, instructional method, etc.method, etc.

VariablesVariables

A variable: any measured characteristic or attribute that differs for A variable: any measured characteristic or attribute that differs for different subjects. different subjects.

Two types:Two types:– Quantitative: Quantitative: sometimes called "categorical variables.“sometimes called "categorical variables.“

measured on one of three scales:measured on one of three scales:– Ordinal: first second or third choice (most of the children Ordinal: first second or third choice (most of the children

preferred red popsicles, and grape was the second choice)preferred red popsicles, and grape was the second choice)– Interval: direct time periods between two events ( time it Interval: direct time periods between two events ( time it

takes a child to respond to a question)takes a child to respond to a question)– Ratio scale: compares the number of times one event Ratio scale: compares the number of times one event

happens in comparison to another event. (example: the happens in comparison to another event. (example: the number of time a black card is pulled in comparison to the number of time a black card is pulled in comparison to the number of times a red card is pulled) number of times a red card is pulled)

– Qualitative:Qualitative: measured on a measured on a nominalnominal scale. scale.

Types of DataTypes of Data Nominal DataNominal Data  -- Data that describe the presence or absence of some   -- Data that describe the presence or absence of some

characteristic or attribute; data that name a characteristic without any characteristic or attribute; data that name a characteristic without any regard to the value of the characteristic; also referred to as regard to the value of the characteristic; also referred to as categorical categorical datadata. Male = 1 Female = 2, blue, green, etc . Male = 1 Female = 2, blue, green, etc

OrdinalOrdinal Data -- Measurement based on the  Data -- Measurement based on the rank orderrank order of concepts or of concepts or variables; differences among ranks need not be equal.variables; differences among ranks need not be equal.

intervalinterval data -- Measurement based on numerical scores or values in  data -- Measurement based on numerical scores or values in which the distance between any two adjacent, or contiguous, data which the distance between any two adjacent, or contiguous, data points is equal; scale without a meaningful or true zeropoints is equal; scale without a meaningful or true zero

Ratio DataRatio Data  -- Order and magnitude…. Measurement for which   -- Order and magnitude…. Measurement for which intervals between data points are equal; a true zero exists; if the score intervals between data points are equal; a true zero exists; if the score is zero, there is a complete absence of the variable.is zero, there is a complete absence of the variable.

– Four levels:Four levels: nominal: assigning items to groups or categories nominal: assigning items to groups or categories

– Examples: Classroom, color, sizeExamples: Classroom, color, size Ordinal: ordered in the sense that higher numbers represent higher Ordinal: ordered in the sense that higher numbers represent higher

values values – Examples 1= freshmen, 2= sophomoreExamples 1= freshmen, 2= sophomore

Interval: one unit on the scale represents the same magnitude on the Interval: one unit on the scale represents the same magnitude on the trait or characteristic being measured across the whole range of the trait or characteristic being measured across the whole range of the scale. scale.

– Interval scales Interval scales do not havedo not have a "true" zero point, a "true" zero point, it is not possible to make statements about how many times higher it is not possible to make statements about how many times higher

one score is than another. one score is than another. Ratio: represents the same magnitude on the trait or characteristic Ratio: represents the same magnitude on the trait or characteristic

being measured across the whole range of the scale. being measured across the whole range of the scale. – DO haveDO have true zero points true zero points

Nominal level of Nominal level of measurementmeasurement

Assigns a number to represent a Assigns a number to represent a group (gender; geography)group (gender; geography)

Numbers represent qualitative Numbers represent qualitative differences (good-bad)differences (good-bad)

No order to numbersNo order to numbers Statistics -- mode, percentages, Statistics -- mode, percentages,

chi-squarechi-square

Ordinal level of Ordinal level of measurementmeasurement

Things are rank-ordered -- >, <Things are rank-ordered -- >, < Numbers are not assigned arbitrarilyNumbers are not assigned arbitrarily Assume a continuumAssume a continuum Examples -- classification (fr, soph, Examples -- classification (fr, soph,

jr, sr), levels of education, Likert jr, sr), levels of education, Likert scalesscales

Statistics--median (preferred), mode, Statistics--median (preferred), mode, percentage, percentile rank, chi-percentage, percentile rank, chi-square, rank correlation.square, rank correlation.

Interval level of Interval level of measurementmeasurement

Equal units of measurementEqual units of measurement Arbitrary zero point--does not indicate Arbitrary zero point--does not indicate

absence of the property absence of the property Example -- degrees, Likert-type Example -- degrees, Likert-type

scales (treatment), numerical gradesscales (treatment), numerical grades Statistics -- frequencies, Statistics -- frequencies,

percentages, mode, mean, SD, t test, percentages, mode, mean, SD, t test, F test, product moment correlationF test, product moment correlation

Ratio level of measurementRatio level of measurement

Absolute zeroAbsolute zero Interval scaleInterval scale Examples -- distance, weightExamples -- distance, weight Statistics -- all statistical Statistics -- all statistical

determinations determinations

Which are these? Which are these?

Never marriedNever married Lower middle ClassLower middle Class Divorced Divorced Age Age SeparatedSeparated Middle classMiddle class Widowed Widowed WeightWeight Religious AffiliationsReligious Affiliations

HeightHeight Political Affiliations Political Affiliations DistanceDistance freshmen freshmen

Which are these? Which are these?

Never married Never married Lower middle Class Lower middle Class DivorcedDivorced Age Age Separated Separated Middle class Middle class Widowed Widowed Weight Weight Religious Affiliations Religious Affiliations

Height Height Political Affiliations Political Affiliations Distance Distance freshmen freshmen Minutes Minutes

O

O

O

N

N

N

N

N

N

I/RI/R

I/RI/R

I/RI/R

I/RI/R

I/RI/R

Key Point Key Point

Statistical Significance must be Statistical Significance must be distinguished from practical significance distinguished from practical significance – Even a small difference in a large sample might Even a small difference in a large sample might

be significant if the sample is largebe significant if the sample is large– No p-value of a .0001 means that 1 in 10000 No p-value of a .0001 means that 1 in 10000

times the difference observed will occur by times the difference observed will occur by chance (no real difference between groups) chance (no real difference between groups)

Example Hypothesis Example Hypothesis

There will be no significant difference in the There will be no significant difference in the EOC scores for schools that use CAERT EOC scores for schools that use CAERT and those that don’t. and those that don’t.

The EOC exam scores for schools using The EOC exam scores for schools using Caert and those that don’t will not be Caert and those that don’t will not be significantly different. significantly different.

The EOC exam scores for schools using The EOC exam scores for schools using Caert and those that don’t will be Caert and those that don’t will be significantly different. significantly different.

Statistics for TeachersStatistics for Teachers

StatisticsStatistics“If you can assign a number to it, “If you can assign a number to it,

you can measure it”you can measure it”Dr. W. Edward DemmingDr. W. Edward Demming

StatisticsStatistics– refers to calculated quantities regardless of whether or refers to calculated quantities regardless of whether or

not they are from a sample not they are from a sample – is defined as a numerical quantity is defined as a numerical quantity – Often used incorrectly to refer to a range of techniques Often used incorrectly to refer to a range of techniques

and procedures for analyzing data, interpreting data, and procedures for analyzing data, interpreting data, displaying data, and making decisions based on data. displaying data, and making decisions based on data. Because that is the basic learning outcomes of a Because that is the basic learning outcomes of a statistics course. statistics course.

What is the mean medium and the mode in this example?

Descriptive statisticsDescriptive statistics Descriptive statisticsDescriptive statistics

– summarize a collection of data in a clear and understandable way. summarize a collection of data in a clear and understandable way. Example: Scores of 500 children on all parts of a standardized test.Example: Scores of 500 children on all parts of a standardized test. Methods: numerical and graphical. Methods: numerical and graphical.

– Numerical: more precise- uses numbers as accurate measureNumerical: more precise- uses numbers as accurate measure meanmean the arithmetic average which is calculated by adding a the arithmetic average which is calculated by adding a

the scores or totals and then dividing by the number of the scores or totals and then dividing by the number of scores.scores.

standard deviation.standard deviation. These statistics convey information These statistics convey information about the average degree of shyness and the degree to about the average degree of shyness and the degree to which people differ in shyness. which people differ in shyness.

– Graphical: better for identifying patternsGraphical: better for identifying patterns stem and leaf displaystem and leaf display : a graphical method of displaying data : a graphical method of displaying data

to show how several data are aligned on a graphto show how several data are aligned on a graph box plot.box plot. Graphical method to show what data are included. Graphical method to show what data are included.

The box stretches from the 25th The box stretches from the 25th percentilepercentile to the the 75th to the the 75th percentile percentile

historgrams. historgrams. Since the numerical and graphical approaches compliment each Since the numerical and graphical approaches compliment each

other, it is wise to use both.other, it is wise to use both.

Inferential statisticsInferential statistics

For choosing a statistical test For choosing a statistical test variables fall into 2 groups variables fall into 2 groups

Continuous variables are numeric values that can Continuous variables are numeric values that can be ordered sequentially, and that do not naturally be ordered sequentially, and that do not naturally fall into discrete ranges.fall into discrete ranges.– Examples include:  weight, number of seconds it takes Examples include:  weight, number of seconds it takes

to perform a task, number of words on a user interfaceto perform a task, number of words on a user interface

Categorical variable values cannot be sequentially Categorical variable values cannot be sequentially ordered or differentiated from each other using a ordered or differentiated from each other using a mathematical method. mathematical method. – Examples include:  gender, ethnicity, software user Examples include:  gender, ethnicity, software user

interfacesinterfaces

Tools for MeasuringTools for Measuring

Measurement is the assignment of numbers to objects or Measurement is the assignment of numbers to objects or events in a systematic fashion. events in a systematic fashion. – Four levels:Four levels:

nominal: assigning items to groups or categories nominal: assigning items to groups or categories – Examples: Classroom, color, sizeExamples: Classroom, color, size

Ordinal: ordered in the sense that higher numbers represent higher Ordinal: ordered in the sense that higher numbers represent higher values values

– Examples 1= freshmen, 2= sophomoreExamples 1= freshmen, 2= sophomore Interval: one unit on the scale represents the same magnitude on the Interval: one unit on the scale represents the same magnitude on the

trait or characteristic being measured across the whole range of the trait or characteristic being measured across the whole range of the scale. scale.

– Interval scales Interval scales do not havedo not have a "true" zero point, a "true" zero point, it is not possible to make statements about how many times higher it is not possible to make statements about how many times higher

one score is than another. one score is than another. Ratio: represents the same magnitude on the trait or characteristic Ratio: represents the same magnitude on the trait or characteristic

being measured across the whole range of the scale. being measured across the whole range of the scale. – DO haveDO have true zero points true zero points

Data AnalysisData Analysis Explaining and interpreting the data:Explaining and interpreting the data:

– Data are pluralData are plural You are looking at more than one number or group of numbers; You are looking at more than one number or group of numbers;

subject-verb agreement is important when writing. subject-verb agreement is important when writing. Central Tendency: measures of the location of the middle or the center Central Tendency: measures of the location of the middle or the center

of the whole data base for a variable or group of variablesof the whole data base for a variable or group of variables– Frequency: the number of times a number appearsFrequency: the number of times a number appears– Mean: the arithmetic averageMean: the arithmetic average– Mode: the number that appears most oftenMode: the number that appears most often– Median: the number in the middle when numbers are arranged by Median: the number in the middle when numbers are arranged by

valuevalue– Skew: A distribution is skewed if one of its tails is longer than the Skew: A distribution is skewed if one of its tails is longer than the

other. Data may be skewed positively or negatively. other. Data may be skewed positively or negatively. Standard deviation: the amount of variance between each sigmaStandard deviation: the amount of variance between each sigma

Inferential statisticsInferential statistics

Inferential statisticsInferential statistics– Infers or implies something about Infers or implies something about populationpopulation from a from a

samplesample.. Population: A total group Population: A total group Sample: A few from the whole groupSample: A few from the whole group Representative sample: a sample that is equally Representative sample: a sample that is equally

propionate to the populationpropionate to the population Random Sample: a sample that is chosen strictly by Random Sample: a sample that is chosen strictly by

chance is not “hand-picked”chance is not “hand-picked”– Probability: the percentage of change that an event will Probability: the percentage of change that an event will

occuroccur

Parameters vs Statistics Parameters vs Statistics Parametric vs Non-Parametric Parametric vs Non-Parametric

Definitions againDefinitions again– Parameter is the true value in the population of Parameter is the true value in the population of

interest (everyone)interest (everyone)– Statistics is a number you calculate from your Statistics is a number you calculate from your

sample data in order to estimate the parametersample data in order to estimate the parameter Example: Example:

– All the Ag Teachers of the stateAll the Ag Teachers of the state– Only 25 teachers selected from the 285 that Only 25 teachers selected from the 285 that

exist exist

What can make the sample different What can make the sample different from the true value/result of the whole? from the true value/result of the whole?

Students taught by teachers using Caert will Students taught by teachers using Caert will score higher on end of course exams than score higher on end of course exams than those who do not.those who do not.– True difference – one group actually has a True difference – one group actually has a

higher capacity to learn. higher capacity to learn. – Random Variations -- The two populations Random Variations -- The two populations

have identical means and the observed have identical means and the observed differences is a coincidence of sampling differences is a coincidence of sampling

– Sampling error (bias) Poorly selected samples Sampling error (bias) Poorly selected samples not representing the population. not representing the population.

Parameters or Parametric DataParameters or Parametric Data Parameter: a numerical Parameter: a numerical

quantity measuring some quantity measuring some aspect of a population of aspect of a population of scores. scores. – Parameters are usually Parameters are usually

estimated by statistics estimated by statistics computed in samples computed in samples

Quantity Parameter Quantity Parameter Greek letters are Greek letters are commonly accepted for commonly accepted for writing formulaswriting formulas

Statistical symbols are Statistical symbols are most common in most common in reporting actual data reporting actual data analysis in reports or analysis in reports or articles. articles.

Quantity Quantity Parameter Parameter Statistic Statistic

MeanMean μμ MM

Standard deviationStandard deviation σσ ss

ProportionProportion ππ pp

CorrelationCorrelation ρρ rr

Greek letters are used to designate parameters

Stats tests & types of data each useStats tests & types of data each use

1 Sample t-test · 1 Sample t-test ·        1 Continuous Dependent Variable with normal distribution ·        0 Independent Variables         1 Continuous Dependent Variable with normal distribution ·        0 Independent Variables   1 Sample Median1 Sample Median ·        1 Continuous Dependent Variable with non-normal distribution ·        0 Independent Variables  ·        1 Continuous Dependent Variable with non-normal distribution ·        0 Independent Variables  Binomial test ·Binomial test ·        1 Bi-level Categorical Dependent Variable ·        0 Independent Variables         1 Bi-level Categorical Dependent Variable ·        0 Independent Variables  Chi-Square Goodness of Fit ·Chi-Square Goodness of Fit ·     1 Categorical Dependent Variable ·        0 Independent Variables·              1 Categorical Dependent Variable ·        0 Independent Variables·          2 Independent Sample t-test ·2 Independent Sample t-test ·    1 Continuous Dependent Variable with normal distribution     1 Continuous Dependent Variable with normal distribution

– 1 (2 level) Categorical Independent Variable1 (2 level) Categorical Independent Variable   Wilcoxon Signed Ranks TestWilcoxon Signed Ranks Test ·    1 Continuous Dependent Variable with non-normal distribution ·   ·    1 Continuous Dependent Variable with non-normal distribution ·  

– 1 (2 level) Categorical Independent Variable1 (2 level) Categorical Independent Variable Chi Square Test ·Chi Square Test ·        1 Categorical Dependent Variable ·        1 (2-level) Categorical Independent Variable        1 Categorical Dependent Variable ·        1 (2-level) Categorical Independent Variable Fisher Exact TestFisher Exact Test ·        1 Categorical Dependent Variable ·        1 (2 level) Categorical Independent Variable ·        1 Categorical Dependent Variable ·        1 (2 level) Categorical Independent Variable Paired t-testPaired t-test     1 Continuous Dependent Variable with normal distribution, · 1 (2 Level) Categorical Independent Variable     1 Continuous Dependent Variable with normal distribution, · 1 (2 Level) Categorical Independent Variable One-way repeated measures ANOVAOne-way repeated measures ANOVA 1 Continuous Dependent Var w/normal distribution 1 Continuous Dependent Var w/normal distribution

– 1 (Multi-Level) Categorical Independent Variable 1 (Multi-Level) Categorical Independent Variable Friedman Analysis of Variance by RanksFriedman Analysis of Variance by Ranks 1 Continuous Dependent Var w/ non-normal distribution 1 Continuous Dependent Var w/ non-normal distribution

– 1 (Multi-Level) Categorical Independent Variable1 (Multi-Level) Categorical Independent Variable One-way ANOVA ·    One-way ANOVA ·        1 Continuous Dependent Variable with normal distribution     1 Continuous Dependent Variable with normal distribution

– 1 (Multi-level) Categorical Independent Variable1 (Multi-level) Categorical Independent Variable Kruskal Wallis  Kruskal Wallis        1 Continuous Dependent Variable with non-normal distribution       1 Continuous Dependent Variable with non-normal distribution

– 1 (Multi-level) Categorical Independent Variable 1 (Multi-level) Categorical Independent Variable  Linear Discriminant AnalysisLinear Discriminant Analysis       1 Categorical Dependent Variable       1 Categorical Dependent Variable

– 1 or more Continuous Independent Variable with normal distribution 1 or more Continuous Independent Variable with normal distribution  Factorial ANOVAFactorial ANOVA     1 Continuous Dependent Variable with normal distribution     1 Continuous Dependent Variable with normal distribution

– 2 or more Categorical Independent Variables 2 or more Categorical Independent Variables Linear RegressionLinear Regression    1 Continuous Dependent Variable with normal distribution    1 Continuous Dependent Variable with normal distribution

– 1 Continuous Independent Variable with normal distribution 1 Continuous Independent Variable with normal distribution Multiple RegressionMultiple Regression 1 Continuous Dependent Variable with normal distribution 1 Continuous Dependent Variable with normal distribution

– Multiple Continuous Independent Variables with normal distributionMultiple Continuous Independent Variables with normal distribution ANCOVA ANCOVA 1 Continuous Dependent Var w/normal distribution 1 Continuous Dependent Var w/normal distribution

– 2 (or more) Categorical or Continuous Independent Variables with normal distribution2 (or more) Categorical or Continuous Independent Variables with normal distribution

ResultsResults

ResultsResults

At the end of the trial experience schools At the end of the trial experience schools using Caert had EOC exam scores that using Caert had EOC exam scores that were 18% that were higher than those were 18% that were higher than those schools that did not use Caert. schools that did not use Caert. – Alpha set at p<.05 Alpha set at p<.05 – Observed P value of .03Observed P value of .03

ConclusionConclusion

Interpretation: Given that there is no true Interpretation: Given that there is no true (other than scores) difference between (other than scores) difference between schools using Caert and those that don’t, schools using Caert and those that don’t, the probability of observing a 3% (.03) or the probability of observing a 3% (.03) or more difference due to chance is less more difference due to chance is less than .05 than .05

ANOVAANOVA

A factorial ANOVA has two or more A factorial ANOVA has two or more categorical independent variables (either categorical independent variables (either with or without the interactions) and a single with or without the interactions) and a single normally distributed interval dependent normally distributed interval dependent variable.  variable. 

ANOVAANOVA

In statistics, ANOVA is short for In statistics, ANOVA is short for analysis of analysis of variance.variance. Analysis of variance is a collection of Analysis of variance is a collection of statistical models, and their associated statistical models, and their associated procedures, in which the observed variance is procedures, in which the observed variance is partitioned into components due to different partitioned into components due to different explanatory variables. explanatory variables. – The initial techniques of the analysis of variance were The initial techniques of the analysis of variance were

developed by the statistician and geneticist R. A. Fisher developed by the statistician and geneticist R. A. Fisher in the 1920s and 1930s, and is sometimes known as in the 1920s and 1930s, and is sometimes known as Fisher's ANOVAFisher's ANOVA or or Fisher's analysis of varianceFisher's analysis of variance, due , due to the use of Fisher's F-distribution as part of the test of to the use of Fisher's F-distribution as part of the test of statistical significance.statistical significance.

Z test Z test

The The Z-testZ-test is a statistical test used in inference is a statistical test used in inference which determines if the difference between a which determines if the difference between a sample mean and the population mean is large sample mean and the population mean is large enough to be statistically significant, that is, if it is enough to be statistically significant, that is, if it is unlikely to have occurred by chance.unlikely to have occurred by chance.

The Z-test is used primarily with standardized The Z-test is used primarily with standardized testing to determine if the test scores of a testing to determine if the test scores of a particular sample of test takers are within or particular sample of test takers are within or outside of the standard performance of test takers.outside of the standard performance of test takers.

Pearson Correlation Pearson Correlation

The PEARSON Correlation is a calculation The PEARSON Correlation is a calculation between the correlation coefficient between two between the correlation coefficient between two measurement variables when measurements on measurement variables when measurements on each variable are observed for each of N subjects.each variable are observed for each of N subjects.– (Any missing observation for any subject causes that (Any missing observation for any subject causes that

subject to be ignored in the analysis.) The Correlation subject to be ignored in the analysis.) The Correlation analysis tool is particularly useful when there are more analysis tool is particularly useful when there are more than two measurement variables for each subject. It than two measurement variables for each subject. It provides an output table, a correlation matrix, showing provides an output table, a correlation matrix, showing the value applied to each possible pair of measurement the value applied to each possible pair of measurement variables.variables.

Two-Sample t-TestTwo-Sample t-Test

The Two-Sample t-Test analysis tools test The Two-Sample t-Test analysis tools test for equality of the population means for equality of the population means underlying each sample. The three tools underlying each sample. The three tools employ different assumptions: that the employ different assumptions: that the population variances are equal, that the population variances are equal, that the population variances are not equal, and that population variances are not equal, and that the two samples represent before treatment the two samples represent before treatment and after treatment observations on the and after treatment observations on the same subjects. same subjects.

Research TechniquesResearch Techniques

Types of hypothesis testing:Types of hypothesis testing:– T-test: comparing the mean of two groupsT-test: comparing the mean of two groups– ANOVA: Analysis of Variance – used to compare the ANOVA: Analysis of Variance – used to compare the

means of several variablesmeans of several variables– Correlation: compares the relationship of two groupsCorrelation: compares the relationship of two groups– Chi Square of independence: explains if is a relationship Chi Square of independence: explains if is a relationship

between the attributes of two variables. between the attributes of two variables. – Linear regression: the prediction of one variable based Linear regression: the prediction of one variable based

on another variable, when the relationship between the on another variable, when the relationship between the variables is assumed to assumed to be linear.variables is assumed to assumed to be linear.

Normal Curve Normal Curve

In practice, one often assumes that data are from an approximately normally distributed population. If that assumption is justified, then about 68% of the values are at within 1 standard deviation away from the mean, about 95% of the values are within two standard deviations and about 99.7% lie within 3 standard deviations. This is known as the "68-95-99.7 rule" or the "Empirical Rule".

Key points Key points

Comparing groups for Sig DiffComparing groups for Sig Diff

Key TermsKey Terms

Use for new terms in profession (cognitive Use for new terms in profession (cognitive processing skills)processing skills)

Give preciseness to ambiguous term (learner)Give preciseness to ambiguous term (learner) General term used in special way (learning style)General term used in special way (learning style) Writing definitionWriting definition

– State termState term– Give broad class to which term belongsGive broad class to which term belongs– Specify how term is used that differsSpecify how term is used that differs

Conclusion – not always usedConclusion – not always used– Summarizes if necessarySummarizes if necessary– Tells reader what to expectTells reader what to expect

Survey ConstructionSurvey Construction

Parts: Parts: – TitleTitle– Directions introduction to surveyDirections introduction to survey

ScalesScales– Items (a list of statements or questions)Items (a list of statements or questions)

Usually with a scale of some typeUsually with a scale of some type– RatingRating– RankingRanking– Semantic differential Semantic differential – Likert type scale Likert type scale

Demographical infoDemographical info

Likert type scaleLikert type scale

Ice cream is good for breakfastIce cream is good for breakfast– Strongly disagree Strongly disagree – Disagree Disagree – Neither agree nor disagree Neither agree nor disagree – Agree Agree – Strongly agree Strongly agree

RatingRating

Scale of 1 to 5 or 1 to 7 , etc….Scale of 1 to 5 or 1 to 7 , etc….– ? 1 = Best or highest? 1 = Best or highest– ? 5 = Best or highest? 5 = Best or highest

Even number of items or odd?Even number of items or odd?– Forced choice – no fence sittingForced choice – no fence sitting– Middle – allows a middle ground responseMiddle – allows a middle ground response– Might allow for not opinion, (NA or NO)Might allow for not opinion, (NA or NO)

Semantic differentialSemantic differential

“In order to succeed you must know what you are doing, like what you are doing, and believe in what you are doing”

Will Rogers

Setting Alpha LevelSetting Alpha Level

Set alpha at something like 0.05Set alpha at something like 0.05 Conduct a statistical testConduct a statistical test Obtain a p-valueObtain a p-value

Parametric tests Parametric tests – Pearson Product Correlation Coefficient Pearson Product Correlation Coefficient – Student t-Test Student t-Test – The z-Test The z-Test – ANOVAANOVA

Nonparametric tests Nonparametric tests – Chi-Squared Chi-Squared – Spearman Rank Coefficient Spearman Rank Coefficient – Mann-Whitney U Test Mann-Whitney U Test – Kruskal-Wallis TestKruskal-Wallis Test