T statistics
Hypothesis testing is used to determine if the difference between the data and the hypothesis is greater
in order to test the hypotheses with the z score we need to now the popular standard deviation
Z score
hypothesis is used to find out more about the unknown population
t statistics shares the same formula as z score except it uses the estimated standard error as the denominator
Uses population variance
uses sample variance
Degrees of freedom: the number of scores in a sample that are independent and free to vary
the greater value of the degrees of freedom the better the sample variance
every sample from a population can be used to compute a z score or a t statistic
The greater the degrees of freedom the better the t distribution approximates normal distribution
the shape of the distribution changes with the degrees of freedom
a t distribution tends to be flatter and more spread out
Distribution
the bottom of the formula varies from one sample to another
the numerator and the denominator of the t statistic vary
as the sample size and the df increases, the variability in the t distribution resembles a normal distribution
the values in the sample must consist of independent observations
the population sampled must be normal
Correlation
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Validity: to determine if the correlation between testing does what it claims
Reliability: Measurement procedure is considered reliable to the extent that it produces stable, consistent measurements.
Theory Verification:prediction of the theory could be tested by determining the correlation between the two variables
Prediction:If two variables are known to be related in some systematic way
Correlation describes the relationship between two variables but it doesn't explain why its related
The value of a correlation can be affected greatly by the range of scores represented in the data
Outliers can have a dramatic effect on the value of a correlation.
partial correlation measures the relationship between two variables while controlling the influence of a third variable by holding it constant
Pearson Correlation
computed for sample data
measures the degree of linear relationship between two variables
Spearman Correlation
used to measure the relationship between X and Y when both variables are measured on ordinal scales