Single Sample t Test Flashcards
Standard Deviation
SD= √ Σ(X-M)^2 / N
Calculating standard deviations from samples when estimating the population standard deviation
SD= √ Σ(X-M)^2 / (N-1)
When do we use t distributions?
if we don’t know σ
As N approaches infinity, the t distribution approaches…
the z distribution
The shape of a smaller sample size curve is…
wider and flatter
Degrees of freedom
the number of scores that are free to vary when we estimate a population parameter from a sample
Calculating degrees of freedom
df= N-1
How do we use the t tale to find critical values for hypothesis testing?
know our degrees of freedom, alpha level, and whether we are using a one-tailed or two-tailed
Assumptions for a one sample t test
- Dependent variable is on a scale measure
- Participants are randomly selected
- Population distribution is approximately normal
Conceptual understanding of the one sample t test
A hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean (or at least suspect a mean), but for which we do not know the population standard deviation
-similar to z statistic
Calculating a t statistic
t= (M-μM) / Sm
Calculating standard error (Sm)
Sm= (S / √N)
Steps for hypothesis testing
- Identify the populations, distribution, and assumptions, and then choose the appropriate hypothesis test
- State the null and research hypotheses, in both words and symbolic notation
- Determine the characteristics of the comparison distribution
- Determine the critical values, or cutoffs, that indicate the points beyond which we will reject the null hypothesis
- calculate the test statistic
- Decide whether to reject or fail to reject the null hypothesis
Equations for 95% confidence interval
Mlower= -t(Sm) + Msample Mupper= t(Sm) + Msample
Cohen’s d
d= (M-μ) / s
