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Statistical Methods/Techniques and Their Applications

Situation: Trying to determine if the population means of 2 groups are significantly different fromone another. The observations are interval data.

Statistical Tool: t-test for two independent samples

equal varianceunequal variance

matched pairs

Situation: Trying to determine if 2 population proportions are significantly different from oneanother. The observations are interval data.

Statistical Tool: z-test for two population proportions

Situation: Trying to determine if observed frequencies (in a fixed number of categories) differ fromexpectations (past or from theory). The observations fall into nominal categories. We are

counting number of observations in each category.

Statistical Tool: Chi-Squared goodness of fit test

Situation: re t!o classifications of a population of nominal data independent of one another" t!o#dimensional contingency table is used that has the count of a number of observations in eachcell.

Statistical Tool: Chi-Squared test for independence

Situation: We are trying to determine !hether or not there is a linear relationship (or correlation)

bet!een t!o interval variables. We !ant to forecast one thing from one other thing$ if possible.

Statistical Tool: Simple linear regression

Situation: We are trying to determine !hether or not the means of a number of (%) groups ofinterval data are significantly different from one another. The observations are interval.

Statistical Tool: One-way ANOA

Situation: We are interested in examining the effects on an interval response variable (orobservations) of t!o factors.

&s there a factor effect" re the means of the groups significantly different for factor "

&s there a factor ' effect" re the means of the groups significantly different for factor '"

&s there an ' interaction effect (the interaction should be analyed first). &s the response forfactor dependent on the level of factor ' and vice#versa"

Statistical Tool: Two-factor ANOA or !"M ANOA

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Situation: We are trying to predict or estimate the value of one variable (interval) from severalother variables (interval or categorical). The relationship bet!een variables (iv and dv) can belinear or non#linear.

Statistical Tool: Multiple #egression

&f the analyst believes there could be a quadratic relationship bet!een iv and dv$ a quadratic termshould be included and tested. That is at middle values for the iv$ the dv values are especiallyhigh (or lo!). &f the scatter plot of the dv versus an iv loo%s approximately as belo!$ !e shouldli%ely test a quadratic term for significance$ using a t test.

&f the analyst !ould li%e to determine if interaction terms are appropriate$ these terms should beincluded and tested using a t test. &f the interaction is significant$ do not interpret the individualvariables in isolation.

xample: *ultiple +egression model !ith 2 predictor variables (one !e believe has a quadraticrelationship !ith the dv)$ and interaction.

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xample: *ultiple +egression !ith one &nterval variable and &ndicator (,ominal-ategorical)variables representing / groups

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Situation: We have historical data and !e !ant to forecast a single variable at some point(s) inthe future. The data has a long term up!ard or do!n!ard trend and seasonality.

Statistical Tool: Time-Series Analysis

tttSIXYF =

t

t

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Ratio

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ssessing the 0orecast or 0orecasting *ethods

periodstimeofnumbern

tperiodtimeatseriestimetheofvalueforecastedF

tperiodtimeatseriestimetheofvalueactualy

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Fy

MAD

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i

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