Please enable JavaScript.

Coggle requires JavaScript to display documents.

descriptive statistics - Coggle Diagram

- - - - types
        
        population mean
        
        sample mean
        
        geometric mean
        
        good for comparing samples with different magnitude or dimension of data, the geometric mean changes proportional to the change ration of data not affected by its original value
      - for distribution function
        
        for PDF, the mean is
        
        there is no simple rules for reading means from either CDF or PDF, unless the data follows normal distribution
    - - the middle value
      - for CDF, the point P(x) =0.5
      - for PDF, the point where
      - if you have 2 middle points (an even number of values), use the mean of 2 central values
    - - most frequently occuring value in the sample
      - in CDF, the mode includes the x value that covers the max slope
      - in PDF, the mode is at the local maxima of the curve
      - for different samples
        
        multiple modes: numbers of the same hignest freq
        
        no mode
        
        sample size too small, even freq
  - - - range
        
        the difference between the highest and the lowest values,
        d = max - min
        
        for CDF, d = xmax - xmin
        
        for PDF, math is complicated, some PDF has infinite tails
      - population variance
        
        the average of the squared distance
        between each value and the mean
        
        square add up variation regardless of direction of values
      - population standard deviation SD #
        
        sqrt of variance
        
        the unit of variance is squared, but SD has same unit as value in samples
      - sample variance
        
        the sum of the squared distance betwen each value and the mean, divided by n-1
        
        why n-1?
        
        adjusts for the underestimation of the population variance inherent in taking a sample
      - sample standard deviation SD
        
        sqrt of sample variance
        
        for continuous distribution
      - coefficient of variance (CofV)/ relative SD
        
        CV = SD/mean
        
        unitless, often expressed as a percent of the mean
        
        allow comparisons of variance between datasets
        
        often used to describe regularity of a frequency distibution (eg: neuron firing
        
        should never be used for data on a interval scale
        
        The interval type allows for the degree of difference between items, but not the ratio between them. Examples include temperature with the Celsius scale, which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals, date when measured from an arbitrary epoch (such as AD), location in Cartesian coordinates, and direction measured in degrees from true or magnetic north. Ratios are not meaningful since 20 °C cannot be said to be "twice as hot" as 10 °C (unlike temperature in Kelvins), nor can multiplication/division be carried out between any two dates directly. However, ratios of differences can be expressed; for example, one difference can be twice another. Interval type variables are sometimes also called "scaled variables", but the formal mathematical term is an affine space (in this case an affine line).
      - percentiles
        
        the number of measures that fall into the given percentage of data
        
        for CDF, the 25th percentiles is the point where the P(x) = 0.25
        
        for PDF, the point where
        
        calculation :star:
        
        npth = (n+1)p/100
        
        if ur data is nor normally distributed, percentiles are more informative than mean and SD
  - - - describes how accurately u measured ur data (variability of possible mean
      - don't confuse with sd
        
        SD describes the dispersion of ur data
      - SEM = SD/sqrt(n
- - - - Pros
        
        show all the data; plot independent measures show correlation
      - cons
        
        messy; not descriptive
    - - pros
        
        show all data; shape of distribution; cumulative histogram show population shift
      - cons
        
        denpendent on bin size; not for small datasets; difficult to compare multiple datasets in 1 graph
    - - pros
        
        show all important descriptive statistics for ur dataset(range, percentiles, median); useful with normal & non-normal distributions; can compare multiple datasets on 1 graph
      - cons
        
        hard to create sometimes
    - - pros
        
        show central measure & the variance; simple to make and read
      - cons
        
        most of the data is hidden; skewed distibution invisible; depends on select right measure of centrality and variance
    - - pros
        
        useful for nominal variables
      - cons
        
        no descriptive statistics; diffcult to read and compare if too many variables
  - - - avoid junk
        
        maximize data-ink ratio
        
        = ink for data/ ink in the graph
      - do not lie with scales
        
        scales can hide or emphasize differences