Tutorial parametric v. non-parametric

Parametric or Nonparametric Methods

This presentation is designed to help you determine if using parametric or non-parametric methods would be most appropriate with the relationship question you are working on.

This presentation is designed to help you determine if using parametric or non-parametric methods would be most appropriate with the relationship question you are working on.

Parametric Method

Non-Parametric Method

What are parametric methods?

Parametric methods are used when we examine sample statistics

Parametric methods are used when we examine sample statistics as a representation of population parameters

Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is normal and the data are scaled.


Normal Distribution


Normal Distribution

A normal distribution tends to have the same number of data

points on one side of the distribution as it does on the other side. These data points

decrease evenly to the far left and far right.


Normal Distribution




50%


Normal Distribution




50%50%


Normal Distribution





Speed


Temperature


Weight


Scaled Data


Data which is scaled have equal points along the scale (e.g., 1 pound is the same unit of measurement across

the weight scale)

Or – parametric tests can be used when the distribution is skewed but the number of research subjects is greater than 30.

A parametric question that deals with relationships might look like this:

Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity. A data sample is provided to the right:


&


Death Anxiety Scale

Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity.) A data sample is provided to the right:

Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity). A data sample is provided to the right:

Measure of Religiosity

Death Anxiety Religiosity38 442 329 1131 528 915 624 1417 919 1011 158 19

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This data has enough spread to be

considered scaled


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Same with this data.


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The skew for this data set is 0.26 (a skewed distribution will

have a skew value greater than +2.0 or less than -2.0). While slightly skewed to the

right, the distribution would be considered normal


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At the end of this module, go to the presentation entitled “Assessing Skew” to learn how to assess the level of skew in your data set in SPSS.

You can access it through the link on the webpage you just left.


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The skew for this data set is 0.03 and therefore the distribution would be considered normal


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Because the data are scaled and the distributions are both normal, this analysis would be

handled with a parametric method.

In summary,

In summary, if the data is scaled and the distribution is normal, then you will use a parametric method or if the data is scaled and the distribution is skewed with more than 30 subjects you will likewise us a parametric method.


Data: ScaledDistribution: Normal or skewed > 30 subjects


Data: ScaledDistribution: Normal or skewed > 30 subjects

Use a PARAMETRIC

Test

What are nonparametric methods?

Non-Parametric methods are used when we examine sample statistics

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed (with less than 30 subjects) or the data are ordinal / nominal.


Skewed Distributions

with less than 30


Or ranked data like percentiles %


1 = American

2 = Canadian


1 = American

2 = Canadian

Nominal data are used as a way of differentiating

groups.


Or

1 = Those who eat colorful vegetables


Or

1 = Those who eat colorful vegetables

2 = Those who don’t eat colorful vegetables

A nonparametric question that deals with relationships might look like this:

Determine whether the following Beatle’s album top 40 rankings is related to the albums’ sales-rankings from 1965 to 1970.


Album Year Top 40Rank

SalesRank

Beatles for Sale 1965 1 1Rubber Soul 1965 2 1Revolver 1966 3 3Sgt. Pepper 1967 1 2Magical Mystery Tour 1967 3 4The Beatles (white album) 1968 6 2Abbey Road 1969 7 3Let it Be 1970 4 5

Album Top 40 & Sales Rank


Album Year Top 40Rank

SalesRank

Beatles for Sale 1965 1 1Rubber Soul 1965 2 1Revolver 1966 3 3Sgt. Pepper 1967 1 2Magical Mystery Tour 1967 3 4The Beatles (white album) 1968 6 2Abbey Road 1969 7 3Let it Be 1970 4 5

Album Top 40 & Sales Rank

Both sets of data are ordinal or rank

ordered


Because the data are ordinal this analysis would be handled with a nonparametric method.

Very Important Note –

When the data are ordinal in at least ONE data set we will automatically use a nonparametric test, regardless of whether the distribution is normal or not.regardless of whether the distribution is normal or not.

Very Important Note –

When the data are ordinal in at least ONE data set we will automatically use a nonparametric test, regardless of whether the distribution is normal or not.

Here is another nonparametric-relationship problem:

Do those from rural areas tend to drink more than 8 ounces of an alcoholic beverage in one sitting than those from urban areas?


Where the subject is from?

Amount of alcohol drunken

SubjectRural = 1City = 2

Less than 8oz = 1More than 8oz = 2

a 1 1b 1 1c 1 2d 1 1e 2 2f 2 1g 2 1h 2 1






a 1 1b 1 1c 1 2d 1 1e 2 2f 2 1g 2 1h 2 1

Both sets of data are nominal

(either/or)






a 1 1b 1 1c 1 2d 1 1e 2 2f 2 1g 2 1h 2 1

Both sets of data are nominal

(either/or)

Because the data are nominal this analysis would be handled with a nonparametric method.

The Same Very Important Note –

When the data are nominal in at least ONE data set we will automatically use a nonparametric test, regardless of whether the distribution is normal or not.regardless of whether the distribution is normal or not.

The Same Very Important Note –

When the data are nominal in at least ONE data set we will automatically use a nonparametric test, regardless of whether the distribution is normal or not.

In summary,

In summary, if the data is scaled and the distribution is normal, or the data is scaled and the distribution skewed with more than 30 subjects then use parametric statistics.


Data: ScaledDistribution: Normal


Data: ScaledDistribution: NormalData: ScaledDistribution: Skewed with less than 30 subjects


Data: ScaledDistribution: NormalData: ScaledDistribution: Skewed with less than 30 subjects

Use a PARAMETRIC

Test

However, if the data are EITHER Ordinal/Nominal or the distribution is skewed with less than 30 subjects, then you will use a NON-parametric method.



Data: Ordinal/Nominal

Data: ScaledDistribution: skewed > 30 subjects





Data: ScaledDistribution: skewed < 30 subjects





Data: ScaledDistribution: skewed < 30 subjects

Use a NON-PARAMETRIC

Test

What type of method would be most appropriate for the data set you are working with?

What type of method would be most appropriate for the data set you are working with?

Parametric Method

Non-Parametric Method

Tutorial parametric v. non-parametric

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