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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
Function:
 **Function
 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.
For example: 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 110 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? Ttest or FTest gives a 110 scales

Chi square Rational and Method
compares?
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, chisquare will be small
If the differences between O and E are large, chisquare will be large
And if chisquare 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 chisquare using the chisquare distribution for your chosen alpha level using...
Using degrees of freedom: (k1)
Reject, at your alpha level (.05), if observed chisquare is greater than tabled value
Reject the Null: Chi obtained must be greater than chi critical

**OneSample Chi Square Interpretation:
A chisquare was performed and showed significant difference among the eight position, x^{2}=(df=k1), n=144)=Chi Obtained, p<.05.

Correlations Definitions
correlation:
coefficient:
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
definiton
calculaton
After calculating a Pearson Productmoment 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.
Definition: 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 Productmoment Correlation Coefficient
 =>Coefficient of Determination = r²

Final words about Correlations:
Correlations DO NOT EVER indicate causation
The Pearson Productmoment Correlation Coefficient requires the measurement of two quantitative variables on each individual
The Pearson Productmoment Correlation Coefficient is only applicable to LINEAR relations

