correlations matching level of measurement to statistical procedures

23
Correlations Matching level of measurement to statistical procedures

Post on 21-Dec-2015

218 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Correlations Matching level of measurement to statistical procedures

Correlations

Matching level of measurement to statistical procedures

Page 2: Correlations Matching level of measurement to statistical procedures

We can match statistical methods to the level of measurement of the two variables

that we want to assess:Level of Measurement

Nominal Ordinal Interval Ratio

Nominal Chi-square

Chi-square

T-test

ANOVA

T-test

ANOVA

Ordinal Chi-square

Chi-Square

ANOVA ANOVA

Interval T-test

ANOVA

ANOVA Correlation

Regression

Correlation

Regression

Ratio T-test

ANOVA

ANOVA Correlation

Regression

Correlation

Regression

Page 3: Correlations Matching level of measurement to statistical procedures

However, we should only use these tests when:

• We have a normal distribution for an interval or ratio level variable.

• When the dependent variable (for Correlation, T-test, ANOVA, and Regression) is interval or ratio.

• When our sample has been randomly selected or is from a population.

Page 4: Correlations Matching level of measurement to statistical procedures

Interpreting a Correlation from an SPSS Printout

Correlations

1 .633**. .000

474 474.633** 1.000 .474 474

Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N

Educational Level (years)

Beginning Salary

EducationalLevel (years)

BeginningSalary

Correlation is significant at the 0.01 level (2-tailed).**.

Page 5: Correlations Matching level of measurement to statistical procedures

A correlation is:

• An association between two interval or ratio variables.

• Can be positive or negative.• Measures the strength of the association

between the two variables and whether it is large enough to be statistically signficant.

• Can range from -1.00 to 0.00 and from 0.00 to 1.00.

Page 6: Correlations Matching level of measurement to statistical procedures

Example: Types of Relationships

Positive Negative No Relationship

Income

($)

Education

(yrs)

Income

($)

Education

(yrs)

Income

($)

Education

(yrs)

20,000 10 20,000 18 20,000 14

30,000 12 30,000 16 30,000 18

40,000 14 40,000 14 40,000 10

50,000 16 50,000 12 50,000 12

75,000 18 75,000 10 75,000 16

Page 7: Correlations Matching level of measurement to statistical procedures

The stronger the correlation the closer it will be to 1.00 or -1.00. Weak correlations will be close

to 0.00 (either positive or negative)

Page 8: Correlations Matching level of measurement to statistical procedures

You can see the degree of correlation (association) by using a scatterplot graph

Current Salary

140000120000100000800006000040000200000

Educational Level (y

ears

)

22

20

18

16

14

12

10

8

6

Page 9: Correlations Matching level of measurement to statistical procedures

Looking at a scatterplot from the same data set, current and beginning salary we can see a

stronger correlation

Current Salary

140000120000100000800006000040000200000

Begin

nin

g S

ala

ry

100000

80000

60000

40000

20000

0

Page 10: Correlations Matching level of measurement to statistical procedures

If we run the correlation between these two variables in SPSS, we find

Correlations

1 .880**. .000

474 474.880** 1.000 .474 474

Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N

Beginning Salary

Current Salary

BeginningSalary

CurrentSalary

Correlation is significant at the 0.01 level (2-tailed).**.

Page 11: Correlations Matching level of measurement to statistical procedures

For these two variables, if we were to test a hypothesis at Confidence Level, .01

Alternative Hypothesis:There is a positive association between beginning and current salary.

Null Hypothesis:There is no association between beginning and current salary.

Decision: r (correlation) = .88 at p. = .000. .000 is less than .01.

We reject the null hypothesis and accept the alternative hypothesis!

(Bonus Question): Why would we expect the previous correlation to be statistically significant at below the p.= .01 level?

Answer: This is a large data set N = 474 – this makes it likely that if there is a correlation, it will be statistically significant at a low significance (p) level.

Larger data sets are less likely to be affected by sampling or random error!

Page 12: Correlations Matching level of measurement to statistical procedures

Another measure of association is a t-test. T-tests

• Measure the association between a nominal level variable and an interval or ratio level variable.

• It looks at whether the nominal level variable causes a change in the interval/ratio variable.

• Therefore the nominal level variable is always the independent variable and the interval/ratio variable is always the dependent.

Page 13: Correlations Matching level of measurement to statistical procedures

Other important information on correlation

• Correlation does not tell us if one variable “causes” the other – so there really isn’t an independent or dependent variable.

• With correlation, you should be able to draw a straight line between the highest and lowest point in the distribution. Points that are off the “best fit” line, indicate that the correlation is less than perfect (-1/+1).

• Regression is the statistical method that allows us to determine whether the value of one interval/ratio level can be used to predict or determine the value of another.

Page 14: Correlations Matching level of measurement to statistical procedures

Important things to know about an independent samples t-test

• It can only be used when the nominal variable has only two categories.

• Most often the nominal variable pertains to membership in a specific demographic group or a sample.

• The association examined by the independent samples t-test is whether the mean of interval/ratio variable differs significantly in each of the two groups. If it does, that means that group membership “causes” the change or difference in the mean score.

Page 15: Correlations Matching level of measurement to statistical procedures

Looking at the difference in means between the two groups, can we tell if the difference

is large enough to be statistically significant?

Group Statistics

258 $20301.4 ********* $567.275216 $13092.0 ********* $199.742

GenderMaleFemale

Beginning SalaryN Mean

Std.Deviation

Std. ErrorMean

Page 16: Correlations Matching level of measurement to statistical procedures

T-test results

Independent Samples Test

105.969 .000 11.152 472 .000 $7,209.43 $646.447 $5939.16 $8479.70

11.987 318.818 .000 $7,209.43 $601.413 $6026.19 $8392.67

Equal variancesassumedEqual variancesnot assumed

Beginning SalaryF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

Page 17: Correlations Matching level of measurement to statistical procedures

Positive and Negative t-tests

• Your t-test will be positive when, the lowest value category (1,2) or (0,1) is entered into the grouping menu first and the mean of that first group is higher than the second group.

• Your t-test will be negative when the lowest value category is entered into the grouping menu first and the mean of the second group is higher than the first group.

Page 18: Correlations Matching level of measurement to statistical procedures

Paired Samples T-Test• Used when respondents have taken both a pre and post-test using the

same measurement tool (usually a standardized test).

• Supplements results obtained when the mean scores for all the respondents on the post test is subtracted from the pre test scores. If there is a change in the scores from the pre test and post test, it usually means that the intervention is effective.

• A statistically significant paired samples t-test usually means that the change in pre and post test score is large enough that the change can not be simply due to random or sampling error.

• An important exception here is that the change in pre and post test score must be in the direction (positive/negative specified in the hypothesis).

Page 19: Correlations Matching level of measurement to statistical procedures

Pair-samples t-test (continued)

For example if our hypothesis states that:Participation in the welfare reform experiment is associated with a positive change in welfare recipient wages from work and participation in the experiment actually decreased wages, then our hypothesis would not be confirmed. We would accept the null hypothesis and accept the alternative hypothesis.

Pre-test wages = Mean = $400 per month for each participant

Post-test wages = Mean = $350 per month for each participant.

However, we need to know the t-test value to know if the difference in means is large enough to be statistically significant.

What are the alternative and null hypothesis for this study?

Page 20: Correlations Matching level of measurement to statistical procedures

Let’s test a hypothesis for an independent t-test

• We want to know if women have higher scores on a test of exam-related anxiety than men.

• The researcher has set the confidence level for this study at p. = .05.

• On the SPSS printout, t=2.6, p. = .03.

What are the alternative and null hypothesis?

Can we accept or reject the null hypothesis.

Page 21: Correlations Matching level of measurement to statistical procedures

Answer

Alternative hypothesis:

Women have higher levels of exam-related anxiety than men as measured by a standardized test.

Null hypothesis: There will be no difference between men and women on the standardized test of exam-related anxiety.

Reject the null hypothesis, (p = .03 is less than the confidence level of .05.) Accept the alternative hypothesis. There is a relationship.

Page 22: Correlations Matching level of measurement to statistical procedures

Computing a Correlation

• Select Analyze

• Select Correlate

• Select two or more variables and click add

• Click o.k.

Page 23: Correlations Matching level of measurement to statistical procedures

Computing a t-test

• Select Analyze• Select Means• Select Independent T-test• Select Test (Dependent Variable - must be ratio)• Select Grouping Variable (must be nominal –

only two categories)• Select numerical category for each group (Usually group 1 = 1, group 2 = 2)Click o.k.