Hypothesis testing with t-test (single sample) EdPuzzle Flashcards
If we don’t know what the standard deviation of a population is, which test is the most appropriate?
t-test
Overview of t-test:
Definition:A statistical test used to determine if there is a significant difference between the mean of a sample and a known or hypothesized population mean
If population variance is not known, a solution is to estimate it from the sample’s variance.
If the sample represents a population, they should have similar variance.
However, if the sample’s variance cannot be used directly as an estimate of the population variance. It can be shown mathematically that a sample’s variance will, on the average, be a bit smaller than its population’s.
Estimated population variance is figured as the sum of squared deviations from divided by the number of participants minus one: s²=ss / (n-1)
On average, how does a sample variance relate to the population variance it comes from ?
It will be smaller
Why should we NOT use a Z-test for this study?
We don’t know the population standard deviation.
Directional Hypothesis
assessed using a one-tailed test, predicts that the populations will differ in a particular direction (e.g. sample has a higher mean than the population). The region of rejection is in one side (tail) of the distribution.
Nondirectional Hypothesis
assessed using a two-tailed test, predicts that the populations will differ, but does not specify a particular direction. The region of rejection is in BOTH sides (tails) of the distribution.
On which side of the t-distribution would we expect to see our sample mean? (hint: we think it will take Longer time)
The positive or Right side
t-distribution graph compared to normal distribution
Because we are using a new measure of spread, we can no longer use the standard normal distribution and the z-table to find our critical values.
For t-tests, we will use the t-distribution.
Heavier tails of t-distribution
Note: As degrees of freedom increase, t-distribution approaches normal distribution
The t-distribution changes shape with what?
Degrees of freedom (df)
Degrees of Freedom
Definition: The number of values in a study that are free to vary
Formula for a single sample t-test: df = n - 1 (where n is sample size)
Importance: Affects the shape of the t-distribution and critical values
Which df looks most like the normal curve?
df=30
What is the critical value when we cross df=3 and alpha=.05?
t=2.353
Calculate the statistic (t-test)
data -> sample size/degrees of freedom -> mean -> sum of squares (x - mean)² -> standard deviation (sum of squares / degrees of freedom and take square root of that) -> standard error (standard deviation / square root of sample size n) -> test statistic.( t = sample mean - population mean / standard error)
To get a deviation score, we subtract the _____ from the _____
mean; score
To get the Sum of Squares, what do you do with all the squared deviation scores?
Add them up
In the simplified formula for the standard deviation, what is the denominator?
degrees of freedom
The standard error of the estimate is based on our ________ NOT the ________.
sample; population
What value goes in the parentheses when reporting our results?
degrees of freedom example t(3) = 3.46, p < .05
What do we do to determine importance of significant research results?
Find the effect size d = ( sample mean - population mean) / sample standard deviation
Cohen’s d Interpretation guidelines
small effect d ~ 0.2
medium effect d ~ 0.5
large effect d ~ 0.8
Assumptions of t-test
Random sampling or random assignment
Normally distributed population (or large enough sample size)
Interval or ratio level data
No significant outliers
