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.

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

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

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.

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

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.

50%

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

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.

50%50%

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

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.

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

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.

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

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.

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.

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.

Speed

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.

Temperature

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.

Weight

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.

Scaled Data

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.

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

the weight scale)

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:

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:

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:

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

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 Religiosity

38 4

42 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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 Religiosity

38 4

42 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

This data has enough spread to be

considered scaled

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

Same with this data.

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

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

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

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

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

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

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

At the end of this module, please 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.

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

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

Death Anxiety Religiosity

38 4

39 3

29 11

31 5

28 9

15 6

24 14

17 9

19 10

11 15

8 19

19 17

3 10

14 14

6 18

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:

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

handled with a parametric method.

In summary,

In summary, if and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

In summary, if and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

Data: ScaledDistribution: Normal

In summary, if and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

Data: ScaledDistribution: Normal

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 or the data are ordinal / nominal.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

Skewed Distributions

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

Skewed Distributions

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

`

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

Or ranked data like percentiles %

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = American

2 = Canadian

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = American

2 = Canadian

Nominal data are used as a way of differentiating

groups.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = American

2 = Canadian

Nominal data are used as a way of differentiating

groups.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = American

2 = Canadian

Nominal data are used as a way of differentiating

groups.

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

Or

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = Those who eat

colorful vegetablesOr

Non-Parametric methods are used when we examine sample statistics as a representation of population parameters when the distribution is skewed or the data are ordinal / nominal.

1 = Those who eat

colorful vegetables

2 = Those who don’t

eat colorful vegetables

Or

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.

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

Album YearTop 40

Rank

Sales

Rank

Beatles for Sale 1965 1 1

Rubber Soul 1965 2 1

Revolver 1966 3 3

Sgt. Pepper 1967 1 2

Magical Mystery Tour 1967 3 4

The Beatles (white album) 1968 6 2

Abbey Road 1969 7 3

Let it Be 1970 4 5

Album Top 40 & Sales Rank

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

Album YearTop 40

Rank

Sales

Rank

Beatles for Sale 1965 1 1

Rubber Soul 1965 2 1

Revolver 1966 3 3

Sgt. Pepper 1967 1 2

Magical Mystery Tour 1967 3 4

The Beatles (white album) 1968 6 2

Abbey Road 1969 7 3

Let it Be 1970 4 5

Album Top 40 & Sales Rank

Both sets of data are ordinal or rank

ordered

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

Album YearTop 40

Rank

Sales

Rank

Beatles for Sale 1965 1 1

Rubber Soul 1965 2 1

Revolver 1966 3 3

Sgt. Pepper 1967 1 2

Magical Mystery Tour 1967 3 4

The Beatles (white album) 1968 6 2

Abbey Road 1969 7 3

Let it Be 1970 4 5

Album Top 40 & Sales Rank

Both sets of data are ordinal or rank

ordered

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

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.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?

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

Subject

Rural = 1

City = 2

Less than 8oz = 1

More than 8oz = 2

a 1 1

b 1 1

c 1 2

d 1 1

e 2 2

f 2 1

g 2 1

h 2 1

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

Subject

Rural = 1

City = 2

Less than 8oz = 1

More than 8oz = 2

a 1 1

b 1 1

c 1 2

d 1 1

e 2 2

f 2 1

g 2 1

h 2 1

Both sets of data are nominal

(either/or)

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

Subject

Rural = 1

City = 2

Less than 8oz = 1

More than 8oz = 2

a 1 1

b 1 1

c 1 2

d 1 1

e 2 2

f 2 1

g 2 1

h 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.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 and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

In summary, if and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

Data: ScaledDistribution: Normal

In summary, if and only if the data are BOTHscaled and the distribution is normal, then you will use a parametric method.

Data: ScaledDistribution: Normal

Use a PARAMETRIC

Test

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method.

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

Use a NONPARAMETRIC

Test

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method.

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

Data: ScaledDistribution: Skewed

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method.

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

Data: ScaledDistribution: Skewed

Use a NONPARAMETRIC

Test

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

Data: ScaledDistribution: Skewed

Data: Ordinal/Nominal

Distribution: Skewed

However, if the data are EITHEROrdinal/Nominal or the distribution is skewed, then you will use a NONparametric method

Data: ScaledDistribution: Normal

Data: Ordinal/Nominal

Distribution: Normal

Data: ScaledDistribution: Skewed

Data: Ordinal/Nominal

Distribution: Skewed

Use a NONPARAMETRIC

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