N318b Winter 2002 Nursing Statistics Lecture 3: Data presentation, distributions and data handling NOTE: Normal distribution deferred to next week.

N318b Winter 2002 Nursing Statistics

Lecture 3: Data presentation,

distributions and data handling

NOTE: Normal distribution deferred to next week

Nur 318b 2002 Lecture 3: page 2

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Institute for Work & Health

Today’s Class(es) Data presentations

bar graphs, pie charts, histograms, lines Skewness and kurtosis

<< 10 min break >> Applying knowledge to assigned readings

(Kilpack et al.; Paulsen & Altmaier)

focuses on preparing a histogram and interpreting the normal distribution

Followed by small groups from 12-2 PM


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A Quick Review from Last Week

Measures of Central TendencyMeanMedianMode

DispersionStandard deviationRange


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meaning of this premise takes on additional value in research studies where you are usually VERY strictly limited in publication spacee.g. 2500 words, 3 tables OR figures

Presentation of Data

What are the major options available for descriptive data presentations?

“a picture tells a thousand words”


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Types of presentations

Know defining features and advantages/disadv

Bar graphs Pie charts Histograms Polygons ( and line graphs) Box plots


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Why use figures? Visual impressions easier to convey “Meaning” of data usually more apparent Create a stronger, longer lasting impression

“Most effective way to describe, explore, and summarize a set of numbers”

Class textbook pg. 8

When are tables a better choice?


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Most appropriate for comparing categories within nominal or ordinal data – e.g. countries

Bar Graphs - notes

Usually used for comparing distinct groups Good for comparing %’s across groups Gaps left between bars used to indicate

non-numeric nature of underlying data


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Bar Graphs – example 1

30.825.3

43.9

0

10

20

30

40

50

Pain status

None/Low

Moderate

High

Percent

Back and/or neck pain frequency in past week

• 1 in 4 nurses have pain most or all of the time


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Bar Graphs – example 2Horizontal bar chart


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Bar Graphs – example 3

Multi-group or cluster bar chart


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Most appropriate for comparing only a few categories within nominal or ordinal data

Pie Charts - notes

Similar to bar chart for usage Gives relative impression of group size Good for comparing %’s across groups Sometimes less intuitive for readers Can sometimes be “exploded”


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Pie Charts – example 1

13%

17%

57%

13%

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

Basic pie chart

Sales by Quarter


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Pie Charts – example 2

13%

17%

57%

13%

70%

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

Exploded pie chart

Sales by Quarter


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Most appropriate for examining distribution of interval or ratio data – e.g. age groups, BP

Histograms - notes

Usually used for illustrating shape of underlying distribution (e.g. skewed?)

Histograms have a total area of 100% Bars typically placed side by side to show

numeric (continuous) nature of data Selecting number of bars and ratio of

width to height are important points


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Histograms – example 1

Choosing size of groups makes a clear difference !

Usually choose a convenient group size (e.g 5 or 10)


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Histograms – example 2For continuous data usually write data labels to the side

How would you describe these data?


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Most appropriate for ratio or interval data when comparing shapes of two distributions

Line graphs - Polygons

Can sometimes give better visual impression of distribution (i.e. smoother)

Good for comparing %’s distributions between two (or three) samples

Area under curve same as for histogram (i.e. 100% of sample)


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Polygons – example 1Histograms and polygons are really just the same thing


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Polygons – example 2Polygons are especially useful when comparing distributions


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Measures of Skew

Mean

Median

Mode

This sample is “left” skewed as the mean < median

In previous class we saw that mean, median and mode of “real” data points rarely align perfectly and the degree of asymmetry refers to skew


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Measures of Skew

Puts a numeric value to asymmetry Range for measure about +/- 1 SD Values of +/- 0.2 indicate skew, with more

extreme values indicating more skew

Pearson’s skewness coefficient

Skewness = (mean – median)/SD


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Measures of SkewSample calculation – marks from first assignment

MEAN Median SD

Before removing zeros

8.5 9 1.92

After removing zeros

8.9 9 0.67

Skew

- 0.26

- 0.15


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What if data are Skewed? Sometimes removing influential

observations is enough (marks example) Transformations may be required:

moderate skew – square root

substantial skew – log transformation

severe skew – inverse transformation Negative skewness corrected first by

“reflecting” data (i.e. create mirror images) Dichotomizing (Y/N) possible (easiest!)

Any problems with transformations?


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Measure of Kurtosis

While skew refers to whether the distribution “leans” to one side or not, kurtosis refers to how “bell-shaped” it is

Indicates whether distribution is too peaked or too flat

No easy calculation (use computer) Values of zero indicate bell-shape Large +’ve values – data too peaked Large -’ve values – data too flat Done only if skew measure is OK


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Example – marks from first assignment

MEAN Median SD Skew

Before removing zeros

8.5 9 1.92 - 0.26

After removing zeros

8.9 9 0.67 - 0.15

Measure of Kurtosis

Kurtosis

14.6

- 0.14


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10 minute break !


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Graphical display using descriptive statistics based on percentiles (box size=IQR)

Box plots - notes

Usually used for comparing several groups Good for identifying outlying values Line in box indicates median (at centre only

if data are evenly distributed) Box ends are 25th and 75th %’iles (IQR) “Whisker” ends are min/max values that are

not outliers


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Box plots – example 1

Extreme Outlier = 3 x IQR from box edge

Minor Outlier = 1.5 x IQR from box edge

Lower whisker (farthest non-outlier from edge)

IQR = 75th-25th %’iles


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Box plots – example 2Box plots give a nice visual summary when comparing group distributions but typically less intuitive than histograms


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Dealing with Outliers

First need to identify them (usually using the box plot method)

Are they “real” or errors? If “real” then can do sensitivity-

type analysis with/without them to show influence on final resultse.g. trimmed mean


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Dealing with Missing Data

First need to identify reasons Design flaw – e.g. confusing or

sensitive questions Is pattern random (OK) or

systematic (more of a problem) Options include listwise or

pairwise deletions or imputations (see page 54-55)


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Part 2: Application to the

Assigned Readings


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Kilpack et al. (1991)

Quick summary of the paper: – an intervention study aimed at decreasing falls in the elderly within medical-surgical specialty units– used rest of hospital as the control group– pre / post quasi-experimental design


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Some questions …How would you describe this distribution?

What might influence these numbers (i.e. bias)?


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Paulsen & Almaier (1995)

Quick summary of the paper: – examined effects of spousal support on pain behaviour– used chronic LBP patients and spouses obtained via a chronic pain clinic– looked at pain behaviours with and without spouse being present– observed a significant spouse effect in both positive and negative driections


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Q1. Which gives you a stronger impression - Table III or Figure 1?

Demonstrates the interpretation advantage gained by graphing data !

A question …


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Next Week - Lecture 4: Normal curve, probability, statistical inference, and

hypothesis testing

For next week’s class please review:1. Page 14 in syllabus2. Textbook Chapter 3, pages 63-80

NO group work next week ! !


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“In Group”Session – Q#1:

Please note:There is an error in the syllabus – mean value should be 92.7 not 90.9

Did not cover last assignment question in lecture but please do it anyway …


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The (Standard) Normal Curve


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The Normal Distribution

N318b Winter 2002 Nursing Statistics Lecture 3: Data presentation, distributions and data handling NOTE: Normal distribution deferred to next week.

Documents

work healthmeaning

work healthmost appropriate

work healthbar graphs

work healthpie charts

work healthwhy use figures

work healtha quick review

ratio data

data handling note