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**Parametric Statistical Tests Vs. Non Parametric Statistical Tests
- **Parametric Statistical Tests
- -Population parameters are specified:
- Shape: i.e. normal
- Variance: i.e. equal
- Interval scale of measurement
- **Non Parametric Statistical Tests
- -Do not specify the parameters of population: doesn't have to be normal, can be skewed.
- -Most require only an ordinal scale of measurement: First, Second, Third.
**Statistical Tests -For Nominal data, Between and Within Designs: Chi Square One Sample Test
- -Assume a data set that can be arranged in mutually exclusive categories; either in blue OR red category, not both. Pregnant or Not Pregnant.
-Question is whether the number of occurrences in each category is different than what would be expected by chance if the null hypothesis were true; we're looking to see if occurrences are different than what we expect vs. what we observed.
Modes of play in children or Opinions about gun control
**Chi square one sample test:
- will allow you to determine whether your observations are different than would be expected by chance
-Are there more aggressive children in this sample than what one would expect from a random sample from the population? If you were perform a T test or anova; Give a scale from 1-10 and give a rating for the child from least agressive to worst.
-Chi square INSTEAD: is a yes or no. That's it.
-Example 2: Are there fewer people in this sample in favor of gun control than would be expected from a random sample from the population? T-test or F-Test gives a 1-10 scales
Chi square Rational and Method
-Observed and Expected Definitons?
Basically, one sample chi square test compares Observed vs. Expected Frequencies.
-Observed frequencies (number of observed occurrences within each category)
-Expected frequencies (number of occurrences within each category expected by chance if null hypothesis is true )
**The logic of the Chi Square:
-If the differences between O and E are small, chi-square will be small
-If the differences between O and E are large, chi-square will be large
-And if chi-square is large enough, then your conclusion will be that the observed frequencies are such that your sample does not come from the population from which the null hypothesis was derived i.e., you reject the null hypothesis (the sample is special)
**Evaluate chi-square using the chi-square distribution for your chosen alpha level using...
-Using degrees of freedom: (k-1)
-Reject, at your alpha level (.05), if observed chi-square is greater than tabled value
-Reject the Null: Chi obtained must be greater than chi critical
**One-Sample Chi Square Interpretation:
A chi-square was performed and showed significant difference among the eight position, x2=(df=k-1), n=144)=Chi Obtained, p<.05.
A correlation is measure of association between two quantitative variables with respect to a single individual
A correlation coefficient is a descriptive statistic that quantifies the degree of the association between two variables
Types of Correlations:
Positive: high values of one variable are associated with high values of the other variable
Negative: high values of one variable are associated with low values of the other variable
Zero: values of one variable are not associated with the values of the other variable
Perfect: each value of one variable is associated with only a single value of the other variable and plot a straight line
Coefficient of Determination
After calculating a Pearson Product-moment Correlation Coefficient you can go a step further by calculating the Coefficient of Determination
-- which indicates how much of the variability in one variable is proportional to the variability in the other variable.
The coefficient of determination is a measure of the proportion of variance that can be accounted for in one variable because of its association with another variable
- Calculation:Square the Pearson Product-moment Correlation Coefficient
- =>Coefficient of Determination = r²
Final words about Correlations:
Correlations DO NOT EVER indicate causation
The Pearson Product-moment Correlation Coefficient requires the measurement of two quantitative variables on each individual
The Pearson Product-moment Correlation Coefficient is only applicable to LINEAR relations