Statistics%20for%20CS%20312

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Statistics for CS 312
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Descriptive vs. inferential statistics

• Descriptive used to describe an existing
  population
• Inferential used to draw conclusions of related
  populations

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Graphical descriptions

• Histograms
• Frequency polygons/curves
• Pie charts

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Measures of central tendency

• Mean average used most often
• Median midpoint value used when data is
  skewed
• Mode most frequently occurring value used
  when interested in what most people think

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Measures of variability

• Range highest value minus lowest value
• Standard deviation average of how distant the
  individual values are from the mean

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Normal curve

• Bell shaped curve 68 of values lie within one
  standard deviation of the mean
• Non-normal skewed either negatively (tail to
  left) or positively (tail to right)
• Percentiles - values that fall between two
  percentile values
• Standard scores distance from mean in terms of
  the standard deviation z (X-m) / s.
• Z scores transformed standard scores Z 10z
  50

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Variables

• Quantitative things that can be measured (age,
  income, number of credits)
• Qualitative things without an inherent order
  (college major, address)

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Populations and samples

• Population entire universe from which a sample
  is drawn
• Sample subset of population
• Symbols mean m, µ standard deviation s, s
  variance s2, s2

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How representative is the sample

• Random sample use random numbers to choose
  members of the sample
• Stratified sample sample that represents
  subgroups proportionally

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Hypothesis testing

• Hypothesis as to relationship of variables
  similar or different
• Inference from a sample to the entire population

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Statistical significance

• Accept true hypotheses and reject false ones
• Based on probability (10 heads in a row occurs
  once in 1024 coin tosses)
• Significant result means a significant departure
  from what might be expected from chance alone
• Example a result two standard deviations from
  the mean occurs 2.3 of the time in a normally
  distributed population

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Null hypothesis

• Assumption that there is no difference between
  two variables
• Example Male and female college students do
  similar amounts of music downloading using
  BitTorrent.
• Example School use of computers is unrelated to
  income of the students families

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Levels of significance

• 5 percent level Event could occur by chance
  only 5 times in 100
• 1 percent level Event could occur by chance
  only 1 time in 100
• Significance level should be chosen before doing
  experiment

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Types of errors

• Type I error Rejection of a true null
  hypothesis
• Type II error Acceptance of a false null
  hypothesis
• Decreasing one type increases the other

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One and two tailed tests

• One tailed test Experimental values will only
  fail the null hypothesis in one direction
• Two tailed test Values could occur on either
  the positive or negative tail of the curve

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Estimation

• Concerns the magnitude of relationships between
  variables
• Hypothesis testing asks is there a relationship
• Estimation asks how large is the relationship
• Confidence interval provides an estimate of the
  interval that the mean will be in

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Sequence of activities

• Description
• Tests of hypotheses
• Estimation
• Evaluation

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Correlation

• Quantifiable relationship between two variables
• Example relationship between age and type of
  computer games played
• Example relationship between family income and
  speed of home computer connection.

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Correlation chart

• Two (or more) dimensional table
• Variables on the axes, could be intervals
• Scattergram positive correlated values scatter
  with positive slope, negative with negative slope

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Product-moment coefficient

• Formula based on deviations from means
• If deviations are the same or similar, values are
  positively correlated
• If deviations are the opposite, values are
  negatively correlated
• Most correlations are somewhere in between 1 and
  -1

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Perfect positive correlation r 1
X Y Y
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Perfect negative correlation r -1
X Y