WEEK 4 - Revision of descriptive statistics and intro to SPSS

Question 1

What are descriptive statistics?

Answer 1

• statistics simply to describe data collected
• To screen data and observe trends

Question 2

What is inferential statistics?

Answer 2

• Use sample to infer something about the population
• Test whether a relationship/difference seen in a sample is sufficiently large to assume it may be real in the population
• Allows us to test hypothesis and make decisions based on sample data

Question 3

How do you characterise a data set?

Answer 3

look at:
1. Central Tendency (mean, median, mode)
2. Variability (sum of squares, variance, SD, range, Standard error)
3. Shape (modality, skew, kurtosis)

Question 4

Under a true (ideal) normal distribution, what would the mean, median and mode be?

Answer 4

The mean, median and mode would all have the same exact value

Question 5

What is modality?

Answer 5

The number of central clusters a distribution possesses

*number of points on the photo**
- bimodal (scores vary around 2 central points)
- Unimodal (scores vary around 1 central point)

Question 6

What is kurtosis?

Answer 6

Preakness (how tightly clustered scores are around the mean)

leptokurtic - small
normal - normal
platykurtic - large

Question 7

What is skew

Answer 7

The symmetry of the tails of the distribution

Question 8

What is the normality assumption?

Answer 8

• The distribution is unimodal
• The distribution has moderate peakiness
• The distribution has symmetric tails

Question 9

What is the mean

Answer 9

The sum of a set of numbers divided by the number of numbers that you have

Question 10

Why is the mean useful?

Answer 10

Tells us something useful about the centre of a data set
But does not tell us anything about the variability around the mean

Question 11

Why is the Sum of Squares useful?

Answer 11

Tells us something about the total variability in the data set but does not really characterise the degree to which each participant varies around the mean

Question 12

What does the SD tell us?

Answer 12

SD tells us the average amount of variability around the mean

Useful in telling us the degree of variability around the mean

Question 13

What is the purpose of central tendency?

Answer 13

Provides an estimate of the level of performance in each condition

Question 14

What is the purpose of variability?

Answer 14

Tells us how reliable our estimate (from the central tendency) is

Question 15

What is the ‘golden rule’ regarding central tendency and variability?

Answer 15

The golden rule here is that a measure of central tendency without an accompanying measure of variability cannot be accurately interpreted

Question 16

What is the formula for a statistic (in general, overall)

Answer 16

estimated effect size/ estimated erro

Question 17

When do we consider something ‘significant’

Answer 17

If the Stat Value is sufficiently far from the centre of the probability distribution (ie. into the tails), we make a judgment that the Stat Value is significantly different from the mean

p< 0.5
p less than.05 is the criteria for what we consider to be significant

Question 18

What is a z sore?

Answer 18

If we know the Mean (M) and the Standard Deviation (SD) of our data set, we can convert any score (X) to a Z-score simply by subtracting the mean, and then scaling (i.e. dividing) by the Standard Deviation

Question 19

What does the z stat tell us

Answer 19

The Z stat is basically telling us how many Standard Deviations away from the Mean a particular score is

Question 20

Z score hypothesis test

Answer 20

In effect we have been asking does this particular individual belong to/differ from a particular population (of which we know the mean and SD)

What is more generally the case is that we are asking questions about a group of people, where the population mean and SD may be unknown.

Question 21

What is a single sample sample z test

Answer 21

If we want to compare the mean of a group of peoples scores (which is normally the case in an experiment) we need to compare this against a a distribution of group mean scores (a distribution of means)

Question 22

What are the three types of distributions?

Answer 22

A) population
B) sample
C) distribution of means

Question 23

The bigger your error variance the ___ your statistic will be q

Answer 23

smaller

Question 24

What is central limit theorem

Answer 24

Basically says that the sampling distribution of the mean is itself a normal distribution it just has a much smaller error and smaller variability than the distribution of the scores itself

Question 25

If we want to test a sample mean we should compare it to..

Answer 25

a distribution of sample means

Question 26

What is the standard error of the mean Sm

Answer 26

SM is the sample SD divided by the square root of the number of observations in the sample

Question 27

What is t?

Answer 27

When we estimate the population distribution, we no longer use the standard normal distribution (since one or more population parameter is unknown)

Instead, we use a special family of distributions called a
t distributions which are approximations of the Z distribution, but which changes shape according to the size of the degrees of freedom (n-1)

Question 28

How are t - distributions different to z and normal distributions?

Answer 28

T distribution very similar to z or normal distribution BUT slightly different on for each sample size ….

Gets closer to normal as sample size increases….

Slightly more error involved as we have estimated population variance so slightly more of distribution in tails

The smaller the sample size, the smaller the df, the larger the critical t value that must be exceeded

Question 29

What are the types of t-tests?

Answer 29

Single sample T-test
Repeated measures T-test

Question 30

What is the difference between a Z and a T test

Answer 30

In a Z test, the population SD is known –>
In a T-test the population SD is unknown –> instead of population SD we use s which is the estimated population standard deviation

Question 31

What is a single sample t -test

Answer 31

Where you just have a mean and you want to know weather its different to some hypothesised value –> could be the population mean or a number like 102

**want to know if the difference between your mean and that comparison value significantly greater than you would expect to find by chance

Question 32

What is a repeated measures T-test

Answer 32

Same as a single sample t-test but for a repeated measure. So, compares someone’s scores from before and after (looks at the difference between before and after)

A repeated measures T-test is actually just a single sample T test on a set of different scores where the comparison value is just zero (zero because that means nothing changed)

So to do a repeated measure T-test , I would take my mean different score and I would subtract the hypothesised different score here, which is zero divide by my standard error of my mean and I would establish whether that was significant or not.