Flashcards in Chapter 13 : Single Sample t-Test Deck (26):
When do you use the Z-test?(2)
-When the mean and standard deviation of the null-hypothesis population are KNOWN.
- Usually you will only have the mean.
When population standard deviation is UNKOWN what test do you use?
What are the three kinds of t-tests?
- Single Sample t-Test
- Correlated samples t-Test
- Independent Samples t-Test
What is the t-test formula, what data does it involve??????Difference with z-test?
- Tobt= Xobt- u/ Sx
**Sx= standard error of sample…
- Z formula uses POPULATION data not sample
Probability distribution of t-values:
- variation in t values?
- Probability ?
- different possible t values for samples of a given N
- Probability of getting each value if sampling is random from the null hypothesis population.
Characteristics of Sampling distribution of T ?
- shaped similarly to z distribution if: (2)
-Sample size X >/= 30
-If Ho population is normally distributed
There is a different curve for each ___(_).
- sample size (N)
What are Degrees of freedom? (df)
- When is this the most relevant ?
- number of scores that are free to vary in calculating any statistic.
- Most relevant when dealing with standard deviation.
What is the formula for the sum of deviations about the mean?
s = \/E(X-Xbar)^2/N-1
What is the formula for Xbar?
T and Z distributions are both ____ at zero. As the df increases, t becomes __ similar to z. As df approaches infinity, t becomes ____ to z. At any value of df ___.
Steps to solving single sample t-test problems?
1. solve for tobt
2. find the df
3. find tcrit on table D using Df and alpha
4. If | tobt |>| tcrit |, reject Ho
What is the formula for calculating Tobt directly from raw scores? Benefit?
- Tobt= Xbar obt - u/ >/SS/N(N-1)
- no need to calculate S
What does the IB has a real effect mean?
- Tobt is greater than Tcrit
- rejected Ho
What is the magnitude of the real effect?
- statistical significance vs practical significance.
Measures of effect size are calculated using what?
- Cohen's d
Cohen's d is?(2)
- relationship between mean difference and effect size, Mean diff= Xobt-u
- main interest is magnitude..absolute value!
Choen's d is _____. Divided by the __ standard deviation.
- standardized, sample
What is the computational equation for effect size for single sample T-tests?
- d= | xobt- u |/ s
Xobt= sample mean
u= population mean
s= sample standard deviation
d= estimated d
Often the ___ mean is unknown. We use the __ mean to estimate the ___ mean.
- uses only one value to estimate population mean
- uses a range of values to estimate population mean
What are confidence intervals?
- range of values which probably contain the population mean.
- values that bound the confidence interval
u lower= Xobt- Sxtcrit (Sx = s/ >/N)
u upper= Xobt + Sxtcrit
- can be CI of 95% or 99%
-If the confidence interval is 99% what is the range?
-what of 95%?
- -t 0.025 <= t 0.005
List the steps to solving for a confidence interval!
1. find Sx
2. examine alpha, if it's one or two tail,
3. find df
4. Solve for the lower and upper limits
5. conclude with the interval.