Studentforelesning 1 1999

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Introduction and descriptive statistics 30th
August 2006 Tron Anders Moger
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New England Journal of Medicine, Editorial, Jan.
6, 2000, p. 42-49

• The eleven most important developments in
  medicine in the past millennium
• Elucidation of human anatomy and physiology
• Discovery of cells and their substructures
• Elucidation of the chemistry of life
• Application of statistics to medicine
• Development of anesthesia
• Discovery of the relation of microbes to disease
• Elucidation of inheritance and genetics
• Knowledge of the immune system
• Development of body imaging
• Discovery of antimicrobial agents
• Development of molecular pharmacotherapy

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Introduction

• A lot of knowledge appear through numbers and
  quantitative data.
• Problems in interpreting statistical results are
  often underestimated.
• Important to learn numerical literacy the
  ability to understand numbers and quantitative
  relationships.

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Number of births in former East Germany
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Mortality in Tanzania and Norway
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Research and numbers

• Numbers often appear in medical research.
• The numbers are often uncertain, they have
  variability
• They must be organized in order to interpret them
• Wish to generalize the results to the general
  population

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Statistical data

• Appear from
• Numerical measurements with an instrument on a
  continuous scale (Continuous data). Examples
• Fever 39.6 (Unproblematic)
• IQ 116 (Problematic)
• Categorization (categorical data). Examples
• Man / woman (Unproblematic)
• Depressed / Not depressed
• (Problematic)

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Variability in the data

• Reliability Precision of data? How much will
  they differ if the measurements are repeated?
• Validity Do we capture what we are really
  interested in? Is the measurement relevant?

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Reliability of lung function measurements6
repeated measurements on 12 students.
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Reliability of questionnaire/interview

• Alcohol use (men 31-50 years)
• Mean number of times alcohol users say that they
  have felt intoxicated
• 1993 (questionnaire) 14.1 times per year
• 1994 (interview) 7.3 times per year
• In 1994 they used the word drunk.

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Reliability of clinical study

• Sackett et al Clinical Epidemiology (Little,
  Brown and Company, 1985). Pictures of the eye of
  100 patients are studied by two clinicians to see
  if there is evidence of retinopathy
• Second
  clinician
• No Yes
• First No 46
  10
• clinician Yes 12 32
• Observed agreement
• (4632)/100 78

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Sources of variation in data

• Laboratory variation
• Observer variation
• Instrument variation
• Measurement variation
• Biological variation between individuals
• Day to day variation within the same
  individual/hospital

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Generalization

• Sample The units, experiments, individuals etc.
  that are in the study E.g.
• 15 patients with migraine
• Neurophysiological study on rats
• Population The collection of units etc. one
  wishes the results to apply for
• All patients with migraine
• All repetitions of the neurophysiological
  experiment

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Pairs of terms

• Sample
• Histogram
• Mean
• Proportion
• Measurements of cholesterol level
• Weather

• Population
• Probability distribution
• Expectation
• Risk
• Cholesterol level in the population
• Climate

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Types of data

• Continuous data. Data measured on a continuous
  scale, e.g. height, weight, age. Can be truly
  continuous (with decimals) or discrete (integers)
• Categorical data. Data in categories, e.g.
  gender, education level, grouped age, hospital
  department. Can be nominal or ordinal.

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Data in SPSS (and other statistical software)

• IMPORTANT One line in the data file always
  correspond to one observation!
• Common to have an id variable for each
  observation
• If a measurement is missing, leave the cell empty
  
• To create a new variable in SPSS, choose
  Data-gtInsert variable in the Data View window, or
  by writing the variable name in Name in the
  Variable View window

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Data coding

• The value of the variable for continuous data
• For categorical data, define a suitable coding,
  e.g. 0male and 1female, or 0grammar schoole,
  1high school and 2college/university degree
• In Variable View, the definition of the coding
  can be defined in Values
• In Label you can write further information about
  the variable

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Descriptive statistics

• Tables
• Graphs, plots
• Measures of central tendency
• Measures of variability

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Types of graphs

• Histogram
• Box-plot
• Scatter plot
• Line plot
• Bar plot

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The age of 100 medical students
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How can you get an overview of these data in
SPSS? Explore!

• Choose Analyze - Descriptive Statistics -
  Explore. Select the relevant variables by
  clicking them, and transferring them to Dependent
  List. Choose Plots, remove the check on Stem
  and leaf and check Histogram instead. Click
  Continue and OK.

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Histogram The distribution of age among the
students (n100)
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Box-plot The distribution of age among the
students
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Measures of central tendency

• Mean
• The students 22.2 years
• Median
• The middle observation when the observations
  are arranged in increasing order
• The students 22.0 years
• The mean is influenced by extreme observation.
  The median is robust

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Measures of variability

• Standard deviation
• The students 3.06 years
• Coefficient of variation s/ 100
• The students 13.8
• Quartiles Arrange the data in increasing order.
  The 25 quartile is at the observation where 25
  of the observations have lower values, and 75 of
  the observations have higher values. (In SPSS
  Check Percentiles in the Statistics meny in
  Explore)
• The students 25 quartile 20.0 years 75
  quartile 23.0 years

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How to get separate plots for each category of a
categorical variable, e.g. gender

• Click Analyze - Descriptive Statistics -
  Explore. Move the continuous variable to
  Dependent List.
• Move gender to Factor List
• Thats it!

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Separate boxplots for each gender
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Relationship between two continuous variables
Scatter plot!

• Choose Graphs - Scatter - Define. Choose a
  variable for the Y-axis and one for the X-axis
• Separate markers for separate groups is achieved
  by transferring the categorical variable to Set
  Markers by
• Can also include regression lines by choosing
  Fit line at total, or a line for each category
  by choosing Fit line at subgroups.

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• Scatter plot, weight versus height for the
  students

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• Scatter plot, weight versus height, with
  regression lines
• Will talk much more about regression later

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Correlation coefficient

• A numerical measure of the relationship between
  two continuous variables x and y
• Range between -1 and 1
• Values close to 0 No relationship
• Values close to 1 or -1 Almost linear
  relationship

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Descriptive statistics for categorical variables

• Not very useful to calculate the mean for e.g.
  educational level
• Would like to find the percentages within each
  category in the study
• Analyze-gtDescriptive Statistics -gtFrequencies
• Move the variable to Variables(s)

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Frequency table
Last column shows the cumulative distribution
always sums up to 100
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Simple bar plot
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Relationships between categorical variables

• Choose Analyze-gtDescriptive Statistics
  -gtCrosstabs
• Move one variable to Rows, and another to Columns
• Click Cells, and check relevant percentages
  (Rows, Columns or Total)

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Crosstable Relationship between race and smoking
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Bar plot Relationship between race and smoking
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Line plot for ordinal categorical variables
(time-series plot)
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Conclusion

• Tons of different options on how to present
  results
• You will (hopefully) learn to understand which
  option is most relevant for each problem during
  this course