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Concept Map 4 - Coggle Diagram

- - - - computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean
    - - The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.
      - the bigger the df the better the sample variance represents the population variance and thus the better t statistic approximates the z-score
        
        the bigger the sample the better it represents the population distribution
        
        t distribution is the set of t values computed for every possible random sample for a specific sample size or a specific degrees of freedom
        
        the t distribution has more variability than a normal z distribution especially when df values are small
        
        the denominator of the t statistic varies from one sample to another and also the numerator, causing the distribution to be more spread out and flat than z scores
        
        the estimated standard error is inversely related to the number of scores in the sample. The larger the sample, the smaller the error
        
        t statistic approximates a normal distribution just as a t statistic approximates a z score, this is determined by degrees of freedom
      - Steps to calculate t statistic:
        
        calculate the sample variance
        
        compute the estimated standard error
        
        compute the t statistic
      - All you need to compute a t statistic is a null hypothesis and a sample from the unknown population
      - the t distribution table has degrees of freedom and α listed to find the t statistic
      - values in the sample must consist of independent observations, This means the occurrence of the first event has no effect on the probability of the second event
      - Population sampled must be normal: With very small samples, a normal population distribution is important. With larger samples, this assumption can be violated without affecting the validity of the hypothesis test
      - estimated Cohen's d measures effect size
        
        use the standard deviation formula to enter in to estimated d
        
        not influenced at all by sample size
      - percentage of variance accounted for by the treatment (r2)
        is a measure of effect size that determines what portion of the variability in the scores can be accounted for by the treatment effect
        
        only slightly affected by changes in the size of the sample
- - - - positive correlation: the two variables tend to change in the same direction
      - negative correlation: the two variables tend to go in opposite directions
      - The form of the relationship- measures straight-line and other relationships
        
        The strength or consistency of the relationship- linear, scattered, or in between
        
        perfect correlation
        relationship where the actual data points perfectly fit the specific form being measured
        
        values between 0 and 1 indicate the degree of consistency
        
        envelope: line around the data points
        
        a football shaped envelope means the correlation is about 0.7. Envelopes that are fatter than a football have correlations closer to 0, and narrower shapes have correlations closer to 1.00
    - - sum of products measure of the degree of covariability between two variables; the degree to which they vary together
        
        Definitional Formula
        
        Find the X deviation and the Y deviation for each individual
        
        Find the product of the deviations for each individual
        
        Add the products
        
        Computational Formula
      - Multiplying, adding or subtracting positive constant does not change the pattern formed by the data points and does not change the correlation
        
        Multiplying by a negative constant produces a mirror image of the pattern and does change the sign of the correlation
      - each X and Y value can be transformed into a z-score
        
        Sample z-score
    - - Correlation is used for: Validity to see if the correlation of one test is alike with a similar test
        
        Correlation is used for: Reliability to determine the relationship between two sets of measurements. When reliability is high, the correlation between two measurements should be strong and positive
        
        By taking two measurements for each individual, it is possible to compute the correlation between the first score and the second score
        
        Correlation is used for: Theory Verification the prediction of the theory could be tested by determining the correlation between the two variables
    - - restricted range: a correlation is computed from scores that do not represent the full range of possible values
        
        outliers: one extreme data point can inflate the size of the correlation
        
        correlation measures the strength of a relationship between two variables on a scale from 0–1.00
        
        coefficient of determination (r2) it measures the proportion of variability in one variable that can be determined from the relationship with the other variable
        
        regression toward the mean When there is a less-than-perfect correlation between two variables, extreme scores for one variable tend to be paired with the less extreme scores (more toward the mean) on the second variable
        
        partial correlation measures the relationship between two variables while controlling the influence of a third variable by holding it constant
    - - null hypothesis is “No. There is no correlation in the population.” or “The population correlation is zero.”
      - alternative hypothesis is “Yes. There is a real, nonzero correlation in the population.”
      - t statistic in correlation
        
        degrees of freedom df= n-2
    - - measure the consistency of a relationship between X and Y, independent of the specific form of the relationship
    - - convert each of the dichotomous variables to numerical values by assigning a 0 to one category and a 1 to the other category for each of the variables
        
        use the regular Pearson formula with the converted scores.