n318b winter 2002 nursing statistics specific statistical tests chi-square ( 2 ) lecture 7

N318b Winter 2002 Nursing Statistics

Specific statistical tests Chi-square (2)

Lecture 7

Nur 318b 2002 Lecture 6: page 2

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Institute for Work & Health

Today’s Class 5 basic statistical tests covered in course Parametric and non-parametric tests Degrees of freedom << 10 min break >> Example of chi-square test Applying knowledge to assigned readings

Turk et al. (1995)

Followed by small groups 12-2 PMFocus on interpreting chi-square results


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“In Group” Session

Focuses on an assigned reading.Q1 example of the chi square test Q2 example of the chi square test Q3 criteria for non-parametric test

Key points from the Turk et al paper will be covered in the 2nd part of the lecture

Missing Table 1


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New Lecture Material

Specific statistical tests: Parametric and non-

parametric tests


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Specific Statistical Tests

Course will cover five major “tests”:

1. Chi-square (2) 2. T-tests

3. Analysis of variance (ANOVA)

4. Correlation

5. Regression


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Statistical Tests – cont’dAll these tests do basically the same 3 things:

3. “test statistic” follows known distributions such that the probability of its value occurring can be determined (i.e. its “p-value”)

2. Generate a “test statistic” whose value increases as difference between groups increases (i.e. larger values more significant)

1. Compare 2 or more study groups to each other (or one group to a reference group)

Example: Z-scores


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Statistical Tests – cont’d

How do you known when to use which test?

Helps to ask some basic questions:1. What kind of data are used?

2. What kind of relationship is of interest?

3. How many groups (samples) involved?- one, two, or more than two

- prediction, association or difference?

- ratio/interval or categorical (ordinal/nominal)- dependent (e.g. follow-up) or independent


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Key point is determining type of data

For categorical (i.e. either nominal or ordinal data) the normal distribution is generally not applicable and population descriptors (parameters) cannot be estimated so non-parametric tests used

Main non-parametric test is the chi-square test that compares expected (E) numbers with actual or observed (O) numbers

Non-Parametric Tests


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For continuous (i.e. either interval or ratio data) the normal distribution applies and population descriptors (parameters, like means) can be estimated thus parametric tests are used instead

Main tests for this course include the t-test, paired t-test and analysis of variance (ANOVA), all of which test means

Parametric Tests


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Parametric vs. non-parametric tests

Data used Examples Comments

Non-parametric

(numbers, %’s)

Nominal, ordinal

(categorical)

Chi-square

Easy to use but limited to simple situations

Parametric

(means, variances)

Interval, ratio

(continuous)

T-tests, ANOVA, regression

More flexible and powerful (also more convincing)


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Degrees of Freedom

SD = (x-)2

n -1

Recall the formula for SD was “adjusted” for imprecision of small samples

The (n-1) term is referred to as “degrees of freedom” since it indicates how many ways that the data can vary in a sample


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Degrees of Freedom – cont’d

Value of “test statistic” derived from many statistical tests is dependent on this idea of “degrees of freedom” thus some sense of what it means is useful (e.g. see textbook page 84-85)

df = number of ways that data can vary (or be categorized)

Example – for chi square test:df = (number of categories –1)


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Example – for chi square test:df = (number of categories –1)

Degrees of Freedom – cont’d

Why?

If total number of subjects is known, and they are categorized into 4 groups, then if three tallies are known the fourth is “fixed” – i.e. it can be derived so it is not “free” to vary

df = (4 –1) = 3


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Chi square (2) test

How do you known when to use 2 test?

1. What kind of data are used?

2. What kind of relationship is of interest?

3. How many groups (samples) involved?

- categorical ( typically nominal)- frequencies (i.e. counts or percentages) - data can be put in a “contingency table”

- association or difference

- usually two or more (“smallish” number)

Referring back to the 3 “basic questions”:


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Chi square test - example

One of the most common statistical tests !

Example: We suspect that students at UWO love statistics a lot so we ask 100 nursing students if they really like Nur 318b?

63 say YES, 37 say NO

Is this more than we might have expected – i.e. are UWO nurses crazy about statistics?


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If we did not think students would be more or less likely to enjoy the course, we would EXPECT 50 to say no and 50 to say YES


2 compares observed vs expected numbers

H0: no difference in OBS versus EXP countsHa: OBS count is NOT equal to EXP

Study hypotheses


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YES NO

at UWO

(observed)

67 33

In general

(expected)

50 50

2 = (O-E)2

E

(67-50)2 + (33-50)2

50 50= = 11.56


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Chi square test - exampleAs with Z-scores, we now look this number (11.56) up in a table of critical values, in this case for the chi square distribution (table value is the probability that observed and expected numbers are the same)

2 (1 df) = 11.56, p < 0.001

Thus we can conclude that UWO nursing students must love stats !!!


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10 minute break !


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Chi square test - assumptions

1. Data are counts, frequencies, percentages

2. Smallest table cell counts ideally >5

3. Data in rows and columns are independent (i.e. subjects can be in one table cell only)

4. Categories or levels set BEFORE testing


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Why is the chi square a nonparametric statistical test?

Chi square test - assumptions

1) it does not assume data are normally distributed (in fact NO assumptions are needed about underlying distribution)

2) categorical/nominal data are used

3) not estimating a population characteristic (i.e. a parameter, like the mean)


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Part 2: Application to the

Assigned Readings


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Turk et al. (1995)

Quick summary of the paper: – a cross-sectional study examining the cognitive-behavioral mediation model of depression in chronic pain patients– 100 chronic pain subjects divided into two groups: 73 randomly chosen younger (<70); and 27 older (70 yrs) patients– found a strong link between pain and depression for older subjects but not for younger ones (i.e. an age effect)


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Some design issues?

Do you have any concerns with design of the study – e.g. using a cross-sectional design to examine chronic pain and depression?

Can pain be more of “social” problem with older people thus “confounding” assessment of depression?

Which came first (“chicken-and-egg”)?

Was assessment of depression “blinded”?


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Chi square test – example 2:the contingency table

Gender young old Total

Male 45.21(33)

37.04(10) 43

Female 54.79(40)

62.96(17) 57

Total 100%(73)

100%(27) 100

Observed counts from Table 1


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Chi square test – example 2:the contingency table

How did we get counts from %’s?Just multiply % by total number in groupe.g. 45.21% male in younger group is equal to 0.4521 x 73 = 33 males

How do we get expected counts?

Expected counts assume no association between groups thus they are calculated according to size of cells in groups


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2 Contingency Table Expected counts

Ri x Cj

NEij =

=

For cell 1,1:

R1 x C1

100E11 =

43 x 73

100= 31.4

For cell 1,2 = 11.6

For cell 2,1 = 41.6

For cell 2,2 = 15.4


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Gender young old Total

Male 33(31.4)

10(11.6) 43

Female 40(41.6)

17(15.4) 57

Total 73 27 100

2 Contingency Table Expected counts

C1 C2

R1

R2


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2 Contingency Table Test statistic

2 = (O-E)2

E

(33-31.4)2 + (10-11.6)2

31.4 11.6= (40-41.6)2 + (17-15.4)2

41.6 15.4

+

2 (1 df) = 0.54, p > 0.20

Can’t reject null hypothesis, thus no association !


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Next Week - Lecture 8:

T-test

For next week’s class please review:1. Page 16 in syllabus2. Textbook Chapter 4, pages 97-1073. Syllabus paper:

Turk et al. (1995)

n318b winter 2002 nursing statistics specific statistical tests chi-square ( 2 ) lecture 7

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