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[MUSIC PLAYING][An Introduction to Inferential Statistical Tests]

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DR. ERIC JENSEN: The role of inferential statisticsis to allow you to generalize to a largerpopulation, such as a community or nation,from your sample with a quantifiable risk of error.[Dr. Eric Jensen, University of Warwick]Through inferential statistics, youcan find out whether a research resultis likely to indicate a real effect in the population--this would be a statistically significant result--

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DR. ERIC JENSEN [continued]: or whether it is due only to chance variation thataffects the process of selecting a sample from a largerpopulation.

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DR. CHARLES LAURIE: One of the key turningpoints in your statistical analysiswill be a decision about whether to useparametric or non-parametric methods.[Dr. Charles Laurie, Director of Research, Verisk Maplecroft]Parametric statistics are generallyused with probability or near-probability samplesgathered through random or systematic sampling,while non-parametric statistics areused with non-probability samples such as quota

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DR. CHARLES LAURIE [continued]: or convenience sampling.One of the most common assumptionsfor parametric statistics is that your datawill be normally distributed.That is, the distribution of the datawill look similar to the classic bell-shaped curve.While the precise nature of this normality assumptiondiffers depending on the statistical test you're using,

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DR. CHARLES LAURIE [continued]: the important point is that you can easilyrun tests to confirm whether your data are normallydistributed.Another common assumption requiredwhen using many parametric statistical testsis that the levels of variabilityacross all parts of your sample data are roughly equivalent.This is called equality of variance or homogeneity

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DR. CHARLES LAURIE [continued]: of variance.When comparing groups, this assumptioncan be confirmed by using the inferential statistic calledLevene's test.

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DR. ERIC JENSEN: Choosing an appropriate inferentialstatistical test is a key part of the process.The correct statistical analysis for your situationwill depend on the number and type of variablesthat you have and the kind of analysis you want to conduct.So let's pause here for a moment to summarizethe different types of variables you might encounter.Understanding the types of different variables

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DR. ERIC JENSEN [continued]: is essential, because it affects your statistical test options.There are three different types of quantitative data.The first is categorical data.A categorical variable is a characteristicthat has two or more categories, but there is no intrinsicordering to those categories.For example, you can't calculate an average

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DR. ERIC JENSEN [continued]: for people of different sexual orientations, genders,ethnicities, or hair colors.People with blonde, red, or black hairare simply in different categories.Other examples of categorical variablesinclude place of birth-- for example,native born versus immigrant-- marital status,like married, single, divorced.

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DR. CHARLES LAURIE: The next type of variable is ordinal.The difference between an ordinaland a categorical variable is that thereis a clear, natural ordering within ordinal variables.For example, the levels of the variables of social classand education level are clearly ordered from higher to lower.However, even though the levels within each variableare ordered, the spacing between each category

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DR. CHARLES LAURIE [continued]: is not the same for ordinal variables.For example, the size of the step from working classto middle class is not the same in termsof income as the step from middle class to upper class.Likewise, the step from a bachelor's degreeto master's degree is not the same as the step from master'sto doctorate.This makes education level an ordinal variable.

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DR. ERIC JENSEN: Next, we have interval variables,which are also known as continuous or scale variables.An interval variable is similar to an ordinal variable,except that the intervals between the valueof the interval variable are equally spaced.For example, annual income measured in US dollarsor British pounds would be interval data,because the step from $1.00 to $2.00 is the same as the step

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DR. ERIC JENSEN [continued]: from $125 to $126 and so on.It's always the same interval, the same spacebetween each value within the variable.The same goes for age measured in years, for example.And variable type matters greatly,because particular statistical analysesare intended for use with certain types of variables.For example, you can't calculate an average of hair color

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DR. ERIC JENSEN [continued]: categories in a room, because the statistical calculationof the arithmetic average requires interval data.

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DR. CHARLES LAURIE: Now we returnto inferential statistical tests.If you are looking to understand group differencesand you have one categorical or ordinal variableas the predictor variable as wellas a categorical or ordinal variable as the outcomevariable, then you would use a chi-square testto evaluate the statistical relationship between the two

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DR. CHARLES LAURIE [continued]: variables.

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DR. ERIC JENSEN: On the other hand,if you had one categorical or ordinal variableas your predictor variable and an interval variableas your outcome measure, then youwould normally use a t-test.If you're looking to understand the statistical relationshipbetween two interval variables, then youwould use a Pearson correlation analysis.

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DR. CHARLES LAURIE: Once you've identifiedthe correct statistical test to use for your situation,you can begin to understand how it works in more detail.

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DR. ERIC JENSEN: Let's go into some detailwith one of the most commonly used statistical tests,the chi-square.You use chi-square and Cramer's Vto determine whether there is a systematic relationshipbetween two variables.You may find yourself needing to evaluatethe statistical relationship between twocategorical variables, such as gender, ethnicity,or religious affiliation.

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DR. ERIC JENSEN [continued]: And when both variables are categorical,you can't produce an arithmetic averageto make that comparison.Therefore to conduct this analysis,you use what is called a contingency table, whichshows the frequency with which cases fallinto each combination of categories,such as woman and Christian or man and Buddhist.

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DR. CHARLES LAURIE: When you conduct statistical analysison categorical data like this, what you are trying to work outis whether there is any systematic relationshipsbetween the different variables being analyzedor whether cases are randomly distributed across the cellsin the contingency table.You do this by comparing what you find in your sample data

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DR. CHARLES LAURIE [continued]: with what would be expected if therewere no relationships between the two variables.This "no relationship" scenario is the null hypothesisfor chi-square tests.

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DR. ERIC JENSEN: Chi-square is a non-parametric statisticaltest, so you don't need to check for normalityor homogeneity of variance like youwould with a parametric test.But there are still a couple of assumptionsto keep in mind for the chi-square statistic.First, you can only use chi-square testswhere at least 80% of the cells in the tablehave an expected value of at least 5.

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DR. ERIC JENSEN [continued]: If you violate this assumption, the testloses power and may not detect a genuine effectthat exists in the data.

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DR. CHARLES LAURIE: The categories must be discreet.That is, no case should fall into more than one category.For example, a respondent cannot be both Christian and Buddhistat the same time if these are separate categories withina variable.Once you have verified these chi-square test assumptions,you can now carry on with your chi-square analysis.

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DR. ERIC JENSEN: For each cell in the contingencytable for a chi-square analysis, thereis an expected frequency, which your statistics softwarepackage will calculate for you and then comparewith the observed frequencies from your sample datato see how much of a difference there is.The expected frequency is what you would get in each cellif they were an exactly equal spread

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DR. ERIC JENSEN [continued]: of the data across the different categories in the table.The statistical test tells you whether the differenceis visible in your data is large enoughto reject the null hypothesis and conclude that the variablesare, in fact, related.The numerical values you get from this testare called a chi-square statistic.If the chi-square result is large enough

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DR. ERIC JENSEN [continued]: to be statistically significant, thismeans that the difference in your sampleis large enough that we would expectto see a result this pronounced due purely to random samplingvariation less than 5% of the timeif there were no real difference between the categoriesin the population.This would mean that the risk of wrongly concludingthat there is a statistically significant relationship when

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DR. ERIC JENSEN [continued]: there isn't one is low enough that youcan reject the null hypothesis and say that thereis, in fact, a relationship between the variables you'reanalyzing.

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DR. CHARLES LAURIE: If you are running your chi-square testin SPSS, you will need to extract the important detailsfrom the table it shows you.First, look at the footnote at the bottom of the table.This tells you whether there are any cellsin the cross-tabular table with an expected count less than 5.If you have cells with expected counts less than 5,you will probably need to combine categories to get

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DR. CHARLES LAURIE [continued]: the expected count up above 5.

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DR. ERIC JENSEN: Second, look at the first row,labeled Pearson Chi-Square, under the column Asymp.Sig.-- 2-sided.This is your p-value.If it is less than 0.05, then the resultis statistically significant.This means you can reject the null hypothesisand conclude that there is a relationship between the twocategorical variables in this analysis.

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DR. CHARLES LAURIE: Next, look at the first row,labeled Pearson Chi-Square, under the column Value.This is your chi-square value, whichis your evidence that the result is or is notstatistically significant.You will need this information whenyou write up the results of your chi-square analysis.

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DR. ERIC JENSEN: At this stage, if you'vedetermined that your chi-square result is statisticallysignificant, you'll next need to determinethe strength of the relationship between the two variables.

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DR. CHARLES LAURIE: If you find a statistically significantrelationship with your chi-square analysis,this means there is likely to be a real patternin the population from which you sampled.However, to determine the size of the effect,you must run a second test, call Cramer's V.This is a proportional reduction in error statisticwhich indicates the strength of association

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DR. CHARLES LAURIE [continued]: in contingency tables.Because it uses standardized values,it also allows you to compare resultsfrom different statistical analysesto decide which is stronger.Another way of describing proportional reduction in erroris that it shows you how much betteryour prediction of the outcome variablewould be if you know something about the predictor variable.

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DR. CHARLES LAURIE [continued]: For example, if you had the variables of teacherand student letter grade result, a Cramer's V resultwould tell you how much of the variation in student lettergrades could be accurately predicted if all you knewwas which teacher students have.Roughly speaking, the following guidelinesfor Cramer's V results indicate the strengthof the relationship between the variables.

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DR. ERIC JENSEN: 0.1 is generallyconsidered a small effect size.0.3 would be a medium effect size.And 0.5 would generally be considered a large effect size.[Writing up your chi-square and Cramer's V results]

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DR. CHARLES LAURIE: We now turn to the howto write up your chi-square test result.The chi-square results tell you if there is a relationshipbetween two variables.When there is a relationship, the Cramer's Vis used to determine the strength of that relationship.When writing up your results, it isimportant to include information on both of these things.

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DR. ERIC JENSEN: Begin your writeupby restating what the analysis is addressing.Follow this up by telling the readerwhether the chi-square result was statistically significantand by providing the relevant statistics from the table,including the p-value, the chi-square statistic, and alsothe results from your Cramer's V testif the chi-square was statistically significant.

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DR. CHARLES LAURIE: Conclude the writeupby restating the findings and by providingthe details of your evidence for your statistical analysis.

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DR. ERIC JENSEN: Now that you knowthe steps involved in a statistical test,conducting an analysis, and writing up the results,remember, it all starts with correctly identifying the typeof variables you're analyzing.[MUSIC PLAYING]

### Video Info

**Publisher:** SAGE Publications Ltd

**Publication Year:** 2017

**Video Type:**Tutorial

**Methods:** Statistical inference, Statistical tests

**Keywords:** mathematical concepts; Software

### Segment Info

**Segment Num.:** 1

**Persons Discussed:**

**Events Discussed:**

**Keywords:**

## Abstract

Dr. Eric Jensen, Professor of Sociology at the University of Warwick and Dr. Charles Laurie, Director of Research at Verisk Maplecroft, provide an outline of inferential statistical testing. Their explanation describes categorical, ordinal, and interval variables, as well as how to run tests on data collected to determine if a null hypothesis can be rejected.