Z tests For Single Scores

Question 1

What does a z-score do?

Answer 1

It’s a statistic that will tell us if a particular score is far from the mean relative to the variability of the rest of the population

Question 2

How do you obtain a z-score?

Answer 2

Divide the difference between the score and the population mean by the Standard Deviation
SCORE - POPULATION / SD
A z score is the number of times bigger your observed difference is compared to your error variability

Question 3

What is a z-score?

Answer 3

A z score is the number of times bigger your observed difference is compared to your error variability
A z score is the number of standard deviations a score lies from the mean of a sample
They are calculated by subtracting the mean from the score (getting the difference) and dividing it by the SD

Question 4

Z score examples

Answer 4

Mean = 4; SD = 2; Flavia's score = 6
Z-score = (6-4)/2 = 1
Mean= 10; SD = 5; Helen's score = 20
Z-score = (20-10)/5 = 2
Mean = 15; SD = 8; Matt's score = 19
Z- score = (19-14)/8 = 0.5
Mean = 8; SD = 3; Daragh's score = 2
Z-score = (2-8)/3 = -2

Question 5

How do you get a standard distribution?

Answer 5

If you convert the scores of any distribution to z-create a standard distribution with a mean of 0 and SD of 1
If the original distribution is normal, converting the scores to z-scores creates a special distribution with very important properties - the standard normal distribution

Question 6

A score that has been converted to a z-score is a ratio and has been standardised. What percentage of the data falls within each section of the standard normal distribution for 1SD and 2SD?

Answer 6

68. 26% of all the data in a standard normal distribution lies between the mean and 1SD (i.e. One z score) either side
69. 44% of all the data Ina standard normal distribution lies between the mean and 2SD’s (i.e. Two z score) either side

Question 7

What does it mean if a point is far away from the mean?

Answer 7

It is unlikely that it is from the same distribution as the other scores
The further from the mean a point lies, the less likely it is that the data point belongs to the same distribution - z scores allow you to quantify just how unlikely that is

Question 8

What percentage of scores lie beyond 1.96 SD’s from the mean?

Answer 8

5%

Question 9

What is significance?

Answer 9

This is how we quantify ‘much bigger than the error variability’

Question 10

How do we measure significance?

Answer 10

If the difference between our score and the mean is so big that it places the score in an Andrea of the distribution where 5% or fewer of scores normally appear, we say we have a ‘real’ or ‘significant’ difference from the mean = p

Question 11

Why is 1.96 the critical value of z?

Answer 11

For all normally distributed samples, there is only a probability of 0.5 (5%) of any scores lying more than 1.96 SD’s (z-scores) away from the mean
Any value greater than that is unlikely to belong to the distribution i.e. It is significantly different

Question 12

What does the null hypothesis always state?

Answer 12

Any differences we find are entirely due to error variability

Question 13

In statistical tests, what are we testing and what are we making references to?

Answer 13

The null hypothesis is what we are testing and then we are making inferences to the experimental hypothesis

Question 14

What does the null hypothesis always state?

Answer 14

Any differences we find are entirely due to error variability

Question 15

What does p

Answer 15

The probability of any statistical result (p value) tells us how like
G it is that we would have obtained the results that we did if the null hypothesis were true i.e. How likely the results we obtained are due purely to the effects of error factors

Question 16

What does it mean if p

Answer 16

It is more likely that the effects are due to some other factor such as the independent variable

Question 17

What happens when a statistical result has a probability of p

Answer 17

You reject the null hypothesis which means that you can infer support for the experimental hypothesis (this is why the experimental hypothesis is sometimes known as the alternative hypothesis)

Question 18

What conditions must be met to test your hypothesis with z-scores?

Answer 18

Must have a single test score, know the population mean, and SD of the distribution you wish to compare your test score with

Question 19

What does a z-score of 1.96 or greater tell us?

Answer 19

There is a less than 5% chance that the score belongs to the null distribution. We can then conclude that the null hypothesis is probably false and the score does not belong to the distribution i.e. Is significantly different