Stats Exam 1

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Stats Exam 1
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2011-02-15 13:27:13
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Stats Exam 1
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  1. Element
    Entity upon which data are collected on

    Ex: Name of player
  2. Observation
    set of measurements obtained for a particular element
  3. Variable
    characteristic of an element
  4. Variable

    Categorical (qualitative)
    non numerical data that is classified into categories

    Ex: Position or team
  5. Variable:
    Categorical:

    Nominal
    categorical data which have no meaningful order

    Ex: position, team
  6. Variable:
    Categorical:

    Ordinal
    categorical data which can be ordered.

    Ex: shirt size – small, medium, large
  7. Variable:

    Quantitative
    numerical data that is measures on a numerical scale

    Ex: Points scored in a game
  8. Variable:
    Quantitative:

    Interval
    numerical data that has no true 0 point

    Ex: Temperature
  9. Variable:
    Quantitative:


    Ratio
    numerical data with a true 0 point

    Ex: points scored
  10. Cross Sectional Data
    data that is collected at the same time

    Ex: points scored in a specific week
  11. Time Series
    data collected over different time periods

    Ex: points scored over multiple seasons
  12. Descriptive Statistics
    uses tables, graphs, and numerical methods to summarize data
  13. Inferential Statistics
    uses data from a sample to make estimates or test hypotheses about the characteristics of a population
  14. Population
    the set of ALL elements in a population
  15. Sample
    a SUBSET of a population. Sample estimates a population
  16. Frequency Distribution
    table that summarizes the number of items that occur in non-overlapping categories
  17. Histogram
    graphical way to display quantitative data. Uses intervals to display frequency table data
  18. Correlation
    shows an association between 2 variables
  19. Measures of Central Tendency

    Mean
    the average of a sample of (n) observations.

    The mean is sensitive to extreme values
  20. Measures of Central Tendency

    Median
    the middle point where exactly ½ of the observations on either side of that point

    The median is resistant to extreme values
  21. Measures of Central Tendency

    Mode
    the observation that occurs most frequently.

    Can have 2 modes (bimodal)

    or more than 2 modes (multimodal)
  22. Statistic
    the numeric measure of SAMPLE data
  23. Parameter
    the numeric measure of POPULATION data
  24. Types of Distribution

    Symmetric
    mean = median
  25. Types of Distribution

    Skewed Right (positive)
    median is best measure

    Mean is greater than the median
  26. Types of Distribution

    Skewed Left (negative)
    median is best measure.

    Mean is less than median
  27. Types of Distribution

    Percentile
    a data value that has at least p% fall at or below a percent value
  28. To find percentile
    o Arrange observations in increasing order

    o Compute the index: I = (p/100)*n

    o If the index (i) is an integer, then take the average of that point and the next increasing point

    o If the index (i) is not an integer, use the location of the next integer greater than i
  29. Quartile Range
    the area between the 25th and 75th percentile. Holds 50% of the data set
  30. Measures of Variability and Dispersion

    Range
    the difference between the largest and smallest values in a data set
  31. Measures of Variability and Dispersion

    Variance
    based on the difference between each value and the mean

    Population variance (σ2)

    • Sample variance (s2)
    • has (n-1) in the denominator
  32. Measures of Variability and Dispersion

    Standard Deviation
    the square root of variance.

    Easier to interpret than variance because it isin the same units as the original data
  33. Measures of Variability and Dispersion

    Coefficient of variation
    measures how large the standard deviation is relative to the mean.

    It is expressed in a percentage.

    • (CV = standard deviation/mean *100).
    • Lower Lower is better.

    Used to compare data which has different Standard deviations and means.
  34. Measures of Distribution Shape and Relative Location

    Z Scores
    gives the number of standard deviations an observation is from the mean.

    A z score of 0 indicates that the value is equal to the mean.
  35. Measures of Distribution Shape and Relative Location

    Outliers
    z scores greater than 2 in highly skewed distributions or greater than 3 in normal distributions
  36. Measures of Distribution Shape and Relative Location

    Chebyshev’s Theorem
    Within +/- 2 standard deviations, 75% of the observations will fall within this range

    Within +/- 3 standard deviations, 89% of the observations will fall within this range
  37. Measures of Distribution Shape and Relative Location

    Empirical Rule (normal distribution)
    Within +/- 1 standard deviations, 68% of the observations will fall within this range

    Within +/- 2 standard deviations, 95% of the observations will fall within this range

    Within +/- 3 standard deviations, 100% of the observations will fall within this range
  38. Measures of Distribution Shape and Relative Location

    Correlation Coefficient
    the relationship between 2 random variables
  39. Measures of Distribution Shape and Relative Location

    Correlation Coefficient

    Univariate
    data collected on one random variable
  40. Measures of Distribution Shape and Relative Location

    Correlation Coefficient

    Bivariate
    data collected on two random variables
  41. Measures of Distribution Shape and Relative Location

    Correlation Coefficient

    Person product moment sample correlation coefficient
    measures the strength of the linear relationship (Rxy).

    The sign depends on the slope of the data.

    Must fall between -1 and +1.

    • This is a POINT measurement.
    • 0.00 – 0.29
    • Little if any correlation

    • 0.30 – 0.49
    • Weak/Low correlation

    • 0.50 – 0.69
    • Moderate correlation

    • 0.70 – 0.89
    • Strong/High correlation

    • 0.90 – 1.00
    • Very strong/very high correlation
  42. Probability

    Experimental Outcome
    A sample point
  43. Probability

    Event
    one or more sample points/experimental outcomes
  44. Probability

    Properties
    The sum of the probabilities must equal 1

    Probabilities must fall between 0 and 1
  45. Probablities

    When to use combination or permutation formula?
    Combination when order is not importants (C)

    Permutations when order is important (P)
  46. Probabilities

    Methods (3)
    Classical - # of outcomes / total # of outcomes

    Relative Frequency – used when an experiment is repeated many times

    Subjective – based on experience or intuition. Used when no relative data is available
  47. Probablities

    Events
    a collection of sample points/experimental outcomes ( has one or more sample points)
  48. Discrete Probability Variables

    Random Variables
    a variable that associates a numerical value with each outcome
  49. Discrete Probability Variables

    Random Variables

    Discrete
    a finite number of values

    Ex: number of defective radios
  50. Discrete Probability Variables

    Random Variables

    Discrete Properties
    0 < f(x) < 1

    Σf(x) = 1
  51. Discrete Probability Variables

    Random Variables

    Discrete uniform probability has the form of?
    f(x) = 1/n
  52. Discrete Probability Variables

    Random Variables

    Discrete

    Expected Value
    the mean of a discrete random variable
  53. Discrete Probability Variables

    Random Variables

    Continuous
    numerical value in one or more intervals on the real number line.

    Can pick 2 points and can find a 3rd between them such as a time measurement.

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