choosing the correct statistical test

7/31/2019 Choosing the Correct Statistical Test

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Choosing the Correct

Statistical TestSPSS Workshop

Jaweria Tariq


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Introduction

This tutorial is designed to help youdevelop a framework for choosing thecorrect statistic to test your

hypothesis. The tutorial begins with aset of questions you should askwhen selecting your test. It isfollowed by demonstrations of the

factors that are important toconsider when choosing yourstatistic. Once you understand how to

choose among statistics, you shouldtest our knowled e b doin the


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Presented below are four questionsyou should ask and answer whentrying to determine which statistical

procedure is most appropriate to testyour hypothesis.

What are the independent and

dependent variables?What is the scale of

measurement of the studyvariables?


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Independent and DependentVariables

Before we can begin to choose ourstatistical test, we must determinewhich is the independent and which is

the dependent variable in ourhypothesis. Our dependent variable isalways the phenomenon or behaviorthat we want to explain or predict.

The independent variable representsa predictor or causal variable inthe study. In any antecedent-

consequent relationship, theantecedent is the inde endent


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Study

It has been traditional for the manrather than the woman to receive thecheck when a couple dines out. A

researcher wondered whether thiswould be true if the woman wasclearly in charge, asking for the winelist, questioning the waiter about

dishes on the menu, etc. A largerandom sample of restaurants wasselected. One couple was used in all

restaurants, but in half the manassumed the traditional in-char e


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Analysis

The behavior that we are trying toexplain is the presentation of the

check. Did the wait staff give thecheck to the man or the woman? Thiswould be the dependent variable inthe study. The independent variable

was manipulated as part of theexperimental design. Theindependent variable was who

was in charge during the dinner.


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Scale of Measurement

Once we have identified theindependent and dependentvariables, our next step in choosing a

statistical test is to identify the scaleof measurement of the variables.All of the parametric tests that wehave learned to date require an

interval or ratio scale ofmeasurement for the dependentvariable. Many psychologists also

apply parametric tests to variableswith an a roximatel interval


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Nonparametric statistics are usedwhen our data are measured on anominal or ordinal scale of

measurement. Chi-square statisticsand their modifications (e.g.,McNemar Test) are used for nominaldata. All other nonparametric

statistics are appropriate when dataare measured on an ordinal scale ofmeasurement. The nonparametric

statistics that we learned in class arelisted below.


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Parametric statistics are usedwhen our data are measured onapproximately interval, interval,

or ratio scales of measurement. Nodistinctions are made among thesescales of measurement, although allparametric statistics have

assumptions that must be met beforeproceeding with statistical analysis.The parametric statistics that we

learned in class are listed below. Thisis not a com lete list -- we did not


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In order to choose among these tests,we must next determine the numberof samples in the study design and

the relationship between samples.

Once we have reviewed our options,the next step is to consider the study

design.


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Let us now return to our studyexample and determine the scale ofmeasurement in our study.

StudyIt has been traditional for the manrather than the woman to receive the

check when a couple dines out. Aresearcher wondered whether thiswould be true if the woman was

clearly in charge, asking for the winelist uestionin the waiter about


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Samples/Groups

Number of SamplesOnce you have identified the scale ofmeasurement of the dependent

variable, you want to determine howmany samples or "groups" are in thestudy design. Designs for which one-sample tests (e.g., Z test; t test;

Pearson and Spearmancorrelations; chi-squaregoodness-of-fit) are appropriate

collect only one set or "sample" ofdata. There must be at least two


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Samples/Groups

One-Sample TestsIt is sometimes difficult to determinefrom a study description how many

samples of data were collected.Typically when the description refersto one type of person from alarger population, the study design

uses only one sample. An examplewould be if we wanted to knowwhether Emory students are like

college students in general. Emorystudents are a s ecific sam le from


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Samples/Groups

Dependent VariableWith single samples and onedependent variable, the one-sample Z

test, the one-sample t test, and thechi-square goodness-of-fit test are theonly statistics that can be used.Students sometimes ask, "but don't

you have population data too, so youhave two sets of data?" Yes and no.Data have to exist or else the

population parameters are defined.But the researcher does not collect


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Samples/Groups

Independent and DependentVariablesWhen we have a single sample and

independent and dependent variablesmeasured on all subjects, we typicallyare testing a hypothesis about theassociation between two variables.

The statistics that we have learned totest hypotheses about associationinclude:

chi-square test of independence


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Samples/Groups

Multiple Sample TestsStudies that refer to repeatedmeasurements or pairs of

subjects typically collect at leasttwo sets of scores. Studies thatrefer to specific subgroups in thepopulation also collect two or more

samples of data. Once you havedetermined that the design uses twoor more samples or "groups", then

you must determine how manysam les or rou s are in the desi n.


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Samples/Groups

Dependent Means

Dependent groups refer to some typeofassociation or link in theresearch design between sets of

scores. This usually occurs in one ofthree conditions -- repeatedmeasures, linked selection, ormatching. Repeated measures

designs collect data on subjects using


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All statistical procedures fordependent or correlated groups treatthe data as linked, therefore it is very

important that you correctly identifydependent groups designs. Thestatistics that can be used forcorrelated groups are the McNemar

Test (two samples or times ofmeasurement), Wilcoxon t Test (twosamples), Dependent Means t Test

(two samples), Friedman ANOVA forRanks three or more sam les


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Samples/Groups

Independent MeansWhen there is no subject overlap

across groups, we define the groupsas independent. Tests of genderdifferences are a good example of

independent groups. We cannot beboth male and female at the sametime; the groups are completelyindependent. If you want to

determine whether samples are


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Samples/Groups

StudyIt has been traditional for the manrather than the woman to receive the

check when a couple dines out. Aresearcher wondered whether thiswould be true if the woman was clearlyin charge, asking for the wine list,

questioning the waiter about dishes onthe menu, etc. A large random sampleof restaurants was selected. One couple

was used in all restaurants, but in halfthe man assumed the traditional in-


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Samples/Groups

AnalysisIn this study, the sample consists ofthe wait staff at randomly selected

restaurants. At each restaurant eitherthe man or the woman assumed thein-charge role. Thus, experimentalprocedures resulted in two separated

samples of subjects -- wait staffserving an "in-charge" man and waitstaff serving an "in-charge" woman.

Given that a couple was diningto ether at each restaurant these

A i


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Assumptions

The final factor that we need toconsider is the set of assumptionsof the test. All parametric tests

assume that the populations fromwhich samples are drawn havespecific characteristics and thatsamples are drawn under certain

conditions. These characteristicsand conditions are expressed in theassumptions of the tests.

Nonparametric tests makeassum tions about sam lin


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choosing the correct statistical test

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