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Describe Data 2. (Different Statistical procedures (Descriptive…

- - - - Formal
        
        Meaningful Data Analysis
        
        Organizing or Summarizing large amount of data
        so that it's Easy to Interpret
        
        brief Descriptive Coefficients that Summarize a given Data set
      - Personal
        
        you have some Data and use some Concepts
        to Understand what it Means
        
        you have Data and you use tools that Describe them
        
        you want the Data to Speak to you, Tell you what they mean
      - Kid
        
        you have some Information and
        want to Understand what they Mean
    - - Variability
        (Spread, Dispersion)
        
        Value: Major or Equal 0
        (No Negtive)
        
        High -> high Variation
        
        0 -> No Varaition (All Observations are Equal)
        
        Range
        
        Difference btw
        Highest and Lowest values
        
        Interquartile Range
        
        Precedure:
        
        put Observations in a Crescent Sequence (as w Median)
        
        take the 25th observation (Q1) and the 75th (Q2)
        
        I.Q. = Q3 - Q1
        
        Standard Deviation
        
        Formal
        
        ca.: Average Distance from Average in the Distribution
        
        Square Root of the Variance
        
        Personal
        
        how Much is it Normal
        to Differ from the Average
        
        Variance
        
        Definition
        
        Formal
        
        Average Squared Distance
        from the Average (arithmetic avrg.)
        
        Expectation of the Squared Deviation of a random variable from its Mean
        
        1 more item...
        
        Personal
        
        Describes the Shape of the
        Function around the Mean
        
        High
        
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        Low
        
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        Z-score
        
        Formal
        
        how many Standard Deviations is
        a particular Data Point from the Mean
        
        z-score = 0 -> the particular value is equal to the mean
        
        z-score = 2 -> a score is 2 SDs Over the mean
        
        z-score = -1 -> a score lies 1 SD Under the mean
        
        Used When:
        
        Comparing Data Points from Different Sets of Data
        
        to Understand Values that would otherwise Say Little
        
        ex. Job satisfaction is 46. What does it mean? If 46 has a z-score of 1 we know that is kind of normal-above average
        
        Normal Distribution
        
        when a Variable has Many Independent Causes
        
        when Smth is Influenced by Many Unrelated things
        
        ex.
        
        many small factors contributing to Height, then will be Height normally distributed
        
        same for extraversion
        
        we can know the Percentage of Observations that lie +/- 1 SD
        
        +/-:
        
        1 SD: .ca 2/3 (ca. 66%)
        
        2 SD: ca. 19/20 (ca. 95%)
        
        3 SD: 99,7%
        
        Not all Distribution
        are Normally Dist.
        
        Skewness
        
        describes how a data
        Distribution Leans
        
        Positive
        
        1 more item...
        
        Negative
        
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        Kurtosis
        
        Mesokurtic: normal
        
        Platykurtic (piatto)
        
        More Variation than expected
        
        Leptokurtic (appuntito)
        
        Less Variation than expected
      - Central Tendencies
        (aka: Averages)
        
        Measures of the Central Position
        in a Distribution
        
        Mode, Median, Mean
        
        Mode
        
        most Frequent, Common value in the Data
        
        Median
        
        Value that Divides the
        Distribution in 2 exact Parts
        
        Mean
        
        Average Value
        
        Sum of the Values / Number of Observations
        
        Similar / Dissimilar
        
        if Similar -> Normal Frequency Distribution
        
        if Dissimilar -> Asymmetrical Distribution
      - Relation
        
        Correlation coefficient
        
        Value from -1 to 1
        
        0: No relation
        
        1: perfect (Positive) relation
        
        -1: perefect (Negative) relation
        
        Says how the
        Relation is on Average
        
        but Same value can Represent Different Distributions
    - - Evaluate Assumptions one had before the collection of Data
        
        See if the Descriptive tools Add relevant Information or New and unexpected Relations
        
        Check eventual Errors in the Data
      - Not necessarily:
        
        reach a Conclusion
        
        Prove an Hypothesis
    - - Graphical representation of Data
        
        Histograms
        
        Cakes
        
        Scatterplot
        
        2 variables
        
        shows Relation btw the Variables
    - - Frequency Distribution
        
        Noteworthy Info:
        
        Central Point in the Distribution
        
        Distribution of Individual Observations
        
        Modality (?) / Mode
        
        Deviance from the Normal Distribution
        
        Outliers
- - - - Quantitative variables
        
        Quantitative method:
        World Properties expressed as Variables
        
        Properties as variables
        can be
        
        Measured (Quantified)
        
        Compared
        
        Measurement or
        Observation
        
        Value of a variable
        
        1 more item...
        
        Numerical
        
        Scales
        
        the Scale determines
        the possible variation
        
        A measurement is determining
        the value (in the variable scale) of a variable
        
        must Vary
        
        not in Time
        
        but in its Values
        
        ex. Male is Not a Quantitative variable
      - Qualitative variables
        
        Nominal
        
        Categorical
  - - - NOI:
        
        Null Point
        
        Order
        
        Interval
        
        NOIR
        
        Ratio
        
        Ex.:
        
        IQ tests
        
        Yes, clear Order
        
        Yes, constant Interval
        
        Yes, absolute null point
        
        Interval
        
        Ex.:
        
        Clock 0-12 hrs
        
        Yes, clear Order
        
        Yes, constant Interval
        
        No absolute null point
        
        Ordinal
        
        Ex.:
        
        Likert scale: bad, quite bad,
        decent, good, very good
        
        Yes, clear Order
        
        No constant Interval
        
        No absolute null point
        
        Nominal
        
        Ex.:
        
        colors
        
        philosophical traditions
        
        No obvious Order
        
        No constant Intervals
        
        No absolute null point