Topic 6 Flashcards
What are characteristics of a population known as?
Known as parameters
What are the population parameters?
- Population mean = μ
- Population Standard Deviation = σ
What are characteristics of a sample known as?
Known as statistics
What are the sample statistics
- Sample mean = x̄
- Sample standard deviation = s
How do we formulate sampling distributions?
- Make a guess about population frequency distribution, hypothesise what μ is
- Take a random sample from the population
- Decide if sample came from a population like the one you guessed in Step 1. (Usually based on how close x̄ is to hypothesised μ)
How do we plot a sampling distribution?
- Assume normal population distribution with μ and σ
- Take repeated samples of size n
- Plot x̄ of each sample
In a generic sampling distribution what is the distribution?
Normal distribution
In a generic sampling distribution how does the mean relate to population mean?
The mean of the sampling distribution is equivalent to the population mean
Describe the standard deviation of a sampling distribution
It is depicted as the standard error σx̅. It’s the standard deviation of the sampling distributions
What is the standard error an expression of?
A numerical expression of the degree to which means differ from one sample to another
If the standard error is large what will the variability be?
Large
If the standard error is small what will the variability be?
Small
What does a small standard error tell us about x̄?
That x̄ likely close to μ
We wouldn’t normally know the value of σ, how would we estimate it?
Using sx̄ = s / square root of n
- > s = standard deviation of a single sample
- > n = number of observations in sample
As n increases, what decreases?
sx̄ decreases due to decreased sample variability, meaning x̄ is a more accurate estimate of μ
What is the Z Score when looking at sample data?
Z = x̄ - μ / σx̅
sample mean - population mean / standard error
What is the amount of area beyond Z?
The probability of finding a score that distant from the mean on the basis of chance alone
Describe the Null Hypothesis
Hypothesis that the treatment has no effect and the observed sample mean is drawn from the population
Describe the Alternative Hypothesis
Hypothesis that the treatment has an effect and observed mean is drawn from population
Why would we retain the Null Hypothesis?
If observed sample mean could have reasonably been obtained from the distribution suggested by Null
Why would we retain the Alternative Hypothesis?
If the likelihood is very small that results could have been obtained from the distribution suggested by the Null
Describe the Significance level
Probability value that defines boundary between rejecting or retaining the Null hypothesis
What is the significance level usually set as?
0.05, sometimes 0.01
What is the region of rejection?
Proportion of area in sampling distribution that represents the sample means that improbable if the null is true
If Z (zobs) is > or equal to 1.64 what do we do?
Reject the null hypothesis
What is the critical value?
1.64
If a Z-Score sits in the region of rejection what does this allow us to do?
Reject the null hypothesis
Describe a one tailed test and when it’s appropriate to use one
- Test used because we have a directional alternative (can predict the direction of the effect)
- Used when there is evidence/theory to suggest that treatment will have an effect in a particular direction
Describe a two tailed test
-Test used when we have a nondirectional alternative
Describe the alpha value in a two tailed test
It is still 0.05 but now divided by 2 (to account for both sides) = 0.025
In which test is it more difficult to reject the null hypothesis?
Two tailed test
What is Zobs for a 2 tailed test?
1.96
Which tail test is more powerful?
One tail
When can the null hypothesis be rejected in a two tailed test?
Zobs < or equal to -1.96
Zobs > or equal to 1.96
