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QM #7 t-test, CI, Regression, & Correlation (Regression (:old_key: …

- - - - :bulb: CI in display
      - :memo: :eye: error bars of same &
        different population
- - - - :key: Observe :couple_with_heart:,
        ~~cause & effect~~
      - :bulb: observe,
        ~~direct intervention~~
  - - - :heavy_plus_sign:ly related
        
        the more I practised my :guitar:,
        the better :guitar: player
        I would become.
        
        :muscle::skin-tone-3::muscle::skin-tone-3::muscle::skin-tone-3: (r = 0.6 ~ 1)
        
        :muscle::skin-tone-3: (r = 0.2 ~ 0.4)
        
        :muscle::skin-tone-3::muscle::skin-tone-3: (r = 0.4 ~ 0.6)
        moderate
      - :heavy_minus_sign:ly related
        
        the more I practised my :guitar:
        the worse a :guitar: player
        I became
        
        :muscle::skin-tone-3: (r = -0.4 ~ -0.2)
        
        :muscle::skin-tone-3::muscle::skin-tone-3: (r = -0.6 ~ -0.4)
        moderate
        
        :muscle::skin-tone-3::muscle::skin-tone-3::muscle::skin-tone-3: (r = -1 ~ -0.6)
      - Not related (r = 0)
        
        as I practise the :guitar: my playing ability remains completely constant
      - :memo: Andy's
        :guitar: practice
    - - Correlation
        Coefficient
        (Pearson's r)
        
        Range: -1 to +1
        
        ±.25 :arrow_forward: small effect
        ±.40 :arrow_forward: medium effect
        ±.60 :arrow_forward: large effect
        
        How to (SPSS)
      - Covariance
        (correlated
        variance)
        
        :heavy_minus_sign: it depends
        upon the scales of
        measurement used
        
        :key: Converting to other scale change the result
        
        Needs
        standardization
        
        SD as
        the standard
        
        standardized covariance
        :arrow_forward: correlation coefficient
    - - The level of the measurement of the variables correlated is continuous.
      - The :couple_with_heart: is approximately linear.
      - The data is approximately
        normally distributed.
      - ~~Significant outliers~~ in the data
    - - CI mainly for r or mean or both
      - p ("Sig." in SPSS)
        
        Reject/no reject
        null hypotesis
        
        p < .05 :arrow_forward: significant
      - r or Pearson's r
        (Pearson correlation coefficient)
        
        :key: variance accounted: effect size
        
        :key: interpreted used a published standard.
        
        :key: In SLA research,
        we use Plonsky & Oswald, 2014
        
        Range: -1 to +1
        
        ±.25 :arrow_forward: small effect
        ±.40 :arrow_forward: medium effect
        ±.60 :arrow_forward: large effect
      - Mean
      - SD
        
        :bulb: A quantity expressing by how much the members of a group differ from the mean value for the group.
- - - - :key: 1 predictor
        variable
    - - :key: several
        predictor
        variables
      - :old_key: values
        
        β coefficient
        
        :bulb: Standardized coefficients beta reflects the relative importance of the variables, and is related to the distribution of the independent variables
      - Hierarchical multiple regression
      - Multiple linear
        regression
  - - - :bulb: The base for
        the prediction
      - Variable X
    - - :bulb: Predicted
        variable
      - Variable Y
    - - The variables r measured
        at the continuous level
      - Linear :couple_with_heart: btwn variables
      - There should be ~~significant outliers~~
      - The data shows homoscedasticity
        (equal variance)
      - The residuals (deviation) of
        the regression line r
        approximately normally distributed
      - There should be
        independence of observations
  - - - :key: a significant regression outcome does not NECESSARILY indicate a causal :couple_with_heart:
  - - - Reject/no reject
        null hypotesis
      - p < .05 :arrow_forward: significant
    - - :key: variance accounted: effect size
      - :key: interpreted used a published standard.
      - :key: In SLA research,
        we use Plonsky & Oswald, 2014
      - Range: -1 to +1 #
        
        ±.25 :arrow_forward: small effect
        ±.40 :arrow_forward: medium effect
        ±.60 :arrow_forward: large effect
    - - :bulb: A quantity expressing by how much the members of a group differ from the mean value for the group.
- - - - To assess whether the mean difference between paired/matched observation is significantly different from 0 (e.g. pre-test and post-test).
    - - :old_key: values
        
        Mean
        
        :bulb: measure of central tendency
        
        SD
        
        :bulb: measure of the variation variability in a dataset
        
        Cohen's d
        
        :key: effect size
        
        d=.40 :arrow_forward: small effect
        d=.70 :arrow_forward: medium effect
        d=1 :arrow_forward: large effect
        
        :hammer_and_wrench: Shows how strong
        the difference is
        
        Effect size calculator
        
        :key: interpreted used a published standard.
        
        :key: In SLA research,
        we use Plonsky & Oswald, 2014
        
        95 % CI of the mean
        
        :bulb: A measure of how stable the mean is
        
        t value (measure of the significant)
        
        difference btwn the means
        :heavy_division_sign:
        SD
        
        p < .05
        
        p < .05 :arrow_forward: significant
        
        :bulb: significant of the test statistics
      - Does the data meet
        the assumptions?
        
        The data consists of
        1 DV that is measured at the continuous level (i.e., it is measured at the interval or ratio level).
        
        :memo: revision time (measured in hours),
        intelligence (measured using IQ score),
        exam performance (measured from 0 to 100),
        weight (measured in kg), etc.
        
        The data consists of 1 IV that consists of 2 categorical, related groups or matched pairs.
        
        There should be ~~significant outliers~~ in the differences between the two related groups.
        
        The distribution of the differences in the DV btwn the 2 related groups should be approximately normally distributed
        
        There needs to be homogeneity of variances
        
        :bulb: the variance of 1 variable is stable (i.e. relatively similar)
        at all levels of another variable.
        
        Use Pitman-Morgan test, ~~Levene's test~~
        
        It should not be significantly different. (p > .05)
      - Interpreting SPSS output
  - - - :old_key: values
        
        SD
        
        Cohen's d
        
        :key: effect size
        
        d=.40 :arrow_forward: small effect
        d=.70 :arrow_forward: medium effect
        d=1 :arrow_forward: large effect
        
        Negative value Cohen's d doesn't matter, it's just the group order
        
        :hammer_and_wrench: Shows how strong
        the difference is
        
        Effect size calculator
        
        :key: interpreted used a published standard.
        
        :key: In SLA research,
        we use Plonsky & Oswald, 2014
        
        95 % CI of the mean
        
        t value
        
        :bulb:
        variance between groups
        :heavy_division_sign:
        variance within groups
        
        Mean
        
        p value
        
        p < .05 :arrow_forward: significant
      - Does the data meet
        the assumptions?
        
        The data consists of
        1 DV that is measured at the continuous level (i.e., it is measured at the interval or ratio level).
        
        :memo: revision time (measured in hours),
        intelligence (measured using IQ score),
        exam performance (measured from 0 to 100),
        weight (measured in kg), etc.
        
        The IV should consist of 2 categorical, independent groups
        
        :memo: gender (2 groups: :male_sign: or :female_sign:),
        employment status (2 groups: employed or unemployed),
        smoker (2 groups: yes or no)
        
        The data should have independence of observations, which means that there is no :couple_with_heart: btwn the observations in each group or between the groups themselves
        
        DV should be approximately normally distributed for each group of the IV
        
        There should be ~~significant outliers~~
        
        There needs to be homogeneity of variances
        
        :bulb: the variance of 1 variable is stable (i.e. relatively similar)
        at all levels of another variable.
        
        Interpreting Levene's test for homogeneity of variances spss
        
        It should not be significantly different. (p>.05)
      - Interpreting SPSS output
    - - Useful for analysing simple experiments or when making simple comparisons between levels of IV