# Significance of significance testing

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Significance of Significance Testing

-by Julius AugustineABC 2012Significance of Significance Testing

Maths is Difficult? Who said?If A = 1, B=2, Z=26

Then

K+N+O+W+L+E+D+G+E = 96%H+A+R+D+W+O+R+K = 98%

BUTA+T+T+I+T+U+D+E = 100%Maths is Religion2Get and 2Give creates many problemsMultiply them by 2 and you get4Get and 4Give solves many problems doesnt it?

So lets RollFirst a Recap of your yester yearsFirst there was the Universe or Population

The qualities or characteristics (e.g. awareness of brands, frequency of shopping, attitudes towards different banks etc.) of the population that we are interested in

Then we wanted to study the Parameters of the Universe / PopulationSo we took a Sample

And then measured the statistics from the sample

Confirmative / Inferential Statistics

Used to make inferences & to draw conclusionsHypothesis Testing To test theories and to confirm or reject your research objectives

Exploratory / Descriptive Statistics

Used to summarize the dataIndividual Variable - DistributionsBi-variables - Cross tabulations

Statistics Two Types

Descriptive Statistics

And how do we measure them?Nominal Data

Can count frequency / Proportion, but cannot calculate mean etc.Ordinal Data

3Can calculate Frequency / Proportion, but Mean?

Direction, but no magnitudeInterval/Ratio

Mean, Median, SDSo to Summarise the Statistic to be usedNominal

Frequency&ProportionsOrdinal

Frequency&ProportionsSometimes MeansInterval/Ratio

Mean MedianStandard Deviation

Inferential Statistics

How do we infer? Lets enter the Courtroom

Researchers >Provide Motive, Forensic report (sig test)

Hypothesis: Innocent until proved guilty

Ho = No difference in means/proportionsH1 = There is enough (95% confident) evidence to say that the difference was real and not due to sampling errorWhich Test to Use

Tests

For MeansFor ProportionsFor relationshipsThree Questions to be AskedDataTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioOrdinal DataSampleOne Sample providing two measuresSampleTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioOne SampleSampleTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioTwo independent SamplesSampleTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioOne sample different variablesPurpose: Test against an Hypothesized valueTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioPurpose: Comparing two statisticsTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioPurpose: Understand RelationshipTest for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioLets work this out -1!In a random survey for a Banking Brand Track, among 300 Singaporeans, it was observed that the average annual household income was SGD 90000 per annum

The average annual household income as per the National Census is SGD 82000.

Can the statistic of the HHI from the sample represent the population of Singapore?DataSamplePurposeIntervalSo the answer is..Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioDataOne SampleTwo different SamplesOne sample different variablesLets work this out -1!In a random survey for a Banking Brand Track, among 300 Singaporeans, it was observed that the average annual household income was SGD 90000 per annum

The average annual household income as per the National Census is SGD 82000.

Can the statistic of the HHI from the sample represent the population of Singapore?DataSamplePurposeIntervalOne SampleSo the answer is..Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioSampleDataOne SampleTwo different SamplesOne sample different variablesLets work this out -1!In a random survey for a Banking Brand Track, among 300 Singaporeans, it was observed that the average annual household income was SGD 90000 per annum

The average annual household income as per the National Census is SGD 82000.

Can the statistic of the HHI from the sample represent the population of Singapore?DataSamplePurposeIntervalOne SampleTest for MeanSo the answer is..Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesLets work this out - 2!As per the Household Income Census is Malaysia 15% of the household population in Klang Valley have an MHHI of RM 10000 and above

In a random survey for 250 on a household FMCG product in Klang Valley 9% of household had an MHHI of RM 10000 and above

Is the statistic representative of the universe?DataSamplePurposeNominalOne SampleTest for ProportionSo the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesLets work this out -3!A QSR client wants to know whether their fried chicken tastes better than competition based on the average score on Taste

The MR agencies conducts a blind test and asks a 100 respondents to rate the clients Fried Chicken and the competitions fried chicken on Taste where 1 is Not tasty to 10 which is Very tasty DataSamplePurposeOrdinalPaired SampleDifference of two means (Paired)So the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataOrdinal/Interval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesSampleLets work this out -4!A QSR client wants to try a new formula for fried chicken which tastes as good or better than their existing product based on the top two box scores. The existing product also went through a similar taste test earlier before it was launched

The MR agencies conducts a blind test and asks a 100 respondents to rate the clients Fried Chicken and on Taste where 1 is Not tasty to 10 which is Very tasty DataSamplePurposeNominalDifferent SamplesDifference of two proportionsSo the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataInterval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesLets work this out -5!A client wants to understand the effect of advertising on purchase intention among their target segment

The MR agency looks at the mean score of PI intention scores where 1 stands for Definitely not buy and 7 stands for Definitely buy for those who said they were Aware of the ad v/s those who said they Werent Aware of the ad (based on a photopic show card)

DataSamplePurposeOrdinalSame Sample but mutually exclusive (independent)Difference of two meansSo the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataOrdinal/ Interval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesLets work this out -6!A client wants to understand the effect of age on purchase intention among their target segment in a survey

i.e. Is there a relationship between age and purchase intentionPI measured on a 1 to 7 PI scale

DataSamplePurposeInterval/OrdinalSame Sample different variablesRelationship between Or/Int variablesSo the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataOrdinal/ Interval/RatioSampleDataPurposeOne SampleTwo different SamplesOne sample different variablesPurposeLets work this out -7!A client wants to understand the effect of gender on purchase intention among their target segment in a survey

i.e. Is there a relationship between gender and purchase intentionPI measured on a 1 to 7 PI scale

DataSamplePurposeNominalSame Sample different variablesRelationship between 2 nominal variablesSo the answer is.Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataOrdinal/ Interval/RatioSampleDataOne SampleTwo different SamplesOne sample different variablesNumerous other TestsAnovaSpearmanKruskal WalisMan WhitneyWhere are these tests called?Test for ProportionDifference of two ProportionsChi-Sqr test for Independence

Regression

%%%Nominal DataOrdinal/ Interval/RatioOne SampleTwo different SamplesOne sample different variablesAnovaZ Testt-Test n

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