What is Statistics?What is Statistics?Set of Set of methodsmethods and and rulesrules for for organizingorganizing summarizingsummarizing, and , and interpretinginterpreting information information

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PopulationPopulation

Sample Sample

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PopulationPopulation and and SampleSample Population:Population: Population is the set of all Population is the set of all

individuals of interest for a individuals of interest for a particular study. particular study. Measurements related Measurements related to Population are PARAMETERS.to Population are PARAMETERS.

Sample: Sample: Sample is a set of individuals Sample is a set of individuals

selected from a population.selected from a population. Measurements related to sample are STATISTICS.Measurements related to sample are STATISTICS.

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StatisticsStatisticsThe people chosen for a The people chosen for a

study are its study are its subjects or subjects or participantsparticipants, collectively , collectively called a called a samplesample

–The sample must be The sample must be representativerepresentative

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Role of Role of StatisticsStatistics in in Research Research Selecting a Selecting a ProblemProblem (Is the (Is the hypothesishypothesis clear, clear,

concise and reasonable?)concise and reasonable?)

Operational Definitions of VariablesOperational Definitions of Variables Ex. The Effects Of Ex. The Effects Of Watching Tv Violence Watching Tv Violence On On ChildrenChildren

InstrumentsInstruments Accuracy of the InstrumentsAccuracy of the Instruments Large Variance, Good Reliability and ValidityLarge Variance, Good Reliability and Validity

Data CollectionData Collection Use of StatisticsUse of Statistics

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Merriam Webster Dictionary and Thesaurus Merriam Webster Dictionary and Thesaurus Definition of Definition of Short-SightedShort-Sighted

1. Near sighted or Myopia1. Near sighted or Myopia

2. Lacking Foresight 2. Lacking Foresight

3. Lacking the power of foreseeing 3. Lacking the power of foreseeing

4. Inability to look forward4. Inability to look forwardMy Operational Definition:My Operational Definition:5. person who is able to see near things 5. person who is able to see near things more clearly than distant ones, needs to wear more clearly than distant ones, needs to wear corrected eyeglasses prescribed corrected eyeglasses prescribed (measured) (measured) by by OphthalmologistOphthalmologist..

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The American Heritage DictionaryThe American Heritage Dictionary Definition of IntelligentDefinition of Intelligent 1. Having or indicating a high or satisfactory 1. Having or indicating a high or satisfactory

degree of intelligence and mental capacitydegree of intelligence and mental capacity My Operational Definition of Intelligent:My Operational Definition of Intelligent: 2. Revealing or reflecting good judgment or 2. Revealing or reflecting good judgment or

sound thought : skillful sound thought : skillful And is And is measuredmeasured by the by the IQ score IQ score from the from the

Stanford-Binet V Stanford-Binet V IQ Test IQ Test ( in the Method ( in the Method section of the research paper we write about section of the research paper we write about the the reliabilityreliability and and validity validity of this of this instrument). Or select WAIS or WISCinstrument). Or select WAIS or WISC

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99

1010

SStatistical tatistical PPackage for the ackage for the SSocial ocial SSciencesciences

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Key TermsKey Terms Constant Constant I.e. I.e. temptemp in in learninglearning and and hungerhunger

Variable: Variable: Any characteristic of a person, object or Any characteristic of a person, object or

event that can change (vary). event that can change (vary).

IV IV manipulate manipulate DV DV measure measure Discrete Numbers 1, 2 , 3, 14Discrete Numbers 1, 2 , 3, 14 Continues Numbers 1.3, 3.6Continues Numbers 1.3, 3.6

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Key TermsKey Terms Measurement:Measurement: Quantifying an Quantifying an

observable observable behavior behavior oror when when quantitative quantitative value is given value is given to a behavior to a behavior

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WHAT IS ALL THE FUSS?WHAT IS ALL THE FUSS?

MeasurementMeasurement should be as should be as preciseprecise as as possible. The possible. The precisions of your precisions of your measurement tools measurement tools will determine the will determine the precession of your research.precession of your research.. .

In psychology, most variables are In psychology, most variables are probably measured at the probably measured at the nominalnominal oror ordinalordinal levellevel

But—how a variable is measured can But—how a variable is measured can determine the determine the level of precisionlevel of precision

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Hypothesis is a Research TopicHypothesis is a Research Topic ““High Cholesterol Can High Cholesterol Can Cause Cause Heart Heart

Attack” Attack” Experimental ResearchExperimental Research

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Hypothesis is a Research TopicHypothesis is a Research Topic ““Heart Attack is related to High Heart Attack is related to High

Cholesterol” Cholesterol” Correlational ResearchCorrelational Research

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Key TermsKey Terms Variable: Variable: Any characteristic of a person, object or Any characteristic of a person, object or

event that can change (vary). event that can change (vary).

Independent Variable, IVIndependent Variable, IV Dependent Variable, DVDependent Variable, DV ConstantConstant Discrete NumbersDiscrete Numbers Continues NumbersContinues Numbers

Confounding VariableConfounding Variable Intervening VariablesIntervening Variables 1818

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Confounding VariablesConfounding Variables Confounding variables are Confounding variables are

variables that the variables that the researcherresearcher failed failed to controlto control, , or eliminate, damaging or eliminate, damaging the internal validity of an the internal validity of an experiment. Also known as a experiment. Also known as a third third variable variable or a mediator variable, can or a mediator variable, can adversely affect the relation adversely affect the relation between the independent variable between the independent variable and dependent variable. and dependent variable.

Ex. NextEx. Next2020

Confounding VariablesConfounding Variables Ex: A research group might design Ex: A research group might design

a study to determine if a study to determine if heavy heavy drinkers die at a younger agedrinkers die at a younger age. . Heavy drinkers may be more likely Heavy drinkers may be more likely to to smokesmoke, or eat , or eat junk foodjunk food, all of , all of which could be factors in reducing which could be factors in reducing longevity. A third variable may longevity. A third variable may have adversely influenced the have adversely influenced the results.results.

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Intervening VariablesIntervening Variables

A variable that A variable that explains a relation explains a relation or or provides a provides a causal link causal link between other between other variables.variables.

Also called Also called “Mediating Variable” “Mediating Variable” oror “intermediary variable.”“intermediary variable.”

Ex. Next slideEx. Next slide

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Intervening VariablesIntervening Variables Ex: The statistical association between Ex: The statistical association between

incomeincome andand longevitylongevity needs to be explained needs to be explained because just having money does not make because just having money does not make one live longer. one live longer.

Other variables Other variables intervene intervene between between money money and long life. and long life. People with high incomes tendPeople with high incomes tend

to have to have better medical care better medical care than those with than those with low incomes. Medical care is anlow incomes. Medical care is an

intervening variableintervening variable. It mediates the relation . It mediates the relation between income and longevity. between income and longevity.

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CONTINUOUS VERSUS CONTINUOUS VERSUS DISCRETE VARIABLESDISCRETE VARIABLES

Discrete variables (categorical)Discrete variables (categorical)– Values are defined by category boundariesValues are defined by category boundaries– E.g., genderE.g., gender

Continuous variablesContinuous variables– Values can range along a continuumValues can range along a continuum– E.g., heightE.g., height

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Role of Role of StatisticsStatistics in in ResearchResearch

DescriptiveDescriptiveVSVSInferentialInferential

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Descriptive & Descriptive & Inferential Inferential StatisticsStatistics Descriptive Descriptive

DescribesDescribes the distribution of scores and the distribution of scores and values by using values by using Mean, Median, Mode, Mean, Median, Mode, Standard Deviation, Variance, and Standard Deviation, Variance, and CovarianceCovariance

InferentialInferential

InferInfer or draw a conclusion from a sample.or draw a conclusion from a sample.

by using by using statistical procedures statistical procedures such as such as Correlation, Regression, t-test, Correlation, Regression, t-test, ANOVA..etcANOVA..etc 2626

Descriptive & Descriptive & Inferential Inferential StatisticsStatistics

Scales of Measurement Scales of Measurement Frequency Distributions and GraphsFrequency Distributions and Graphs Measures of Central TendencyMeasures of Central Tendency Standard Deviations and Variances Standard Deviations and Variances Z ScoreZ Score t-Statistict-Statistic CorrelationsCorrelations Regressions………etc.Regressions………etc.

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Scales of Measurement (Scales of Measurement (NOIRNOIR))Nominal ScaleNominal Scale

Qualities Example What You Can Say

What You Can’t Say

Assignment of labelslabels

Gender— (male ormale or femalefemale))Preference—(like or dislike)Voting record—(for or against)

Each observation

belongs belongs in its in its own own categorcategoryy

An observation represents “more” “more” or “less” or “less” than another observation 2828

ORDINAL SCALEORDINAL SCALE

Qualities Example What You Can Say

What You Can’t Say

Assignment of values along some underlying dimension (order)(order)

Rank in Rank in collegecollegeOrder of finishing a race

One observation is ranked above above or below or below another.

The amount amount that one that one variable variable is more is more or less or less than another

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INTERVAL SCALEINTERVAL SCALE

Qualities Example What You Can Say

What You Can’t Say

Equal Equal distances distances between between pointspoints

““arbitrary arbitrary zero”zero”

Number of words spelled correctly onIntelligence test scoresTemperaturTemperaturee

One One score score differs differs from from another another on some measure that has equally appearing intervals

The The amount of amount of difference difference is an exact is an exact representation of differences of the variable being studied

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RATIO SCALERATIO SCALE

Qualities Example What You Can Say

What You Can’t Say

Meaningful and non-non-arbitrary arbitrary zerozeroAbsolute Absolute zerozero

AgeAgeWeightWeightTime?Time?

One One value is value is twice as twice as much much as another or no quantity of that variable can exist

Not much!

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LEVELS OF MEASUREMENTLEVELS OF MEASUREMENT

Variables are measured at one of these four levelsVariables are measured at one of these four levels Qualities of one level are characteristic of the next level upQualities of one level are characteristic of the next level up The more precise (higher) the level of measurement, the The more precise (higher) the level of measurement, the

more accurate is the measurement processmore accurate is the measurement process

  

   

Level of Level of MeasurementMeasurement

For ExampleFor Example Quality of LevelQuality of Level

RatioRatio Rachael is 5Rachael is 5’’ 10 10”” and Gregory and Gregory is 5is 5’’ 5 5””

Absolute zeroAbsolute zero

IntervalInterval Rachael isRachael is 55”” taller taller than than GregoryGregory

An inch is an inch is an An inch is an inch is an inchinch

OrdinalOrdinal Rachael isRachael is tallertaller than Gregorythan Gregory Greater thanGreater than

NominalNominal Rachael is Rachael is taltall l and Gregory is and Gregory is shortshort

Different fromDifferent from

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CHAPTER 2CHAPTER 2

Frequency Frequency DistributionsDistributions

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Graphs/ChartsGraphs/Charts http://www.sao.state.tx.us/resources/Manuals/Method/data/11GRPHD.pdf

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Frequency Distributions and Graphs Frequency Distributions and Graphs BarBar

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Frequency Distributions and Graphs Frequency Distributions and Graphs HistogramHistogram

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PolygonPolygon

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Frequency Distributions and GraphsFrequency Distributions and Graphs

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4040

4141

4242

4343

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Mesokurtic, Mesokurtic, Normal,Normal, Platykurtic, Platykurtic, Leptokurtic, Leptokurtic,

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Frequency DistributionsFrequency Distributions

Frequency Distributions (ƒ)Frequency Distributions (ƒ)

FD is the number of FD is the number of frequencies,frequencies,

Or when a score repeat itself in Or when a score repeat itself in a group of scores. a group of scores.

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Frequency DistributionsFrequency Distributions Frequency Distributions (ƒ)Frequency Distributions (ƒ)

2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 4, 2 4, 2

Σƒ=N=14Σƒ=N=14

ΡΡ=ƒ/N =ƒ/N PProportion roportion

%=P x 100 %=P x 100 μ=ΣƒX/Σƒ μ=ΣƒX/Σƒ mean for mean for

frequency distribution onlyfrequency distribution only 4848

Frequency DistributionsFrequency Distributions Frequency Distributions (ƒ)Frequency Distributions (ƒ) X f fX X f fX Ρ=Ρ=ƒ/N %=P x 100 Cum%ƒ/N %=P x 100 Cum%

6 1 6 1/14=.07 7%6 1 6 1/14=.07 7%

5 25 2

4 24 2

3 33 3

2 42 4

1 21 24949

Frequency Distribution TableFrequency Distribution Table

X f fX P=f/n %=px100

Cumulative %

6 1 6 1/14=.07 7% 7%

5 2 10 2/14=.14 14% 21%

4 2 8 2/14=.14 14% 35%

How do you Calculate Cumulative Percent ?How do you Calculate Cumulative Percent ?

Add each new individual percent to the running Add each new individual percent to the running tally of the percentages that came before it. tally of the percentages that came before it.

For example, if your dataset consisted of the four For example, if your dataset consisted of the four numbers: numbers: 100, 200, 150, 50 100, 200, 150, 50 then their individual then their individual values, expressed as avalues, expressed as a percent percent of the total of the total (in this (in this case case 500), 500), are are 20%, 40%, 30% and 10%. 20%, 40%, 30% and 10%.

The cumulative percent would be:The cumulative percent would be:1.Proportion 2.percentage1.Proportion 2.percentage

100/500=0.2x100: 20%100/500=0.2x100: 20% 200: 200: (i.e. (i.e. 20% 20% from the step before + from the step before + 40%)40%)= = 60% 60% 150: 150: (i.e. (i.e. 60% 60% from the step before + from the step before + 30%)30%)= = 90%90% 50: 50: (i.e. (i.e. 90% 90% from the step before + from the step before + 1010%) %) == 100% 100%

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Frequency DistributionsFrequency Distributions

X=2, f=4, N=14X=2, f=4, N=14 Ρ=Ρ=ƒ/Nƒ/N

P=4/14=.29P=4/14=.29 %=P x 100= 29%%=P x 100= 29% X=3, f=4, N=14X=3, f=4, N=14 P=3/14=.21P=3/14=.21 %= 21%%= 21%

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