Descriptive and Inferential Statistics Part 1 2013 2014

8/12/2019 Descriptive and Inferential Statistics Part 1 2013 2014

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Descriptive statistics andinferential statistics


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Preparing Data for AnalysisScoring proceduresTabulation and coding


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What does it means scoring data?Scoring data means that the researcherassigns a numeric score (or value) toeach response category for eachquestion on the test/instrument tocollect the data


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Categorizing dataThe statistical tests- depend on the typeof data being collectedIt is important to understand the typesof data before scoring procedure isconducted


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Types of categorical and quantifiable data

Data

Categorical Quantifiable

Nominal Ordinal Interval Ratio


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What is categorical data?Data which cannot be quantifiednumerically

BUTPlace into sets or categories ( nominaldata ) or ranked in some way ( ordinaldata )


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What is quantifiable dataData can be measured numericallyMore preciseConsist of interval data and ratio data


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Four kinds of measurement

scalesNominalOrdinalIntervalRatio


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Nominal data A name value or category with no orderor ranking

Example:-Type of schoolTypes of teaching methodGenderRace


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Ordinal dataComprises an ordering or ranking ofvalues

ALTHOUGHThe ranks are not intended to be equal(for example, an attitude questionnaire)


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ExampleHow of often you felt like insulting astudent (Please tick one)Every dayOnce a weekSometimesNever


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Other examples of ordinal

dataQuestions that rate the quality ofstudents performance (for example,very good, good, fair, poor)

Agreements of attitude towards science(Strongly agree, Agree, Disagree,Strongly disagree)


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Interval dataNumerical values are assigned along aninterval scale withEqual intervalsThere is no zero point where the traitbeing measured does not exist


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Number of students scoring withinvarious ranges in IQ test

Scores Frequency76-80 181-85 0

86-90 491-95 1096-100 21

101-105 25106-110 48111-115 18

116-120 11


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Other examples of interval dataTemperature

Blood pressure


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Ratio dataSame characteristics with interval data

BUTThere is an absolute zero that representsome meaning

Example:-Costs, sales, number of students, number

of teachers,


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Types of categorical and quantifiable data

Data

Categorical Quantifiable

Nominal Ordinal Interval Ratio


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Example of the scoring dataStudents should be given an opportunityto select a school of their choiceStrongly agree _____

Agree _____Disagree _____Strongly Disagree _____


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A numeric score (or value) to

each response category

Strongly agree 4 Agree 3Disagree 2

Strongly Disagree 1


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Other example of scoring dataHow of often you felt like insulting astudent (Please tick one)Every dayOnce a weekSometimesNever


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each response category

Every day 4Once a week 3Sometimes 2

Never 1


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An example of multiple choice

questionThe quantity of charge which passesthrough a circuit is measure in

A. AmpsB. VoltsC. Coulombs *D. Watts


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each response categoryCorrect response- 1 mark,Incorrect response- 0 mark

A. Amps 0B. Volts 0C.

Coulombs 1D. Watts 0


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Scoring Procedures for Open

Ended itemsEach participant tests should be scoredin the same way and with one criterionGreatly facilitated if a standardizedinstrument is usedScoring key should be providedRecheck the consistencyClean the data


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Clean the dataWhen a large number of variables andmany individual records, it is easy toenter a wrong figure or to miss an entryDo frequency analysis on a column datato throw up any inconsistent/ spurious

figures


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Scoring Procedures forMore complex if is involved open endedquestions

Develop a marking scheme Advisable to have at least one other personindependently score some of the tests

Tried out by administering the tests to similarpopulation as one from the actual study


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Example of open ended questionDefine population and sample

________________________________ ________________________________ ________________________________

(2 marks)


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The marking schemePrecise and complete definition = 2Precise but incomplete definition= 1Incorrect definition= 0


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Tabulation and coding After test/instruments have been scoredTransfers to summary data sheet/computer. For example SPSS data sheetOrganize data in the SPPS to facilitatesexamination and analysis of the data


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Tabulation and CodingTabulation is organizing data

Identifying all information relevant to the analysis

Separating groups and individuals within groupsListing data in columns

Coding Assigning names to variables

EX1 for pretest scoresSEX for genderEX2 for posttest scores

Objectives 2.1, 2.2, & 2.3


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Tabulation and CodingCoding

Assigning identification numbers to

subjects Assigning codes to the values of non-numerical or categorical variables

Gender: 1=Female and 2=Male

Subjects: 1=English, 2=Math, 3=Science, etc.Names: 001=Ahmad, 002=Rahman,003=Salleh, 256=Karim

Objectives 2.2 & 2.3


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Example A study investigating the interactionbetween two types of instruction andtwo levels of ability (A 2 x 2 factorialdesign)Four subgroups are involved


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68 marks70 marks79 marks




Method A Method B

High ability

Low ability


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4 column involvedStudents id Types of instructionLevel of abilityTotal scores


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Students id1 represents Ahmad2 represents Bakar3 represents Malik4 represents Abu

Etc..


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Types of instructionTwo types of instruction, namely :cooperative and traditional method1 represents cooperative method2 represents traditional method


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Level of abilityHigh and low ability1 represents high ability2 represents low ability


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Total ScoresExample: 50 items/questionsCorrect answer- 1 mark

Incorrect answer 0 markFull mark: 50 marksExample:-If 20 items are answered correctlyby Ahmad, that means he will get20 marks for his total scores


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Another example A study investigating the effect ofschool location on learning motivation

among male and female students


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Four columns involvedStudents idSchool locationStudents gender Learning motivation


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Students id1 represents Ahmad2 represents Bakar3 represents Malik4 represents AbuEtc..


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School locationUrban or rural1 represents urban2 represents rural


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Students gender Male and female students1 represent male2 represent female


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Learning motivation5 itemsLikert scale

Example:-I like to study in order to get good marks inthe examinationStrongly agree 4

Agree 3Disagree 2Strongly Disagree 1


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How to calculate item which have

Likert scale respons

Total up all the items response for eachperson to get the total scoresDivide the total scores by the number ofthe items to get the mean of learningmotivation for each students


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Item 1 = 4Item 2 = 3Item 3 = 4Item 4 = 2Item 5 = 1

Total scores= 4+3+4+2+1=14

How many items? 5 itemsMeans scores of learning motivation= 14/5 = 2.5


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After you have prepared for dataanalysis, how do you analyse thedata?


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How to analyse the dataDescriptive statisticsInferential statistics


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Descriptive statisticsDescribe trends in the data to a singlevariable on your instrument

Example:What is the learning motivation ofsecondary school students?


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Descriptive statisticsWhat is the learning motivation ofsecondary school students?

In order to answer that, we needdescriptive statistics that indicategeneral tendencies in data, the spread

of scores, or relative position


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Central TendencyPurpose to represent the typical scoreattained by subjects

Three common measuresModeMedian

Mean

Objective 4.1


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Spread of scores (variability)Purpose to measure the extent towhich scores are spread apart

Four measuresRangeQuartile deviation

VarianceStandard deviation

Objective 5.1


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The normal curve


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The Normal CurveIf a sufficient number of subjects aremeasure, possibly a variable or

variables yield a normal, bell-shapedcurveIf a variable is normally distributed,

then several things are true

50% of the scores are above the


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50% of the scores are above themean and 50% of the scores are

below the mean


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The mean, median and the mode

are the same


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The Normal Curve

MostScores Fewer Number of

Subjects who Attained the Scores

Fewer Number ofSubjects who

Attained the Scores


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The Normal Curve

MostScores Fewer Number of

Subjects who Attained the Scores


Attained the Scores


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The Normal Curve


Attained the Scores


Attained the Scores

MostScores


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The Normal Curve


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The Normal CurveFourth, the same number, orpercentage, of scores is between the

mean and plus one standard deviation(mean + 1 SD) as is between the meanand minus one standard deviation

(mean 1 SD), and similarly for mean+ SD and mean + SD


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If scores are normally distributed

Mean + 1.0 SD = approximately 68% ofthe scores

Mean + 2.0 SD = approximately 95% ofthe scoresMean + 3.0 SD = approximately 99.7%

of the scores


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Skewed DistributionsResearch data usually more or lessapproximate a normal curve

When a distribution is not normal, it issaid to be skewed, and the values ofthe mean, the median and the mode

are differentIn a skewed distribution, there aremore extreme scores at one end than

the other


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Skewed DistributionsIf the extreme scores are at lower endof the distribution, the distribution is

said to be negatively skewedIf the extreme scores are at the upper,or higher, end of the distribution, the

distribution is said to be positivelyskewedThe mean is pulled in the direction of

the extreme scores


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Which one is positively skewedand negatively skewed?


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Skewed DistributionsFor a negatively skewed distribution,the mean is always lower, or smaller

than the medianFor a positively skewed distribution, themean is always higher or greater than

the median

For a negatively skewed


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For a negatively skeweddistribution, the mean is always

lower, or smaller than themedian

For a positively skewed distribution


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For a positively skewed distribution,the mean is always higher or

greater than the median


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Assessing normality using SPSS

Click on AnalyzeClick on Descriptive Statistics , thenExploreClick the variable/s you are interestedClick the arrow button to move theminto Dependent ListClick on the Plots button


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Under Descriptive , click theHistogram

Click on Normality Plots with TestClick on ContinueClick OK


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Interpretation of output fromexplore

Skewness and kurtosis valuesTest of Normality (Kolmogorov Smirnovstatistic)HistogramNormal Probability plots (Normal Q-QPlots)


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Kurtosis A measure of the peakedness or the flatness of a distribution A kurtosis value near zero (0) indicates ashape close to normal

A positive value of kurtosis indicates a shapeflatter than normal

A positive value of kurtosis indicates a shape

more peaked than normal A range of kurtosis value between -1.0 and+1.0 is considered as excellent, but a valuebetween -2.0 and +2.0 is consideredacceptable


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Kurtosis


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SkewnessMeasures to what extent a distributionvalues deviates from symmetry around

the mean A value of zero represents a symmetricor evenly balanced distribution

A positive skewness indicates a greaternumber of smaller values

A negative skewness indicates a greaternumber of larger values


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Skewness

es o orma y o mogorovS i i i )


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y gSmirnov statistic)

Test of Normality which is KolmogorovSmirnov statistic assesses the normality

of the distribution scores A non-significant result (significantvalue of more than 0.05) indicates

normality A significant result (significant value of0.05 or less than 0.05) suggestsviolation of the assumption of normality


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Histogram and Normal Q-Q Plots

The actual shape of distribution can be seenin histogram

In order to support the claim that the data isnormally distributed, refer to normal Q-Q plotNormal Q-Q plot- the observed value for eachscore is plotted against the expected valuefrom the normal distribution

A reasonably straight line suggests a normaldistribution


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Graphic representationBar chartHistogramPie chart


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Inferential statistics

h h f f l


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What is the purpose of inferentialstatistics?

To compare two or more groups on theindependent variable in terms of the

dependent variable ( for example: Isthere a significant differencebetween boys and girls on selfesteem ?)

Independent variable : gender (boysand girlsDependent variable : self esteem

I f i l i i i l


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Inferential statistics involveshypothesis testing

Null hypothesis: There is no significancedifference between boys and girls on

self esteem Alternative hypothesis: There is asignificant difference between boys and

girls on self esteem

O h f i f i l


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Other purpose of inferentialstatistics

Relate two or more variables (forexample: Does self esteem relate to

academic achievement?)Null hypothesis: There is no significantrelationship between self esteem andacademic achievement

Alternative hypothesis: There is asignificant relationship between selfesteem and academic achievement


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Types of Inferential Statistics

Two issues discussedSteps involved in testing for significanceTypes of tests


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Steps in Statistical TestingState the null and alternativehypotheses

Set alpha levelIdentify and compute the test statisticCompare the computed test statistic tothe criteria for significance

Objectives 20.1 20.9


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Alpha Level

An established probability level whichserves as the criterion to determinewhether to accept or reject the nullhypothesisCommon levels in education

.01

.05 (the most common)

.10


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Reject the null hypothesis

If the probability values is less than

or equal to the significance level,then reject the null hypothesis, andconclude that the research findingis statistically significant

Objective 20.9


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Inferential Statistics


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T-TestDetermine whether two means aresignificantly different at a selected

probability level


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Independent Samples T-TestDetermine whether there is a probablya significant difference between means

of two independent samples


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Independent samplesTwo samples that are randomly formedwithout any type of matching

The members of one sample are notrelated to members of the other samplein any systematic way other than they

are selected from the same population


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Example

Group 1 Test Scores Group 2 Test Scores

34567

23334

Are these two sets of scores significantlydifferent? They are different, but are they

significantly different?


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Presenting the results for


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Presenting the results forindependent samples t-test

An independent samples t-test wasconducted to compare the achievement

test scores for boys and girls. Therewas no significant difference in scoresfor boys (M=34.02, SD= 4.91), andgirls (M= 33.17; SD = 5.71; t (434) =1.62, p =0.11).


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Non independent sample t-testor

Paired samples t-test


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Nonindependent sample t-testWhen samples are not independent, themembers of one group are

systematically related the members of asecond groupThe most familiar example is if the

same group takes the test at twodifferent timesIn SPSS, it is known as Paired Samples

T-Test


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Presenting the results for paired


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Presenting the results for pairedsamples t-test

A paired samples t-test was conductedto evaluate the impact of the

intervention on students achievementscores. There was statisticallysignificant decrease in achievementscores from Time 1 (M=40.17, SD=5.16) to Time 2 (M= 37.5, SD= 5.15),t(29) = 5.39, p ,0.005.

One Way Analysis of Variance


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One Way Analysis of Variance(One Way ANOVA)

To determine whether there is asignificant difference between more

than two means a selected probabilitylevel


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ExampleGroup 1 Test

ScoresGroup 2 Test

ScoresGroup 3 Test

Scores

12223

23456

44457

Are these three sets of scores significantlydifferent? They are different, but are they

significantly different?


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Multiple comparisonIf the F ratio is determined to benonsignificant, the party is over

But what if it is significant?Multiple comparison are used todetermine which means are significantly

different from other means


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ExampleGroup 1 Test

ScoresGroup 2 Test

ScoresGroup 3 Test

Scores1

222

3

2

345

6

4

445

7

ANOVA results show that there are significantdifference between the means of three groups


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The use of Multiple


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pComparison

Multiple comparison procedure used todetermine whether the means of:-

- group 1 differs from group 2, OR- group 1 differ from group 3, OR- group 2 differs from group 3?

Example of multiple comparison


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Example of multiple comparisontechnique

Tukey TestScheffe Test

Duncan TestBonferroni TestHSD Test


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Presenting the results from one


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Presenting the results from oneway ANOVA with post hoc test

A one way between group analysis ofvariance was conducted to explore thedifference of achievement scoresbetween three group (Group 1, Group2, Group 3). There was a statisticallysignificant difference at the p


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Presenting the results from oneway ANOVA with post hoc test

Post-hoc comparisons using the Tukeytest indicated that the mean score for

Group 1 (M=21.36, SD= 4.55) wassignificantly different from Group 3 (M=22.96; SD= 4.49). Group 2 (M= 22.10,SD= 4.15) did not differ significantlyfrom either Group 1 or 3.


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Two Way ANOVA Analysis of data which involve factorialdesign

What is factorial design?


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Factorial designWhen two or more independentvariables involved in a study


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ExampleMethod A Method B

High ability

Low ability

2 X 2 Factorial Design


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2 ways ANOVADetermine main effect on achievementfor method (determine there is a

significant difference between meanscores of Method A and Method B)


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2 ways ANOVADetermine main effect on achievementfor ability (determine there is a

significant difference between meanscores of high and low ability)


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Multiple RegressionMore advance than correlation and linearregressionCorrelation- relationship between two

variable (Ex: relationship between attitudetowards learning and academic achievement)Linear regression- the relationship betweenpredictor variable and dependent variable(Ex: Can attitude towards learning predictacademic achievement of students?)


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Multiple RegressionMultiple regression- a combination of twoor more variables to predict a dependentvariable

(Ex: Can attitude towards learning andthinking ability predict academicachievement of students?)

Documents

Descriptive and Inferential Statistics Part 1 2013 2014