Statistics Statistics

Data measurement, Data measurement, probability and statistical probability and statistical

teststests

Learning AimsLearning Aims

By the end of this session you are going to totally ‘get’ levels of significance and why we do statistical tests!

Levels of measurementLevels of measurement

These are These are quantitative quantitative measures of data measures of data which are of which are of extreme extreme importance when importance when conducting conducting statistical testsstatistical tests

There are There are 44 levels levels of measurementof measurement

Also known as levels of dataAlso known as levels of data

Nominal:Nominal: Counting Counting into categories, into categories, e.g. there are 4 e.g. there are 4 men and 4 women men and 4 women in the roomin the room

Ordinal:Ordinal: Results are put Results are put in order, they are in order, they are ranked. E.g. we could ranked. E.g. we could rank the place that rank the place that each horse came in a each horse came in a racerace

Levels of measurementLevels of measurement IntervalInterval: Data is defined as : Data is defined as

being a specific measure, this being a specific measure, this can be measured on an can be measured on an instrument, there are equal instrument, there are equal intervals between each piece intervals between each piece of data. E.g. We can record of data. E.g. We can record the exact temperature using the exact temperature using a thermometera thermometer. (can be minus). (can be minus)

Ratio: Ratio: This is like This is like interval data except the interval data except the scale has a meaningful scale has a meaningful value of zero. E.g. time value of zero. E.g. time and length. and length.

Why do we need to conduct Why do we need to conduct statistical tests?statistical tests?

Statistical tests tell Statistical tests tell us the significance us the significance of a set of findings- of a set of findings- did the IV really did the IV really effect the DV or effect the DV or were the findings a were the findings a fluke?!fluke?!

The more significant The more significant a finding is the more a finding is the more effect the IV had on effect the IV had on the DVthe DV

Probability:Probability: We need to use inferential statistics to tell us if the We need to use inferential statistics to tell us if the

result that we have found is due to chance or not.result that we have found is due to chance or not. To establish if our results are reliable we have to To establish if our results are reliable we have to

look at the probability of a result being due to look at the probability of a result being due to chance or not.chance or not.

The minimum accepted level of probability The minimum accepted level of probability commonly used in psychology is commonly used in psychology is 5%,5%, this is this is represented as represented as 0.050.05. .

If the level of significance achieved from a test is If the level of significance achieved from a test is equal to or less 0.05equal to or less 0.05 than the results are said to be than the results are said to be significant. significant.

This would mean that we are This would mean that we are 95%95% sure that the IV sure that the IV caused the change in the DVcaused the change in the DV

Probability:Probability: Can be expressed as:Can be expressed as:

A proportion: a 1 in 5 chance.A proportion: a 1 in 5 chance. As a percentage: 20%As a percentage: 20% More commonly expressed as a decimal in psychology: 0.2.More commonly expressed as a decimal in psychology: 0.2.

In psychology: In psychology: 10%=0.10, 5%=0.05, 1%=0.01 and 10%=0.10, 5%=0.05, 1%=0.01 and 0.1%=0.0010.1%=0.001

To go from % to decimal divide by 100, move To go from % to decimal divide by 100, move decimal place 2 spaces to the left.decimal place 2 spaces to the left.

Remember the more stringent (lower) the level of Remember the more stringent (lower) the level of significance you set the more significant the results significance you set the more significant the results areare

Observed valueObserved value:: Every time you perform a statistical test Every time you perform a statistical test

you get an you get an OBSERVED VALUE.OBSERVED VALUE. This observed value tells you the extent to This observed value tells you the extent to

which your results are valid, you then have which your results are valid, you then have to compare this observed value to a table to compare this observed value to a table of of CRITICAL VALUESCRITICAL VALUES to see of your results to see of your results are significant or not.are significant or not.

To be significant the observed value To be significant the observed value should be greater or less than the critical should be greater or less than the critical value depending on the type of testvalue depending on the type of test

Note that there will be a different table of Note that there will be a different table of values for different statistical tests.values for different statistical tests.

Interpreting results:Interpreting results:

Usually in psychology if the results are significant it means that the probability of the result being due to chance is 5% or less

P<0.05 means the results are significant- so we would accept the experimental hypothesis and reject the null hypothesis

Interpreting results:Interpreting results:

P is used to represent “the probability that P is used to represent “the probability that is due to chance”is due to chance”

>> =means greater than =means greater than

<< =means less than =means less than

≥≥ means greater than or equal to.means greater than or equal to.

≤≤ means less than or equal to.means less than or equal to.

SO………………SO………………

PP<<0.05 means that the probability that the 0.05 means that the probability that the result is due to chance is less than 5%.result is due to chance is less than 5%.

Test your understandingTest your understanding

Answer the questions on the handoutAnswer the questions on the handout

Type 1 and type 2 errors:Type 1 and type 2 errors:

The 5% level of significance has been The 5% level of significance has been accepted as it represents a reasonable accepted as it represents a reasonable balance between the chances of balance between the chances of making a making a type 1 or type 2 errortype 1 or type 2 error

These can occur because:These can occur because:

Level of probability accepted is either too Level of probability accepted is either too lenient (too high) or too stringent (too low)lenient (too high) or too stringent (too low)

Type 1 and type 2 errorsType 1 and type 2 errors

Type 1 error:Type 1 error: Occurs when we Occurs when we

conclude that there conclude that there IS a significant IS a significant difference when difference when there is NOTthere is NOT

This can happen if This can happen if the accepted level the accepted level of probability is set of probability is set TOO LENIENTTOO LENIENT

Significance level Significance level set at 20%set at 20%

Type 2 error:Type 2 error: Occurs when we Occurs when we

reject the reject the experimental experimental hypothesis and hypothesis and accept the null accept the null when there IS a when there IS a differencedifference

This can happen if This can happen if the probability level the probability level is TOO STRINGENTis TOO STRINGENT

Significance level Significance level set at 1%set at 1%

Deciding on a statistical testDeciding on a statistical test

You must decide the following:You must decide the following:Are you trying to find out if your samples Are you trying to find out if your samples

are related (correlate) or different?are related (correlate) or different?What design you have used- related, non What design you have used- related, non

related, matched pairsrelated, matched pairsWhat level of measurement you have What level of measurement you have

used. used.

You can use the following table to help You can use the following table to help decide:decide:

DesignDesign NominalNominal Ordinal, Ordinal, interval, ratiointerval, ratio

Correlation/Correlation/

associationassociationChi-square Chi-square test of test of associationassociation

rr

Independent Independent measuresmeasures

Chi-squared Chi-squared test of test of independent independent samplessamples

uu

Repeated Repeated MeasuresMeasures

Sign TestSign Test tt

What test to use?

Test your understanding!Test your understanding!

Using your newly found knowledge identify the test Using your newly found knowledge identify the test that would be suitable for the following: that would be suitable for the following:

An experiment with nominal data and an An experiment with nominal data and an independent groups designindependent groups design

Ordinal data on both measures in a study to see if Ordinal data on both measures in a study to see if two measures are associatedtwo measures are associated

An experiment with and independent groups An experiment with and independent groups design in which the DV is measured on a ratio design in which the DV is measured on a ratio scalescale

A study using a correlational technique in which A study using a correlational technique in which one measure is ordinal and the other is ratio. one measure is ordinal and the other is ratio.

A study testing an association using a nominal A study testing an association using a nominal level of measurementlevel of measurement

An experiment in which all participants were An experiment in which all participants were tested with alcohol and without alcohol on a tested with alcohol and without alcohol on a memory testmemory test

An experiment in which reaction time was An experiment in which reaction time was tested using an independent subject designtested using an independent subject design

• An experiment with nominal data and an An experiment with nominal data and an independent groups design = independent groups design = chi-squared test

• Ordinal data on both measures in a study to Ordinal data on both measures in a study to see if two measures are associated = see if two measures are associated = Spearman’s rank correlation

• An experiment with and independent groups An experiment with and independent groups design in which the DV is measured on a ratio design in which the DV is measured on a ratio scale = scale = Mann-Whitney U test

A study using a correlation technique in which A study using a correlation technique in which one measure is ordinal and the other is ratio one measure is ordinal and the other is ratio =–=–Spearman’s rank

A study testing an association using a nominal A study testing an association using a nominal level of measurement = level of measurement = Chi-Square test of Chi-Square test of associationassociation

An experiment in which all participants were An experiment in which all participants were tested with alcohol and without alcohol on a tested with alcohol and without alcohol on a memory test = memory test = Wilcoxon’s T testWilcoxon’s T test

An experiment in which reaction time was An experiment in which reaction time was tested using an independent subject design = tested using an independent subject design = Mann-Whitney U testMann-Whitney U test