Ryerson Research Methods Data Analysis 1

Front 1

Measurement (3 points)

Back 1

Measurementis fundamental to the research process

Surveyquestionnaires aim to measure particular concepts and phenomena

Theyallow us to convert an ambiguous concept into a precise empiricalmeasurement

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Measurement (3 more points)

Back 2

oThetask is to convert the questions & answers from the survey into precisemeasurements oForexample:The question “How old are you” gets converted for statistical purposes into avariable named “age” – all survey responses to the age question get coded andstored under the “age” variable

oThe“age” variable and its data becomes an empirical measurement and is stored in adatabase for statistical analysis

Front 3

3 levels of measurement

Back 3

oNominal level

oOrdinal level

oInterval-ratio level

Front 4

Nominal Level (3 points and some examples)

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oNominallevel categories simply name the different attributes in a variable

oThesecategories are mutually exclusive or dichotomous

oThereis no overlap, the categories are completely separate and independent from eachother

oExample:religion,political party affiliation, month of year born, are good examples

Front 5

Ordinal Level (3 points and some examples)

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oOrdinallevel measurements are nominal level categories that are ranked

oMutuallyexclusive, but also organized in some special order

oRankedfrom high to low; from small to large; worst to best

oForexample: Education Level: elementaryschool, high school; some post secondary, completed post secondary; postgraduate education

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Ordinal Variable: 2 points and an example

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oIf the level of measurement in avariable is “ordinal” then the variable is referred to as an “ordinal variable”

oOrdinal variables are used forspecific statistical tests that look at differences between the quality of “rankordering”

oFor example:differences between the very educated, the somewhat educated, and the not veryeducated on hours of weekly exercise

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Inter-ratio Level (2 points)

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oInterval-ratiolevel categories share all the same qualities associated with nominal andordinal variables, but also allows us to measure the distance between thecategories

oThe distances between the categories are numerical, incremental and precise –ranging from 0 to infinity

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Interval-ratio Variable (2 points and an example)

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oIfthe level of measurement in a variable is “interval-ratio” then the variable isreferred to as an “interval-ratio variable”

oInterval-ratiovariable are used for statistical tests that look at specific differencesbetween the categories

oForexample: The average GPA score across first year students

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Measurement Options: how could "income level" be coded as interval-ratio, nominal and ordinal variables?

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income is often coded a interval-ratio variable

But can be collapsed into an ordinal measurement Low, middle and high income

Can be collapsed into a nominalmeasurementIncome: Yes or no

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2 more levels of measurements and their benefits

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oDiscreteor Continuous variables

oThese distinctions give us information about the underlying characteristics ofthe variableoAllowthe researcher to understand whether these values can be divided into smallerunits or numbers

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Discrete Variables (3 points and some examples)

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oVariableswhose values are completely separate from each other – mutually exclusive

oThesevalues cannot be reduced or sub-divided into smaller units or numbers

oTheyinclude nominal, ordinal or inter-ratio variables that cannot be broken downfurther o

oForexample: Discrete: # ofsiblings, education level, political affiliation, favourite color

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Continuous Variables (3 points and some examples)

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oVariableswhose values are are not restricted, but can occupy any value over a continuous range

oThesevalues can be reduced or sub-divided into smaller units or numbers

oTheyprimarily include inter-ratio variableso

oForexample: Continuous: Height, mass, time, density, volume

Front 13

Definition and 3 aspects to univariate analysis

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The examination of the distribution of cases of only one variable:

oMeasures of Central Tendency

oDispersion or Variability

oDistributions

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Measures or central tendency (also known as ______?) 4 points, three categories

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Also known as "averages"

oExpresses the typical value of avariable

oOne value that best represents anentire group of scores

oReduces data to most manageableform

These averages come in threeforms:Mean Mode Median

oEach provides a different type ofinformation about the distribution of scores

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Definitions for Mean, Median and Mode

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oTheMean is an arithmetic calculation:Dividing the sum of the variables by the total number of cases

oTheMode is the most frequently occurring value or attribute

oTheMedian is the “middle” attribute or value in the ranked distribution ofobserved scores, 50 percent above and 50 percent below

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Dispersion: also known as _______

Definition and 3 common measures of dispersion

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VARIABILITY

summarizes the way values are distributed or spread around some centralvalue like the mean

The three most common measures of variability:

oRange

oVariance

oStandard Deviation

Front 17

Range Definition (2 points) and example

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oThesimplest measure of dispersion

oThedistance separating the highest and lowest value in a variable

oExample:Besidesreporting the mean age of first year cohort, we might also indicate the agerange from 18 to 32 years of age

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Variance - 2 points and process for deriving mathematically

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omeasures how far each numberin the set is from the mean

oA variance of zero indicates thatall the values are identical

oVariance = Average of the squareddifferences of each data point from the Mean

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Standard Deviation (3 points)

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oIsan index of the amount of variability in a set of scores

oHighstandard deviation indicates that the data are more dispersed or spread outaround the central value – like the mean

oAlower standard deviation indicates that the data are more bunched together

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Standard Deviation (4 more points)

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oInpractical terms, it is the average distance from the mean

oThelarger the standard deviation, the larger the average distance each score isfrom the mean

oIfthe standard deviation equals zero, there is no variability in set of scores

oCalculation:mathematical formula!! (Square root of average distance from the mean)

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SD formula (4 steps)

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o SD formula finds the difference between each individual score and the mean

oSquareseach difference and sums them all together

oThendivides the size of the sample

oTakesthe square root of the results

Front 22

Normal Curve (4 points)

Back 22

oNormalcurve or bell-shaped curve is a visual representation of a distributions ofscoresoNormaldistribution – the mean, mode and median are equal to one another

oIfthe median and mode are different, then the distribution is skewed in onedirection or another

oThenormal curve is perfectly symmetrical about the mean – one half of curve is amirror image of other

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Skewed Distribution (2 points)

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oIs the measure of the lack ofsymmetry or lopsidedness of a distributionoIf the median and mode aredifferent, then the distribution is skewed in one direction or another

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Two types of skew

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oPositively (right) skew – Large occurrence of scores at the low end, the relatively few scores at the high end create a right skew with a long right (positive) tail

oNegatively (left) skew – Large occurrence of scores at the high end, the relatively few scores at the low end create a left skew and a long left tail