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Intro to the t Statistic - Coggle Diagram
Intro to the t Statistic
The t Statistic: An Alternative to z
Problem with z-scores
z-score formula requires more information than usually available
requires we know the value of the population standard deviation
t-Statistic
The estimated standard error is used as an estimate of the actual standard error when the value of o is unknown.
the t-statistic is used to test hypotheses about an unknown population mean when the value is unknown
Degrees of Freedom
describe the number of scores in a sample that are independent and free to vary
degrees of freedom = df = n-1
t-Distribution
complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df)
approximates the shape of a normal distribution
Shape of t Distribution
t distribution is flatter and more spread out
As sample size of df increases, the variability in the t distribution decreases, resembling a normal distribution
Hypothesis Tests with the t Statistic
Formulas
t = sample mean (from the data)-population mean (hypothesized from Ho)/estimated standard error (computed from the sample data
z to t= actual difference between sample (M) and the hypothesis (u)/expected difference between M and u with no treatment effect
Assumptions of the t Test
the values in the sample must consist of independent observations
the population sampled must be normal
Measuring Effect Size for the t Statistic
Percentage of Variance Accounted for by the Treatment
r^2= variability accounting for by the treatment effect/total variability
Criteria for interpreting the value of r^2
r^2 = 0.01... small effect
r^2 = 0.09... medium effect
r^2 = 0.25... large effect
Confidence intervals for estimating u
estimating an unknown population mean involves constructing a confidence interval
a confidence interval is an interval or range of values centered around a sample statistic
Directional Hypotheses and One-Tailed Tests
Directional hypothesis test w/ a t statistic
state the hypothesis and select alpha level
locate the critical region
calculate the t statistic
make a decision
Critical Region for One-Tailed Test
left hand tail is the critical region
