chapter 7/8/9 Flashcards
what is a z test
Determines the probability of obtaining a particular sample mean from a population just by chance
what is the z test based on
The Z test is based on a theoretical concept called the “distribution of sample means”
distribution of sample
A theoretical probability distribution that reflects the probability of obtaining different sample means from a population (given a particular sample n and given a known μ and σ .)
what can you do if you have the distribution of sample?
You can calculate the mean of the means: The Expected Mean (also often called the “Grand mean”).
It will be equal to μ (the pop mean).
what is the standard error of the mean?
the SD of all the means instead of scores. On average how far the sample means deviate from the grand mean
is the Standard error of the mean much smaller or larger than the SD of each sample
the SEM will be much smaller than the SD of each sample. sample means tend to be much more consistent less variable than raw scores
what happens to standard error of the mean as sample size increases?
it decreases the larger the sample, the less likely it will be to deviate substantially from μ
central limit theorem
Sample means drawn from a population will be normally distributed, even if the parent population is not normal.
(As long as sample n = ~ 30 or larger)
are extreme sample means common
no much rarer than extreme scores
is the amount that individual sample means will deviate from the grand mean, small or large
small especially when samples are large
if the sample n is large will there be small differences between M and μ that are found by chance?
If the sample n is large, even smallish differences between M and μ are unlikely to be found by chance.
what is happening when M does not exactly equal u
There are 2 possibilities:
1.) Sampling Error: by chance we obtain a sample mean that does not equal the population mean
2.) The sample is truly different from the population (due to an experimental manipulation or maybe because it is actually a different population. This may be a big deal depending on the explanation.)
what does it mean when p < .05?
The sample seems to represent a different population than the comparison population, the difference is statistically significant
type I error
rejecting the null hypothesis when it’s actually true or a false positive
Type II error
failing to reject the null hypothesis (retaining the null) when it’s actually false. false negative
confidence intervals
Significance testing tells us if the sample means is different from the population mean.
Confidence intervals are used to estimate the likely mean of the population represented by the sample.
when do you use a z test?
when you are comparing a sample mean to a known μ, and you know σ.
when do you use one sample t test
when you are comparing a sample mean to a known μ, and you don’t know σ.
when do you use a two-sample t test?
Comparing two sample means, don’t know μ or σ
what is the denominator of a one-sample t test
Denominator called the estimated
standard error of the mean: sx
pearsons r
is the most common way of measuring a linear correlation. It is a number between -1 and 1 that measures the strength and direction of the relationship between two variables.
what is the denominator of a z test
the average distance between M and u that would be expected if the null was true
As alpha increases, what happens to the risk of type 1 error? Liklihood of rejecting the null?
both increase
What is the numerator of the z score formula?
actual distance between M and u
what is the z obtained
the difference between the observed sample mean and the hypothesized population mean divided by the standard error of the mean
what does it mean when the z obtained is in the critical region
reject the null hypothesis
what does it mean when the data is not in the critical region?
sample data are not located in the critical region; the data do not provide strong evidence that the null hypothesis is wrong; decision: fail to reject the null hypothesis
what it means to reject the null
It is very unlikely* (p < .05) that the difference between your groups is due to chance
assumptions of the z test
1.) data are interval or ratio
2.) you know both the mean and the standard deviation of the population.
power
The probability of rejecting the null hypothesis if the null hypothesis is false.
power and sample size relationship?
The larger your sample size, the more power.
power and effect size
The strength of the relationship that truly exists between IV and DV. (How far apart are the means in the population?)
cohens d
form of effect size. the difference between two means divided by a standard deviation for the data
difference between t test and z test
z-tests (population) are used when we have large sample sizes (n > 30), whereas t-tests are most helpful with a smaller sample size (n < 30) (sample).
