Comments for

1
Session 7

• Comments for
• Classical Tests

2
Mean, Median, Mode - are three kinds of
"averages".

• The mean is the sum of the observations divided
  by the number of observations.
• The median of a finite list of numbers can be
  found by arranging all the observations from
  lowest value to highest value and picking the
  middle one.
• The mode of a data sample is the element that
  occurs most often in the collection.

3
Variance

• The variance and the closely-related standard
  deviation are measures of how spread out a
  distribution is. In other words, they are
  measures of variability.
• The variance is computed as the average squared
  deviation of each number from its mean.

µ mean x data points n number of data
points in set
4
Standard deviation

• The standard deviation formula is very simple it
  is the square root of the variance. It is the
  most commonly used measure of spread.
• In a normal distribution, about 68 of the scores
  are within one standard deviation of the mean and
  about 95 of the scores are within two standard
  deviations of the mean.

5
Standard deviation (contd)

• Dark blue is less than one standard deviation
  from the mean. For the normal distribution, this
  accounts for about 68 of the set (dark blue),
  while two standard deviations from the mean
  (medium and dark blue) account for about 95, and
  three standard deviations (light, medium, and
  dark blue) account for about 99.7.

6
Normal Distribution

• In probability theory and statistics, the normal
  distribution or Gaussian distribution is a
  continuous probability distribution that
  describes data that clusters around a mean or
  average.
• The graph of the associated probability density
  function is bell-shaped, with a peak at the mean,
  and is known as the Gaussian function or bell
  curve.

7
Probability density function
The continuous probability density function of
the normal distribution is the Gaussian function
with µ 0 and s 1
µ mean, median s2 variance s standard
deviation
8
µ mean, median s2 variance s standard
deviation
The red line is the standard normal
distribution
9
P-value

• A p-value is an estimate of the probability that
  a particular result, or a result more extreme
  than the result observed, could have occurred by
  chance, if the null hypothesis were true.
• In short, the p-value is a measure of the
  credibility of the null hypothesis.
• If something is sufficiently unlikely to have
  occurred by chance (say, plt0.05),we say that it
  is statistically significant.

10
Degrees of freedom

• In statistics, the number of degrees of freedom
  is the number of values in the final calculation
  of a statistic that are free to vary.
• DF n k,
• n - sample size
• k - number of parameters, estimated from the data

11
Reference

• Wikepedia.com