Statistics for CS 312

Descriptive vs. inferential statistics Descriptive – used to describe an existing population Inferential – used to draw conclusions of related populations

Graphical descriptions Histograms Frequency polygons/curves Pie charts

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

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

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

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

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

How representative is the sample Random sample – use random numbers to choose members of the sample Stratified sample – sample that represents subgroups proportionally

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

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

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

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

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

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

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

Sequence of activities Description Tests of hypotheses Estimation Evaluation

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.

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

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

Perfect positive correlation: r = +1 ABC D ABC D X Y Y

Perfect negative correlation: r = -1 ABC D CBA D X Y