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THE WORLD OF STATISTICS (:star:DESCRIBING DATA (:explode:VARIABLE TYPES…

- - - - Each group in the data set must
        have its own separate measure of central
        tendency
        
        MEDIAN: MIDDLE
        (n+1)/2
        
        MODE: MOST
        
        MEAN: AVERAGE
    - - :checkered_flag:STANDARD DEVIATION
        
        is a measure that quantifies how much
        variation and dispersion is found in the data set
        
        DEVIANCE
        
        how far are the individual
        scores from the mean?
        
        2.DEVIANCE SQUARED:
        when individual
        scores are added up you will often get 0 because 0
        is the central point of the data set.
        You need square the individuals scores to get the Deviance squared
        
        Deviance Squared is used
        to calculate the SUM OF SQUARED ERRORS
        
        3.:black_flag:SUM OF SQUARED ERRORS/ SUM OF SQAURES 3
        
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      - RANGE
        
        is the easiest to calculate
        
        is calculated by minimising the highest
        score from the lowest score in the data set
      - INTERQUARTILE RANGE
        
        is the difference between the upper
        quartile and the lower quartile
    - - Historgrams
      - Bar Charts
      - Pie Charts
      - Box plots and Whisker charts
  - - - Ordinal= rank. scores can
        be arranged on a scale
      - Interval: Scores are ordered and the
        distance between each score is equal.
      - Ratio: scores can be ordered,
        difference between each score is equal
        and the scale has a true absolute 0
      - *Nominal: **catergories are assigned
        arbitrary numbers/ eg Gender can be assigned
        a 1 or 2. these numbers do not give any information
        regarding the score
- - - - :black_flag:HYPOTHESIS TESTING
        
        ALTERNATIVE HYPOTHESIS
        :is the outcome you expect to find from
        conducting your research
        
        NON-DIRECTIONAL HYPOTHESIS
        
        Two tailed analysis. Occurs when
        we evaluate more then two
        variables/groups
        
        DIRECTIONAL HYPOTHESIS
        
        One tailed analysis. occurs when
        we evaluating the association
        between two varaibles/groups
        
        :black_flag:PROBABILITY
        
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      - :black_flag:CONFIDENCE INTERVALS
        
        is an interval estimate of
        the population parameters.
        it is used when we do not know
        the population mean
        
        95% CONFIDENCE INTERVALS
        
        The confidence interval allows us to communicate how accurate our population mean estimate is likely to be in a specific data range
        
        CALCULATING CONFIDENCE INTERVALS
        
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        Confidence intervals are effected by
        the variation in population and the sample size
        
        CENTRAL LIMIT THEORIM
        Central limit theorem argues regardless of the shape of the population, parameter estimates of that population will have a normal distribution provided the samples are big enough.
      - :black_flag:NORMAL DISTRIBUTION
        
        Normal distrbutions are assessed by
        using histograms
        
        a distribution is consider
        normal when
        
        Distribution is symmetrical
        from the mid point
        
        Mean, Median and Mode
        are the same
        
        variable in the distribution is continous
        
        distribution looks like a bell shape
        
        TESTS ASSESSING NORMALITY
        Parametric tests
        
        KOLMOGOROV-SMIRNOV
        K-S TEST
        
        assess whether sample distribution
        is normally distrbitued
        
        compares the scores in the sample
        to a normally distributed set of scores
        with the same mean and SD
        
        p<.05 significant difference: the sample distribution
        is significantly different from a normal disbribution
        
        p>.05 non significant: it tells use the distrbution
        from the sample is not significantly different to the
        normally distribution
        
        SKEWNESS
        
        Postive skew
        too many low scores
        
        Negative Skew
        build up of high scores
        
        KURTOSIS
        
        negative kurtosis
        flat and light tail
        
        positive kurtosis
        pointy and heavy tail
        
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      - :black_flag:STANDARDISED SCORES
        
        Standardised scores allows
        you to compare apple and oranges
        . you convert the scores from the different
        data sets into a common numerical score
        
        MEAN AND STANDARD DEVIATION
        are examples of variable scores being
        standardised
        
        Z SCORES
        These calculation allow you to
        identify how far your score
        is from the mean, in terms of
        standard deviation
        
        Z=(raw score-mean)/standard deviation
        
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        zscores can also be used to calculate
        the probability based on normal distribution.
        based on the score you get, it will tell you probability of
        obtaining that score.
      - :black_flag:STATISTICAL POWER
        
        EFFECT SIZE
        
        The effect size is the measure the size is an effect of the experimental manipulation. To calculate he effect size you can take the means of two experimental groups and minus them. The difference in the means equals the effect size
        
        we then use tests to identify if the effect size is significant
        
        PEARSON CORRELATION
        
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        COHEN'S D
        
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        POWER
        
        as SD decreases, power
        of analysis increases
        
        Power increases with sample size
        
        alpha level: .01 or .05
- - - - Regression analysis does not
        prove causality
        
        RESIDUALS
        the difference between the actual scores
        predictor scores. The line of best fit are the
        predictor scores
        
        Least Square Regression
        is used to fit the regression line:
        y=a+bx
    - - Regression models should
        only be applied if distribution is normal
      - LINEARITY
        The assumption of additivity and linearity means the outcome variable is linearly related to any predictors.Their relationship can be summed up by a straight line
      - OUTLIERS
        are data scores with lage residuals.
        outliers can impact on regression analysis
      - MULTICOLLINEARITY
        variables that have very high
        correlations can suggest the variables
        are measuring similar things. It doesn't allow
        you to ascert independent influence
      - HOMOGENEITY OF VARIANCE
        This assumption means that the variance of the outcome variable should be stable at all levels of the predictor variable.
        The error variance is assumed to be the same at all points of a linear relationship
        
        Confidence intervals can be extremely inaccurate when homogeneity of variance cannot be assumes.
        
        heteroscedastic errors
        If you have Heteroscedastic errors it means there is another system in the data that is at work tha5t can explain the outcome variable
- - - - MANN-WHITNEY U TEST
        Non-Parametric
      - INDEPENDENT T-TEST
        Parametric
    - - ONE-WAY-BETWEEN GROUPS ANOVA
        Parametric
      - TWO-WAY-BETWEEN GROUPS ANOVA
        Parametric
      - KRUSKAL-WALLIS ANOVA
        Non-Parametric
  - - - PAIRED T-TEST
        Parametric
      - WILCOXON SIGN RANK TEST
        Non-Parametric
    - - ONE-WAY WITHIN GROUPS ANOVA
        Parametric
      - TWO-WAY WITHIN GROUPS ANOVA
        Parametric
      - FRIEDMAN'S ANOVA
        Non-Parametric