Chapter 9: Intro to t-statistic , Chapter 14: Correlation and Regression -…
Chapter 9: Intro to t-statistic
t-statistic : hypothesis testing tool that uses estimated standard error in the denominator of the z-score formula
used to test an unknown population mean when standard deviation is unknown
Estimated Standard Error: approximation of the standard distance between a sample mean and the population mean
Degrees of Freedom: Value of scores in a sample that are independent and allowed to vary
An alternative method for measuring effect size is to determine how much the variability in the scores is explained by the treatment effect
Confidence Interval: a range of values, centered around a sample statistic
Two basic assumptions when doing hypothesis tests with a t-statistic
The population sampled must be normal
The values in the sample must consist of independent observations
T- Distributions: will form if t-values are computed for every possible random sample for a specific sample size, or a specific degree of freedom; usually have a flat and spread out shape
z-score distributions: will form if all possible samples of a population size are selected, and a z-score for each sample mean is completed
is directly related to sample variance so large variance means larger error and small variance means smaller error
Chapter 14: Correlation and Regression
Pearson correlation: measures the degree and the direction of the linear relationship between two variables.
Positive correlation: two variables go in the same direction; as the value of the X variable increases , the Y variable also tends to increase; when the X variable decreases, the Y variable also decreases.
Negative correlation: two variables go in opposite directions; as the value of the x variable increases , the y variable tends to decrease; when the x variable decreases, the y variable increases
Relationship between X & Y with Correlation:
the direction of the relationship
the form of the relationship
the strength of consistency of the relationship
Correlation: a statistical technique that is used to measure and describe the relationship between two variables. usually requires two scores for each individual; identified as X & Y
Spearman Correlation: measures consistency, rather than form. If two variables are consistently related, their ranks are also related lineraly
Correlation is applicable to :
regression: statistical technique for finding the best-fitting straight line for a set of data
regression line: the resulting straight line after finding the regression
standard error of estimate: gives a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data.
Point - Biserial correlation: measures the relationship between two variables where one variable is regular/numerical and the other has only two values
Binomial Variable: a variable with only two values
sum of products of deviation: used to measure the variability shared between two variable
Phi - Coefficient: the correlation between two variables, when both variables (X and Y) measured for each individual are dichotomous,
To compute the phi-coefficient:
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.
The value r² is called the coefficient of determination because it measures the proportion of variability in one variable that can be determined from the relationship with the other variable