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Data Analysis / Applied Statistics & Excel

Fraser Health Authority, 2011

The Fraser Health Authority (FH) authorizes the use, reproduction and/or

modification of this publication for purposes other than commercial redistribution. Inconsideration for this authorization, the user agrees that any unmodifiedreproduction of this publication shall retain all copyright and proprietary notices. Ifthe user modifies the content of this publication, all FH copyright notices shall beremoved, however FH shall be acknowledged as the author of the sourcepublication.

Reproduction or storage of this publication in any form by any means for the purposeof commercial redistribution is strictly prohibited.

This publication is intended to provide general information only, and should not berelied on as providing specific healthcare, legal or other professional advice. TheFraser Health Authority, and every person involved in the creation of this publication,disclaims any warranty, express or implied, as to its accuracy, completeness orcurrency, and disclaims all liability in respect of any actions, including the results ofany actions, taken or not taken in reliance on the information contained herein.

Michael Wasdell, MA

EpidemiologistEvaluation & Research Services

[email protected]

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Susan ChunickSusan Chunick DirectorDirector

Camille VirayCamille Viray Education and CommunicationsEducation and Communications

CoordinatorCoordinator

Dina ShafeyDina Shafey Research Ethics CoordinatorResearch Ethics Coordinator

Magdalena SwansonMagdalena Swanson Research and GrantResearch and Grant

Development FacilitatorDevelopment Facilitator

Michael WasdellMichael Wasdell EpidemiologistEpidemiologist

Department of Evaluation and Research ServicesDepartment of Evaluation and Research Services

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http://http://research.fraserhealth.caresearch.fraserhealth.ca//
http://research.fraserhealth.ca/http://research.fraserhealth.ca/http://research.fraserhealth.ca/http://research.fraserhealth.ca/http://research.fraserhealth.ca/http://research.fraserhealth.ca/http://research.fraserhealth.ca/

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ObjectivesObjectives

Understand the relationshipUnderstand the relationship

between the research question,between the research question,research designs/method, typeresearch designs/method, typeof data and statistical analysis;of data and statistical analysis;

Use tools and resources toUse tools and resources toidentify the appropriateidentify the appropriate

statistical analysis, and;statistical analysis, and;

Learn how to use the ExcelLearn how to use the ExcelData Analysis utility.Data Analysis utility.

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What is Statistics?What is Statistics?

The collecting, summarizing, andThe collecting, summarizing, and

analyzing of data.analyzing of data. The term also refers to raw numbers, orThe term also refers to raw numbers, or

statsstats, and to the summarization of data., and to the summarization of data.

Why is a physician held in much higher esteem than aWhy is a physician held in much higher esteem than a

statistician?statistician?

A physician makes an analysis of a complex illnessA physician makes an analysis of a complex illnesswhereas a statistician makes you ill with a complexwhereas a statistician makes you ill with a complex

analysis!analysis!

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Descriptive StatisticsDescriptive Statistics: Describe research: Describe research

findingsfindings e.g. Frequencies, averages.e.g. Frequencies, averages.

Inferential StatisticsInferential Statistics: Makes inferences: Makes inferencesabout the population,about the population, usuallyusually based on abased on arandom sample.random sample.

Allows generalization to population.Allows generalization to population.

QuasiQuasi--experimental research does notexperimental research does not

employ randomization, but might useemploy randomization, but might useinferential statistics.inferential statistics.

Types of StatisticsTypes of Statistics

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Statistics made simple

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1. Identify overall research goal.

2. Identify independent and dependent

variables.3. Describe the level of the data.

4. Identify the number and pairing ofgroups.

5. Check assumptions about data.

Tasty Statistics

veryone

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Identify OverallIdentify Overall

Research GoalResearch GoalDescribeDescribe

AssociateAssociate

PredictPredict

CompareCompare

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DescribeDescribe

Concerned with describing the status orConcerned with describing the status or

characteristics of a phenomenoncharacteristics of a phenomenon Case StudyCase Study

an inan in--depth investigation of an individual, group, incident, ordepth investigation of an individual, group, incident, orcommunitycommunity

Cross sectionalCross sectional

involve the collection of data from selected individuals in ainvolve the collection of data from selected individuals in asingle time period.single time period.

LongitudinalLongitudinal

involve data collection at two or more times in order toinvolve data collection at two or more times in order todescribe changes over time.describe changes over time.

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AssociateAssociate

Concerned withConcerned with identifying relationships and theidentifying relationships and thestrength of relationships between two variablesstrength of relationships between two variables

Required before additional research is done toRequired before additional research is done toassess causationassess causation

Two variables from the same subject areTwo variables from the same subject are

assessed for associationassessed for association Two different variables at the same point in timeTwo different variables at the same point in time

(cross(cross--sectional)sectional)

Same variable at two different points in timeSame variable at two different points in time(longitudinal)(longitudinal)

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PredictPredict

Suspect certain factors contribute to a phenomenonSuspect certain factors contribute to a phenomenon

Concerned withConcerned with identifying variables that are predictiveidentifying variables that are predictiveof particular outcomesof particular outcomes

Independent (predictor) and dependent (outcome)Independent (predictor) and dependent (outcome)variables are identifiedvariables are identified

There may be more than one independent variableThere may be more than one independent variable There is a temporal orderThere is a temporal order

Independent variable occurs before the dependent variableIndependent variable occurs before the dependent variable

Involves discovering a mathematical equation that canInvolves discovering a mathematical equation that canbe used to predict values for the data.be used to predict values for the data.

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CompareCompare

Interested inInterested in

identifying statistical differences between twoidentifying statistical differences between twoor more groupsor more groups

Identifying statistical differences betweenIdentifying statistical differences between

repeated observations within the same grouprepeated observations within the same group

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Identify independent andIdentify independent and

dependent variables.dependent variables.AnAn independent variableindependent variable is the variableis the variable

that you believe will influence some otherthat you believe will influence some othervariable.variable. manipulated/assigned by researchermanipulated/assigned by researcher

(assigned to a treatment, workshop etc.)(assigned to a treatment, workshop etc.) prepre--existing characteristic, not under controlexisting characteristic, not under control

of researcher (sex, age, exposure orof researcher (sex, age, exposure or

treatment)treatment)AA dependent variabledependent variable is the variable that isis the variable that is

influenced by the independentinfluenced by the independent

variable(svariable(s

).).

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Describe the LevelDescribe the Level

of the Dataof the Data

Levels of MeasurementLevels of Measurement CategoricalCategorical

OrdinalOrdinal ContinuousContinuous

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VariablesVariables Level of MeasurementLevel of Measurement

CategoricalCategoricalmutually exclusivemutually exclusive

unordered categories. E.g. food types,unordered categories. E.g. food types,gender, eyegender, eye colourcolour, ethnicity., ethnicity.

Categories cannot be arranged in anyCategories cannot be arranged in any

particular order.particular order.

Can assign number codes, but calculationsCan assign number codes, but calculations

would be meaningless.would be meaningless. Nominal, Dichotomous, BinaryNominal, Dichotomous, Binary

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OrdinalOrdinal -- categories with an implied order,categories with an implied order,

but distance between intervals not alwaysbut distance between intervals not alwaysequal or unimportant.equal or unimportant.

E.g. Low, middle and high income, or rating aE.g. Low, middle and high income, or rating a

brand of soft drink on a scale of 1brand of soft drink on a scale of 1--5.5.

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ContinuousContinuous

IntervalInterval -- equal distance between each interval.equal distance between each interval.E.g. 1,2,3.E.g. 1,2,3. Arbitrary zero pointArbitrary zero point

CelciusCelcius scale for temperaturescale for temperature -- temperature does nottemperature does not

cease to exist at 0 degrees.cease to exist at 0 degrees. RatioRatio -- similar to interval scale, but has true zerosimilar to interval scale, but has true zero

point meaning there is none of the variable. E.g.point meaning there is none of the variable. E.g.Weight, salary ($0=$0).Weight, salary ($0=$0).

with ratio variables, you can make assumptions aboutwith ratio variables, you can make assumptions aboutthe ratio of two measurementsthe ratio of two measurements 6 grams is twice as6 grams is twice asmuch as 3 grams.much as 3 grams.

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Identify the NumberIdentify the Number

and Pairing of Groupsand Pairing of Groups Study design and types of comparisons are

important determinants of statistical tests How many groups are involved?

Are they paired (matched) in some way?

If the study uses a pre-post design, each participant isassessed on the same measure at different points intime.

Paired groups (two times)

Matched groups (three or more times)

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Check AssumptionsCheck Assumptions

About DataAbout Data There are various assumptions for each statistical test.There are various assumptions for each statistical test.

Before you select a test, be sure to check theBefore you select a test, be sure to check theassumptions of each test.assumptions of each test.

Some examples of common assumptions are:Some examples of common assumptions are: The dependent variable will need to be measured on a certainThe dependent variable will need to be measured on a certain

level e.g. Continuous.level e.g. Continuous. The independentThe independent variable(svariable(s) will need to be measured on a) will need to be measured on a

certain level e.g. Categorical.certain level e.g. Categorical.

The population is normally distributed (not skewed).The population is normally distributed (not skewed).

If your data do not meet the assumptions for a specificIf your data do not meet the assumptions for a specifictest, you may be able to use a nontest, you may be able to use a non--parametric testparametric testinstead.instead.

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Parametric TestsParametric Tests

Parametric tests assume that the variable in question isParametric tests assume that the variable in question isfrom a normal distribution (continuous).from a normal distribution (continuous).

ItIts a good idea to have a minimum of 30 cases for eachs a good idea to have a minimum of 30 cases for eachgroup.group.

NonNon--parametric tests do not require the assumption ofparametric tests do not require the assumption ofnormality.normality.

Most nonMost non--parametric tests do not require aparametric tests do not require a

continuous/interval level of measurement; can be usedcontinuous/interval level of measurement; can be usedwith nominal/ordinal level data.with nominal/ordinal level data.

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1. Identify overall research goal.2. Identify independent and

dependent variables.3. Describe the level of the data.4. Identify the number and

pairing of groups.5. Check assumptions about

data.

Having this recipe willallow you to select anappropriate statistical test.

Statistical testdecision tools link

recipe componentswith the requiredstatistic.

Results in successfulstatistical planning andanalysis.

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1. Identify overall

research goal.

2. Identify independent

and dependent variables.

3. Describe the level ofthe data.

4. Identify the numberand pairing of groups.

5. Check assumptionsabout data.

Type of Dependent Variable Data

Goal Continuous

Normal

Ordinal

Non-normal

Categorical

Describe one

group

Mean, SD Median, interquartile

range

Proportion

Compare one

group to a

hypothetical value

One-sample ttest Wilcoxon test Chi-square

Compare two

unpairedgroups

Unpaired ttest Mann-Whitney test Fisher's test

(chi-square for large

samples)Compare two

paired groups

Paired ttest Wilcoxon test McNemar's test

Compare three or

more unmatched

groups

One-way ANOVA Kruskal-Wallis test Chi-square test

Compare three or

more matched

groups

Repeated-measuresANOVA

Friedman test Cochrane Q

Quantify

association

between two

variables

Pearson correlation Spearman correlation Contingency coefficients

Predict value

from another

measured

variable

Simple linear regressionor

Nonlinear regression

Nonparametric

regression

Simple logistic regression

Predict value

from several

measured or

binomial

variables

Multiple linear regressionor

Multiple nonlinearregression

Multiple logistic regression

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Statistical Test Selection Group

tatistical Test Selection Group

xercisexercise

Using your table, select the appropriateUsing your table, select the appropriate

statistical tests for the researchstatistical tests for the researchscenarios.scenarios.

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During the group exerciseDuring the group exercise

Steps to choose the appropriate statistical methodSteps to choose the appropriate statistical methodfor the data analysis:for the data analysis:

1.1. Identify whether the research goal is one ofIdentify whether the research goal is one of describe,describe,associate, predict, or compare (difference).associate, predict, or compare (difference).

2.2. IdentifyIdentify dependentdependent andand independentindependent variables.variables.

3.3. Identify theIdentify the level of measurementlevel of measurement in the dependentin the dependentvariable (Categorical, Ordinal, Continuous).variable (Categorical, Ordinal, Continuous).

4.4. Identify theIdentify the number of groups. Are the groupsnumber of groups. Are the groups

paired/matchedpaired/matched (same group before and after)(same group before and after) ororindependentindependent (not at all related, looking at different(not at all related, looking at differentgroups)?groups)?

5.5. Select an appropriate statistical test using the decisionSelect an appropriate statistical test using the decisionchart.chart.

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What is the goal:What is the goal: CompareCompare

IndpendentIndpendent variable:variable: Type of therapyType of therapy

Dependent variable:Dependent variable: Memory TestMemory Test

How many groups:How many groups: 22

Paired/matched or independent:Paired/matched or independent: IndependentIndependentWhat is the level of measurement:What is the level of measurement: ContinuousContinuous

1. A pilot experiment designed to test the effectiveness of a1. A pilot experiment designed to test the effectiveness of anew approach to electrode placement for Electroconvulsivenew approach to electrode placement for ElectroconvulsiveTherapy (ECT) has been conducted over a one year timeTherapy (ECT) has been conducted over a one year time

period.period.Patients fromPatients from two different mood disorder clinicstwo different mood disorder clinics participated inparticipated inthis study. Patients from Clinic X received ECT therapythis study. Patients from Clinic X received ECT therapyaccording to current practice guidelines. Patients from Clinic Yaccording to current practice guidelines. Patients from Clinic Y

received a new exploratory ECT treatment. Patients in eachreceived a new exploratory ECT treatment. Patients in eachclinic were matched for age, gender, and type of disorder. Aclinic were matched for age, gender, and type of disorder. Arandom sample of 30 was selected from each site for inclusionrandom sample of 30 was selected from each site for inclusionin the study. At the end of one year, patients were administeredin the study. At the end of one year, patients were administered

a memory test yielding a totala memory test yielding a total score out of 100score out of 100. What statistical. What statisticalprocedure needs to be selected toprocedure needs to be selected to test for differencestest for differences amongamonggroups of patients on the memory test.groups of patients on the memory test.

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Statistical Analysis withStatistical Analysis with

Excel Data AnalysisExcel Data Analysis Check to seeCheck to see

if you haveif you haveexcel Dataexcel DataAnalysisAnalysis

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Descriptive StatisticsDescriptive Statistics

Measures of central tendency (mean,Measures of central tendency (mean,

median, mode)median, mode) Variability (range, variance, standardVariability (range, variance, standard

deviation)deviation) Shape of Distribution (Shape of Distribution (skewnessskewness, kurtosis), kurtosis)

Standard ErrorStandard Error

Confidence LevelConfidence Level

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HistogramHistogram

Graph showing theGraph showing thefrequency of datafrequency of datafalling withinfalling withinvarious ranges.various ranges.

Provides a visualProvides a visualrepresentation ofrepresentation ofthe centralthe centraltendency,tendency,variability andvariability andshape of theshape of thedistribution.distribution. From http://www.microbiologybytes.com/maths/1011-17.html

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Histogram ProcedureHistogram Procedure

ToolsTools

Data AnalysisData Analysis HistogramHistogram

Input RangeInput Range Bin RangeBin Range

LabelsLabels Chart OutputChart Output

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AssociateAssociate -- CorrelationCorrelation

Allows an examination of the associationAllows an examination of the association

between variablesbetween variables Information about the strength of associationInformation about the strength of association

Information about the direction of the associationInformation about the direction of the association

A correlation coefficient of 0 means that there isA correlation coefficient of 0 means that there is

no relationship between the variables,no relationship between the variables, --11negative relationship, 1 positive relationship.negative relationship, 1 positive relationship.

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Correlation ProcedureCorrelation Procedure

ToolsTools

Data AnalysisData Analysis CorrelationCorrelation

Input RangeInput Range Rows/ColumnsRows/Columns

Output OptionsOutput Options

Is there an association between age and pre-surgical functioning?

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PredictPredict Linear RegressionLinear Regression

Linear RegressionLinear Regression

Focuses on predictionFocuses on prediction Involves discovering the equation for a lineInvolves discovering the equation for a line

that is the best fit for the given data.that is the best fit for the given data.

The resulting linear equation is then usedThe resulting linear equation is then usedto predict values for the data.to predict values for the data.

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Linear Regression ProcedureLinear Regression Procedure

ToolsTools

Data AnalysisData Analysis RegressionRegression

Input Y RangeInput Y Range(dependent variable)(dependent variable)

Input X RangeInput X Range

(independent(independentvariable)variable)


Does pre-surgical functioning predict post-surgical functioning?

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CompareCompare TT--TestTest

Independent Samples TIndependent Samples T--TestTest

Allows the comparison of the means of 2Allows the comparison of the means of 2nonnon--paired groups.paired groups.

Compares actual difference between twoCompares actual difference between twomeans in relation to the variation in themeans in relation to the variation in thedata (expressed as the standard deviationdata (expressed as the standard deviation

of the difference between the means).of the difference between the means).

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Two Sample TTwo Sample T--Test ProcedureTest Procedure

ToolsTools

Data AnalysisData Analysis

TT--test: Two Sampletest: Two SampleAssuming EqualAssuming EqualVariancesVariances

Input 1 RangeInput 1 Range(dependent variable for(dependent variable forgroup 1)group 1)

Input 2 RangeInput 2 Range(dependent variable for(dependent variable forgroup 2)group 2)


Is there a difference in age between males and females?

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CompareCompare TT--TestTest

Paired Samples TPaired Samples T--TestTest

Allows the comparison of the means of 2Allows the comparison of the means of 2paired measures (paired measures (egeg., pre., pre--postpost

measurement, repeated measurementmeasurement, repeated measurementunder different conditions).under different conditions).

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Paired Samples TPaired Samples T--Test ProcedureTest Procedure

ToolsTools Data AnalysisData Analysis TT--test:test: PairedTwoPairedTwo

Sample for MeansSample for Means Input 1 RangeInput 1 Range

(dependent(dependentvariable at time 1)variable at time 1)

Input 2 RangeInput 2 Range

(dependent(dependentvariable at time 2)variable at time 2)


Is there a difference in functioning after surgery?

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CompareCompareANOVA Single FactorANOVA Single Factor

Single Factor (One Way) Analysis of VarianceSingle Factor (One Way) Analysis of Variance

TT--test can only be used for comparison of twotest can only be used for comparison of twogroupsgroups

ANOVA allows us to identify differences amongANOVA allows us to identify differences among

the means of one variable measured in two orthe means of one variable measured in two ormore independent groups.more independent groups.

One way ANOVA comparing only two groupsOne way ANOVA comparing only two groupsprovides similar outcomes to the tprovides similar outcomes to the t--testtest

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Single Factor ANOVA ProcedureSingle Factor ANOVA Procedure

ToolsTools Data AnalysisData Analysis ANOVA: SingleANOVA: Single

FactorFactor Input 1 RangeInput 1 Range

(dependent(dependentvariable organizedvariable organizedwith one column orwith one column or

row of data perrow of data pergroup)group) Output OptionsOutput Options

Is there a difference in pre-surgical functioning betweenthe three major age groups ?

Type of Data

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Goal Continuous Ordinal or Non

Normal

Categorical

Describe one group Mean, SD Median, interquartilerange

Proportion

Compare one group

to a hypothetical

value

One-sample t test Wilcoxon test Chi-squareorBinomial test **

Compare twounpaired groups

Unpaired t test Mann-Whitney test Fisher's test(chi-square for largesamples)

Compare two paired

groups

Paired t test Wilcoxon test McNemar's test

Compare three or

more unmatchedgroups

One-way ANOVA Kruskal-Wallis test Chi-square test

Compare three or

more matched

groups

Repeated-measuresANOVA

Friedman test Cochrane Q**

Quantify association

between two

variables

Pearson correlation Spearman correlation Contingencycoefficients**

Predict value from

another measured

variable

Simple linearregressionorNonlinear regression

Nonparametricregression**

Simple logisticregression*

Predict value from

several measured orbinomial variables

Multiple linear

regression*orMultiple nonlinearregression**

Multiple logistic

regression*

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ResourcesResources

Choosing a statistical testChoosing a statistical test

http://www.wadsworth.com/psychology_d/templahttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/tes/student_resources/workshops/stat_workshp/

chose_stat/chose_stat_01.htmlchose_stat/chose_stat_01.html

http://www.whichtest.info/http://www.whichtest.info/

Online statistical calculatorsOnline statistical calculators

http://statpages.org/http://statpages.org/
http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.whichtest.info/http://www.whichtest.info/http://statpages.org/http://statpages.org/http://statpages.org/http://www.whichtest.info/http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.htmlhttp://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stat_workshp/chose_stat/chose_stat_01.html

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