Introduction to data display Useful questions to ask when - - PowerPoint PPT Presentation

Introduction to data display

Useful questions to ask when considering how to display information

• What do you want to show?
• What methods are available for this?
• Is the method chosen the best? Would

another have been better?

Recommendations for the presentation of numbers

• When summarizing categorical data, both

frequencies and percentages can be used. However, if percentages are reported, it is important that the denominator (i.e. total number of observations) is given.

• To summarize continuous numerical data, one

should use the mean and standard deviation,

• r if the data have a skewed distribution use

the median and range or interquartile range.

Recommendations when presenting data and results in tables

• Tables, including column and row headings,

should be clearly labeled and a brief summary

• f the contents of a table should always be

given in words, either as part of the title or in the main body of the text.

• The amount of information should be

maximized for the minimum amount of ink.

Recommendations for construction of graphs

• The amount of information should be maximized

for the minimum amount of ink.

• Each graph should have a title explaining what is

being displayed.

• Axes should be clearly labeled.
• Gridlines should be kept to a minimum.
• Avoid three-dimensional graphs as these can be

difficult to read.

• The number of observations should be included.

Table or graph?

Examples for badly displayed data

Describing categorical data

Clustered data

Displaying quantitative data

Tables for multiple outcome measures

Stem and leaf plot

Histogram

Showing distribution

Skewed data

Box–whisker plots

Displaying the relationship between two continuous variables

Regression

ROC curve

Tabulating categorical outcomes

Tabulating the results of logistic regression analysis

Tabulating quantitative outcomes

Tabulating the results of regression analyses

Patient flow diagram

Forest plots

Funnel plots

Survival

Displaying results in presentations

• Keep slides simple.
• Text is meant to be read. Ensure that your slides are legible.
• For slides use light text on a dark background.
• Keep information layout, colors, patterns, text styles, and

transitions and build effects consistent for all slides in a presentation.

• Maximum of six lines per slide and six words per line.
• Use graphics and animation effects sparingly.
• San serif fonts such as Arial are the more legible for slides.
• Use a minimum font size of 28 points for titles and 18

points for the body of text

Thanks for your attention

Statistical Methods

Descriptive vs. Inferential

• Descriptive statistics summarize your group.

– average age 78.5, 89.3% white.

• Inferential statistics use the theory of probability to

make inferences about larger populations from your sample. – White patients were significantly older than black and Hispanic patients, P<0.001.

Enter your data with statistical analysis in mind.

• For small projects enter data into Microsoft

Excel or directly into SPSS.

• For large projects, create a database with

Microsoft Access.

• Keep variables names in the first row, with <=8

characters, and no internal spaces.

• Enter as little text as possible and use codes

for categories, such as 1=male, 2=female.

Screen your data thoroughly for errors and inconsistencies before doing ANY analyses.

• Check the lowest and highest value for each variable.

– For example, age 1-777.

• Look at histograms to detect typos.
• Cross-check variables to detect impossible

combinations. – For example, pregnant males, survivors discharged to the morgue, patients in the ICU for 25 days with no complications.

Analyze, descriptive statistics, frequencies, select the variable

• Std. Dev iation

AGE

• Std. Dev = 26.54

Analyze, Descriptive Statistics, Crosstabs

Correct the data in the original database or spreadsheet and import a revised version into the statistical package.

• The age of 777 should be checked and

changed to the correct age.

• Suspicious values, such as an age of 106

should be checked. In this case it is correct.

Run descriptive statistics to summarize your data.

• Std. Dev iation

49-DAYS IN HOSPITAL

• Std. Dev = 18.03

P Value

• A P value is an estimate of the probability of results

such as yours could have occurred by chance alone if there truly was no difference or association.

• P < 0.05 = 5% chance, 1 in 20.
• P <0.01 = 1% chance, 1 in 100.
• Alpha is the threshold. If P is < this threshold, you

consider it statistically significant.

Univariate vs. Multivariate

• Univariate analysis usually refers to one

predictor variable and one outcome variable

– Is gender a predictor of pneumonia?

• Multivariate analysis usually refers to more

than one predictor variable or more than one

• utcome variable being evaluated

simultaneously.

– After adjusting for age, is gender a predictor of pneumonia?

Difference vs. Association

• Some tests are designed to assess whether there are

statistically significant differences between groups. – Is there a statistically significant difference between the age of patients with and without pneumonia?

• Some tests are designed to assess whether there are

statistically significant associations between variables. – Is the age of the patient associated with the number of days in the hospital?

Unmatched vs. Matched

• Some statistical tests are designed to assess

groups that are unmatched or independent.

– Is the admission systolic blood pressure different between men and women?

• Some statistical tests are designed to assess

groups that are matched or data that are paired.

– Is the systolic blood pressure different between admission and discharge?

Level of Measurement

• Categorical vs. continuous variables

– If you take the average of a continuous variable, it has meaning.

• Average age, blood pressure, days in the hospital.

– If you take the average of a categorical variable, it has no meaning.

• Average gender, race, smoker.

Level of Measurement

• Nominal - categorical

– gender, race, hypertensive

• Ordinal - categories that can be ranked

– none, light, moderate, heavy smoker

• Interval - continuous

– blood pressure, age, days in the hospital

Examples of Normal and Skewed

44-DAYS IN ICU

• Std. Dev = 3.99

35-SYSTOLIC BLOOD PRESSURE FIRST ER

• Std. Dev = 27.74

Commonly used statistical methods

• 1.

Chi-square

• 2.

Logistic regression

• 3.

Student's t-test

• 4.

Fisher's exact test

• 5.

Kaplan-Meier method

• 7.

Wilcoxon rank-sum test

• 8.

Log-rank test

• 9.

Linear regression analysis

Commonly used statistical methods

• 10.

One-way analysis of variance (ANOVA)

• 12. Mann-Whitney U test
• 13. Kruskal-Wallis test
• 14. Repeated-measures analysis of

variance

• 15. Paired t-test
• 16. Wilcoxon signed-rank test

Chi-square

• The most commonly used statistical test.
• Used to test if two or more percentages are

different.

• For example, suppose that in a study of 933

patients with a hip fracture, 10% of the men (22/219) of the men develop pneumonia compared with 5% of the women (36/714).

• What is the probability that this could happen

by chance alone?

• Univariate, difference, unmatched, nominal,

=>2 groups, n=>20.

Chi-square example

4 8 7 8 5 2 2 3 6 5 8 9 4 3 C % C % C % A P P C 4 T A A E

• t

u a r 7 b 1 7 4 1 2 2 1 1 1 8 9 1 7 9 3 3 P C

a

L F L N a l d f m p s i d c t s i d c t s i d C a . b

Fisher’s Exact Test

• This test can be used for 2 by 2 tables when

the number of cases is too small to satisfy the assumptions of the chi-square.

– Total number of cases is <20 or – The expected number of cases in any cell is <1 or – More than 25% of the cells have expected frequencies <5.

u a r 5 b 1 4 1 3 2 1 9 1 1 9 3 3 P C

a

L F L N a l d f m p s i d c t s i d c t s i d C a . 1 b

6 . 9 9 t a b u 5 5 . 5 . 5 . % % % % % % 5 5 3 5 8 . 5 . 5 . % % % % % % 5 8 3 . . . % % % % % % C E % C 4 % C C E % C 4 % C C E % C 4 % C A P P C 4 T S E S O L

• t

Student’s t-test

• Used to compare the average (mean) in one

group with the average in another group.

• Is the average age of patients significantly

different between those who developed pneumonia and those who did not?

• Univariate, Difference, Unmatched, Interval,

Normal, 2 groups.

n t S 7 4 1 9 3 1 9 9 5 9 2 5 4 1 9 6 2 5 E E A F S i g e s t a r i t d f S i g ta i e ffe r . E ffe r

• w

p p fi d e D i ff u a l

Mann-Whitney U test

• Same as the Wilcoxon rank-sum test
• Used in place of the Student’s

t-test when the data are skewed.

• A nonparametric test that uses

the rank of the value rather than the actual value.

• Univariate, Difference,

Unmatched, Interval, Nonnormal, 2 groups.

Paired t-test

• Used to compare the average for

measurements made twice within the same person - before vs. after.

• Used to compare a treatment group and a

matched control group.

• For example, Did the systolic blood pressure

change significantly from the scene of the injury to admission?

• Univariate, Difference, Matched, Interval,

Normal, 2 groups.

Wilcoxon signed-rank test

• Used to compare two skewed continuous variables

that are paired or matched.

• Nonparametric equivalent of the paired t-test.
• For example, “Was the Glasgow Coma Scale score

different between the scene and admission?”

• Univariate, Difference, Matched, Interval,

Nonnormal, 2 group.

ANOVA

One-way used to compare more than 3 means from independent groups. “Is the age different between White, Black, Hispanic patients?” Two-way used to compare 2 or more means by 2

• r more factors.

“Is the age different between Males and Females, With and Without Pnuemonia?”

Kruskal-Wallis One-Way ANOVA

• Used to compare continuous variables that

are not normally distributed between more than 2 groups.

• Nonparametric equivalent to the one-way

ANOVA.

• Is the length of stay different by ethnicity?
• Analyze, nonparametric tests, K independent

samples.

Repeated-Measures ANOVA

• Used to assess the change in 2 or more continuous

measurement made on the same person. Can also compare groups and adjust for covariates.

• Do changes in the vital signs within the first 24 hours
• f a hip fracture predict which patients will develop

pneumonia?

• Analyze, General Linear Model, Repeated Measures.

Pearson Correlation

• Used to assess the linear association between

two continuous variables.

– r=1.0 perfect correlation – r=0.0 no correlation – r=-1.0 perfect inverse correlation

• Univariate, Association, Interval

• .030
• .008

• .079*

• .033
• .028

• .033

• .030

• .079*
• .028

• .100**

• .008

• .100**

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

Spearman rank-order correlation

• Use to assess the relationship between two
• rdinal variables or two skewed continuous

variables.

• Nonparametric equivalent of the Pearson

correlation.

• Univariate, Association, Ordinal (or skewed).

• .146**
• .008

• .091**

• .014
• .076*

• .014

• .146**

• .091**
• .076*

• .038

• .008

• .038

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

• Sig. (2-ta

Summary of Inferential Tests

Unpaired vs. Paired

• Student’s t-test
• Chi-square
• One-way ANOVA
• Mann-Whitney U test
• Kruskal-Wallis H test
• Paired t-test
• McNemar’s test
• Repeated-measures
• Wilcoxon signed-rank
• Friedman ANOVA

Parametric vs. Nonparametric

• Student’s t-test
• One-way ANOVA
• Paired t-test
• Pearson correlation
• Correlated F ratio

(repeatedmeasures ANOVA)

• Mann-Whitney U test
• Kruskal-Wallis test
• Wilcoxon signed-rank
• Spearman’s r
• Friedman ANOVA

A Good Rule to Follow

• Always check your results with a

nonparametric.

• If you test your null hypothesis with a

Student’s t-test, also check it with a Mann- Whitney U test.

• It will only take an extra 25 seconds.

Linear Regression

• Used to assess how one or more predictor

variables can be used to predict a continuous

• utcome variable.
• “Do age, number of comorbidities, or

admission vital signs predict the length of stay in the hospital after a hip fracture?”

• Multivariate, Association, Interval/Ordinal

dependent variable.

• 4.4

• .236

• 8.0

• .014
• .425

• Std. Error

Logistic Regression

• Used to assess the predictive value of one or more

variables on an outcome that is a yes/no question.

• “Do age, gender, and comorbidities predict which hip

fracture patients will develop pneumonia?”

• Multivariate, Difference, Nominal dependent

variable, not time-dependent, 2 groups.

1 Total number of comorbidities 2 Cirrhosis 3 COPD 4 Gender 5 Age

Draw Conclusions

• We reject the null hypothesis.
• Patients who are at high risk of developing

pneumonia during their hospitalization for a hip fracture can be identified by:

– total number of pre-existing conditions – cirrhosis – COPD – male gender

Survival Analysis

• Kaplan-Meier method

– Used to plot cumulative survival

• Log-rank test

– Used to compare survival curves

• Cox proportional-hazards

– Used to adjust for covariates in survival analysis

Thanks for your attention

Introduction to Statistics

Descriptive Analysis

Review of Descriptive Stats.

• Descriptive Statistics are used to present

quantitative descriptions in a manageable form.

• This method works by reducing lots of data

into a simpler summary.

Univariate Analysis

• This is the examination across cases of one

variable at a time.

• Frequency distributions are used to group

data.

• One may set up margins that allow us to

group cases into categories.

• Examples include:

– age categories – price categories – temperature categories.

Distributions

Two ways to describe a univariate distribution

• a table
• a graph (histogram, bar chart)

Distributions (con’t)

Ditribution of participants of the research methodology workshop by sex

Sex No % Men 12 60 Women 8 40 total 20 100

Distributions (con’t)

Workshop participants by specialty

Distributions (cont.)

Category Percent Under 35 9 36-45 21 46-55 45 56-65 19 66+ 6

A Frequency Distribution Table

Distributions (cont.)

10 20 30 40 50 Under 35 36-45 46-55 56-65 66+ Percent

A Histogram

Central Tendency

• An estimate of the “center” of a distribution
• Three different types of estimates:

– Mean – Median – Mode

Mean

• The most commonly used method of describing

central tendency.

• One basically totals all the results and then divides

by the number of units or “n” of the sample.

• Example: The pretest mean was determined by the

sum of all the scores divided by the number of students taking the exam.

Working Example (mean)

• Lets take the set of scores:

11,10,8,9,12,11,6,13

• The Mean would be 80/8=10

Median

• The median is the score found at the exact

middle of the set.

• One must list all scores in numerical order,

and then locate the score in the center of the sample.

• Example: if there are 500 scores in the list,

score #250 would be the median.

• This is useful in weeding out outliers.

Working Example (median)

• Lets take the set of scores:

11,10,8,9,12,11,6,13

• First line up the scores.

6, 8, 9, 10, 11, 11, 12, 13

• The middle score falls at 10.5. There are 8

scores and score #4 and #5 represent the halfway point.

Mode

• The mode is the most repeated score in the

set of results.

• Lets take the set of scores:

11,10,8,9,12,11,6,13

• Again we first line up the scores

6, 8, 9, 10, 11, 11, 12, 13 #11 is the most repeated score and is therefore labeled the mode.

Dispersion

• Three estimates:

– Range – Mean Absolute Deviation – Standard Deviation

• Standard Deviation is more accurate/detailed,

because an outlier can greatly extend the range

Range

• The range is used to identify the highest and

lowest scores.

• Lets take the set of scores:

6, 8, 9, 10, 11, 11, 12, 13

• The range would be 6-13. This identifies the

fact that 7 points separates the highest to the lowest score.

Standard Deviation

• The Standard Deviation is a value that shows

the relation that individual scores have to the mean of the sample.

• If scores are said to be standardized to a

normal curve then there are several statistical manipulations that can be performed to analyze the data set.

Standard Dev. (con’t)

• Assumptions may be made about the percentage of

scores as they deviate from the mean.

• If scores are normally distributed, then one can

assume that approximately 68% of the scores in the sample fall within one standard deviation of the

• mean. Approximately 95% of the scores would then

fall within two standard deviations of the mean.

Working Example (stand. dev.)

• Lets take the set of scores:

11,10,8,9,12,11,6,13

• The mean of this sample was found to be 10.
• Again we use the scores

11,10,8,9,12,11,6,13.

• 11-10=1, 10-10=0, 8-10=-2, 9-10=-1,12-10=2,

11-10=1, 6-10=-4,13-10=3

Working Ex. (Stan. dev. con’t)

• Square these values.

1, 0, 4, 1, 4, 1, 16, 9

• Total these values 36.
• Divide 36 by 7: 5.15
• Take the square root of 5.15: 2.27
• 2.27 is your Standard Deviation.

Interquartile range

• The median is the same as the 50th percentile.
• The 25th and 75th percentiles are called the lower and

upper quartiles.

Interquartile range

Definition: A set of n measurements on the variable x has been arranged in order of magnitude.

• The lower quartile (first quartile), Q1, is the value of x that

exceeds one-fourth of the measurements and is less than the remaining 3/4.

• The second quartile is the median.
• The upper quartile (third quartile), Q3, is the value of x

that exceeds three-fourths of the measurements and is less than one-fourth.

Thanks