BASIC STATISTICS

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BASIC STATISTICS

• DR MURALEEKRISHNAN K S

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Some important concepts Statistics -Analysis
and Interpretation of numerical data Data-
Collection and compilation of relevant
information Nature of data -Raw and
Processed Sources of Data - Surveys, Clinical
trials - Questionnaires and personal
interviews - Secondary sources Probability - (
No. of favorable outcomes) / (Total no. of
mutually exclusive, equally likely and
exhaustive events)
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• Distribution of data
• Tabulation plan
• Determination of class intervals
• Determination of number of class intervals
• Quartiles -
• Centiles/Percentiles

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• Prevalence and Incidence Rates
• Two fundamental statistics in epidemiology
• Expressed per 100
• Expressed per 1000 or 10,000

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• Types of Health Studies/Clinical Trial
• Cross sectional surveys
• Longitudinal cohort based studies
• - Retrospective
• - Prospective
• Randomized Controlled Trials or Experiments
• - Case-Control studies
• - Drug evaluation trials
• - Simple (Placebo-controlled)
• - Blinded (single or double)

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DESCRIPTIVE STATISTICS

• Describes
• Summarises
• Presents
• Interprets data
• Makes meaning out of numbers

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VARIABLES

• Variables are attributes that vary between
  subjects
• Height, weight, blood pressure
• Can be grouped as
• Qualitative variable
• Quantitative variable

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QUANTITATIVE VARIABLES

• Discreet variable
• Countable,but only whole numbers
• Continuous variable
• Countable as a continuum

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QUALITATIVE VARIABLES

• Do not possess numerical values
• Colour of hair,gender,blood group
• Three types
• Ordinal
• Dichotomous
• Nominal

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MEASURES OF CENTRAL TENDENCY

• The mean
• The median
• The mode

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• Measures of central tendency
• Mean
• - Arithmetic mean ( )
• - Geometric mean
• - Harmonic mean
• Mode
• - Most frequently occurring observation
• Median
• - Middle value

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THE MEAN

• Arithmetic average of all observations
• Influenced by extreme values
• Non resistant measure

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THE MEDIAN

• Middle value of all observations
• Resistant measure
• Not influenced by extreme values

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2 data set

• 8
• 10
• 12
• Mean 10

• 6
• 10
• 14
• Mean 10

Is the 2 data set same
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• Measures of Dispersion
• Range - (minimum, maximum)
• Variance and Standard deviation
• Variance
• Standard deviation ( )
• Standard error

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STANDARD DEVIATION

• Measure of spread
• Used extensively in normal distribution
• Calculated using mathematical formulae
• Large SD means
• Small SD means

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STANDARD DEVIATION

• Advantage of SD
• - measuring the variability in single figure
• - estimating the probability of observed
  differences between two means
• Unit as that of mean

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• Graphical presentation/distribution of data
• Bar diagram
• Histogram
• Line diagram
• Pie-chart
• Scatter-plot

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• Some fundamental distributions
• Bernoulli distribution
• Binomial distribution
• Poisson distribution
• Negative binomial distribution
• Normal distribution

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• Testing of Hypothesis
• Hypothesis
• - A statement relating to objective
• Null hypothesis ( )
• - Hypothesis of no difference or no effect
• Alternative hypothesis ( )
• - Hypothesis of one way or two way difference or
  effect

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• Common Statistical Tests
• Large sample tests (z test)
• Small sample tests (student t test)
• Paired t test
• Chi-square test

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• Chi Square test for finding association
• Non-parametric test
• Easy to understand and execute
• Does not involve any assumptions but the cell
  frequency should not fall below5
• If cell frequency falls below 5, apply Yates
  Correction
• General formula for Chi-square test
• For the previous example-
  giving plt0.001 with one d.f.

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• Students t-test
• Small sample test preferably up to 30
  observations
• For comparing means
• Easy to understand and apply
• Most popular and frequently used
• Types of t-test
• - Paired t-test for comparing pre and post
  treatment means in
• the same set of subjects
• - Take differences between obs.
• - Compute mean of the differences
• - Compute standard error of the differences
• - Divide mean by the standard error to get
  t-statistic
• - Compare the calculated value of t with the
  tabulated value at the
• required d.f.

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• Students t-test (contd.)
• Two sample t-test
• - Applicable with two independent samples
• - Not necessarily of the same size
• - Compute mean and standard deviations of the
  two samples
• - Compute difference of the two means
• - Compute standard error of the above
  difference
• - Divide difference of the means with the
  standard error to obtain
• value of the
  t-statistic
• - Compare calculated value of t with the
  tabulated value at the
• required d.f.
• With large sample size the t-statistic tends to
  Z-statistic
• Hence for large samples the Z-test (standard
  normal test) should be used in place of
• t-test

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• Test of difference between two proportions
• Two sample test
• Clearly defined dichotomy
• Use -test or Z-test
• - Proportion of people with the attribute under
• investigation should be known in
  the two samples
• Easy to use and understand

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• Non-parametric tests of significance
• For t-test normality of parent population is
  assumed
• In case of non-normality of the parent
  population, non-parametric tests should be
  employed to assess significance of the difference
  e.g.
• - Sign test, Run test, Mann Whitney U-test etc.
• Deal with positional information
• Does not estimate the parameters
• Possible to analyze qualitative data

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• Determination of sample size
• Importance of Sample size
• - Appropriateness
• - Validity of results
• - Applicability of statistical tools
• Situation demands
• - New treatment better than the standard
• - Discard the new treatment if slightly better
• - Does not wish to drop if new treatment is
  substantially superior

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Thank You
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