Summarising Data: central tendency; variability; z-scores; effect size.

Question 1

What do we need for data to be Effectively Summarised?

Answer 1

• the typical response and

- how much responses differ across participants.

Question 2

What are examples of Central Tendency?

Answer 2

• Mean
• Median
• Mode (rarely used)
• Trimmed mean (rarely used)

Question 3

What is the Mean and how do you calculate it?

Answer 3

Mean (M): sum up all scores, then divide by the total number of scores.

M =ΣX/N

X = Individual score(s)
Σ = sum of X
N = sample size

Question 4

What is the Median and how do you calculate it?

Answer 4

Median separates higher from lower half of scores.

• Order scores from highest to lowest; score in the middle is median
• IF 2 values in the middle, find their mean

Question 5

What is the Mode and how do you calculate it?

Answer 5

Mode: most frequent score in sample.

Eg: 1, 1, 3, 8 => 1 is the mode

Question 6

What is the Trimmed Mean and how do you calculate it?

Answer 6

Trimmed mean: disregards proportion of scores at either end of distribution; then calculates mean.

E.g., -3, 1, 2, 3, 4, 5, 6, 7, 8, 17 (without -3 and 17)
Mean trimmed 20% = 4.5

Question 7

Why is variability important?

Answer 7

Although a mean can be similar, the distribution of results can highly impact the result.

Question 8

What are the Measures of Variability?

Answer 8

Variance and standard deviation most important measures of variability

Question 9

How do you calculate Varience?

Answer 9

1. Subtract mean from each score (results in deviation score).
2. Square each deviation score (results in the squared
   deviation scores).
3. Add up all squared deviation scores.
4. Divide this sum by number of scores.

S^2 =Σ(X - M)^2/N

Question 10

What are the disadvantages of Variance?

Answer 10

Variance useful for computations in statistics. But we lack intuitive understanding.

Question 11

What is the advantage of Standard Deviation?

Answer 11

It is intuitively more plausible than variance

Question 12

How do you calculate Standard Deviation (S or SD)?

Answer 12

S = √S^2 (Square root of Variance)

approximates scores’ average distance from M (mean score)

Question 13

What is the Z-score?

Answer 13

Z-score: number of standard deviations a raw score is

above or below the mean. (how far a raw score is from a mean in the units of standard deviation)

Question 14

How do you calculate Z-score?

Answer 14

Z = X – M / SD

Subtract mean from raw score, then divide by standard
deviation.

Question 15

What are the Characteristics of Z-scores?

Answer 15

For z-scores always
M = 0
SD = 1.

Question 16

How can you calculate the raw score from the Z-score?

Answer 16

X = Z x SD + M

Question 17

How do we communicate results of an experiments?

Answer 17

Compare means for same variable across groups

Question 18

What is Cohen’s d?

Answer 18

a method to compare results by using standard “currency” to express magnitude of effect.

Question 19

How do you calculate Cohen’s d?

Answer 19

Cohen’s d = µ1- µ2 / σ

µ1 and µ2 = the population means
σ = the pooled population SD .