statistics for cs 312. descriptive vs. inferential statistics descriptive – used to describe an...
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![Page 1: Statistics for CS 312. Descriptive vs. inferential statistics Descriptive – used to describe an existing population Inferential – used to draw conclusions](https://reader035.vdocuments.mx/reader035/viewer/2022062314/56649d805503460f94a63f5f/html5/thumbnails/1.jpg)
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, σ; variance s2, σ2
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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
A B C
D
A B C
D
X Y Y
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Perfect negative correlation: r = -1
A B C
D
C B A
D
X Y