7. The Normal Distribution: t-tests. Flashcards
What does a normal distribution show?
The true relative frequency of all possible values of a continuous random variable
What are known characteristics of a normal distribution?`
- symmetric around the mean
(mean=mode=median) - 68.3% of the area is within 1SD of the mean
- 95% of the area within 1.96SD of the mean
What is a z-score?
a test statistic used to calculate probabilities for any data that has a normal distribution
(observed mean - distribution mean) / SD of population
what is needed if we are estimating the population standard deviation using the sample standard deviation?
we use the z-score to standardise our estimate
- first work out SD of the sample mean
s/root(n) - use this to carry out a students t-test
(same equation for z-score but with sample SD calculation)
What does a one-sampled t-test do?
Compares the means of a random sample to the mean of the population under the null hypothesis
What are the assumptions of a one sample t-test?
- The data are a random sample from the population.
- The variable is normally distributed in the population.
(Note: the t‐test is robust to minor violations of the
normality assumption.)
How do you create a confidence interval for the population mean
observed mean +/- 1.96(t-test statistic)
What is the difference between a paired sample t-test and an independent sample t-test?
paired sample:
- Makes a comparison of measures made from units with shared features
independent sample:
- compares measures from independent sample units
when is a paired sample t-test useful
when controlling for other sources of variation that contribute to a measurement than the treatment in question
When is an independent two sample t-test useful?
when it is difficult/not possible to use a paired‐design
What are the assumptions of a paired samples t-test
Each of the two samples is a random sample from its population
The numerical variable (i.e. the response variable) normally distributed in each population
The standard deviation (and variance) of the numerical variable is the same in both populations
What are the assumptions of an independent two samples t-test?
The sampling units are randomly sampled from the population
The paired differences have a normal distribution in the population
What does an f-test do?
tests for equality of variances for two independent samples
H0: var1 = var2
H1: var1 =/ var2
Why do we need a f-test?
In reality the variance between two groups is not the same
- there may be overlapping confidence intervals
- and the difference in means may be small
