Z-scores

Question 1

What are some examples of different scales used to measure the same variable?

Answer 1

• Height: feet/inches vs. meters
• Weight: stones vs. kilograms
• Temperature: Celsius vs. Fahrenheit vs. Kelvin
• Speed: miles per hour, km per hour, knots
• Drink size: pint and half-pint (UK) vs “large” and “small” (Europe)

Question 2

Why does measurement context matter in comparisons?

Answer 2

Different scales of measurement make comparisons complicated.
* For example, the cost of beer in the UK vs Slovakia may be difficult to compare due to differences in volume and currency.

Question 3

How does the cost of beer in the UK compare to Slovakia when taking volume and currency into account?

Answer 3

• UK: Pint of beer costs £4.79, volume = 568ml.
• Slovakia: Large beer costs 1.10€, equivalent to £0.92, volume = 500ml (equivalent to £1.25 for a pint).**

Question 4

How does the cost of beer compare relative to average monthly wages in the UK and Slovakia?

Answer 4

UK: A pint costs 0.16% of the average monthly wage (£3000).
Slovakia: A pint costs 0.10% of the average monthly wage (€1484 ≈ £1236), which is equivalent to £2.80 on a UK salary.

Question 5

What types of things are measured in psychology?

Answer 5

Direct biological responses like heart rate and reaction times.
Complex concepts like well-being, anxiety, depression, creativity, etc.

Question 6

How are psychological constructs usually measured?

Answer 6

• Psychological measures often consist of multiple “items” or questions, rated on a Likert Scale (e.g., 1-5 from “Strongly disagree” to “Strongly agree”).
• The final score is calculated by summing or averaging the responses to get a measure of the construct.

Question 7

Why are there so many different scales for the same psychological concepts?

Answer 7

• New scales may be developed to improve upon existing ones, for profit, or to provide open-source alternatives.
• This results in a variety of scales being used to measure the same concept.

Question 8

What are some examples of well-being scales in psychology?

Answer 8

1. WHO-5 Well-Being Index (5 items, 1-6)
2. Ryff’s Psychological Well-Being Scales (42 items, 1-6)
3. Satisfaction with Life Scale (5 items, 1-7)
4. Warwick-Edinburgh Mental Well-being Scale (14 items, 1-5)
5. Flourishing Scale (8 items, 1-7)
6. Positive and Negative Affect Schedule (30 items, 1-5)

Question 9

What are some examples of depression scales in psychology?

Answer 9

• Beck Depression Inventory-II (21 items, 0-3)
• Patient Health Questionnaire-9 (9 items, 0-3)
• Center for Epidemiological Studies Depression Scale (20 items, 0-4)
• Hamilton Depression Rating Scale (17 items, 0-4)
• Geriatric Depression Scale (30 items, 0-1)
• Zung Self-Rating Depression Scale (20 items, 1-4)

Question 10

What is the issue with using different anxiety scales in research?

Answer 10

Different scales can yield different results, making it difficult to compare findings.
For example, a difference of 3 on a scale of 0-100 is less meaningful than a difference of 3 on a scale of 0-5.

Question 11

How does the scale of measurement affect interpreting results?

Answer 11

A score difference on a larger scale (e.g., 0-100) can seem small, while the same difference on a smaller scale (e.g., 0-5) may be more significant.

Question 12

What is the difference between extroversion and introversion?

Answer 12

• Extroverts: Prefer social interaction, seek group support under stress, and enjoy activities involving others.
• Introverts: Prefer solitude, tend to withdraw in stressful situations, and enjoy solitary activities.

Question 13

How can two different measures of extroversion lead to conflicting results?

Answer 13

Example: One person scores 18 on Eysenck’s Personality Inventory (0-24), while another scores 30 on the Big 5 Inventory (0-40). The scale ranges are different, making it unclear who is more extroverted.

Question 14

How do Z-scores standardize different measurements?

Answer 14

• Z-scores convert raw scores into standard deviation units, making it easier to compare different scales.
• A Z-score tells us how far a score is from the mean in standard deviations.

Question 15

How is a Z-score calculated?

Answer 15

Formula: Z = (X - μ) / σ
* X = score
* μ = mean of the sample
* σ = standard deviation of the sample

Question 16

What do positive and negative Z-scores indicate?

Answer 16

• Positive Z-scores: The score is above the mean.
• Negative Z-scores: The score is below the mean

Question 17

How do Z-scores help in comparing two different distributions?

Answer 17

Z-scores standardize scores, allowing us to compare them across different distributions, even if they have different scales.

Question 18

What are the key characteristics of a normal distribution in terms of Z-scores?

Answer 18

~68% of scores fall within ±1 Z-score from the mean.
~95% of scores fall within ±1.96 Z-scores from the mean.
~99% of scores fall within ±2.58 Z-scores from the mean.

Question 19

What Z-score range is considered to represent extreme or outlier values?

Answer 19

Z-scores greater than |3.29| are considered extreme and are often flagged as potential outliers (occur in less than 0.1% of cases).

Question 20

What is the caution when using Z-scores to identify outliers?

Answer 20

• Removing cases based solely on Z-scores is not recommended as outliers should be investigated.
• Extreme Z-scores may not always indicate errors or invalid data, and removing them can bias results.

Question 21

Why does context matter when using Z-scores to compare distributions?

Answer 21

Z-scores assume identical circumstances for collecting data. If distributions are from different contexts (e.g., different populations), the comparison may be misleading.

Question 22

How do Z-scores relate to normal distributions?

Answer 22

• Z-scores are used to describe how far values are from the mean in a normal distribution.
• They help quantify the proportions of scores expected within certain distances from the mean.

Question 23

What proportion of data falls within 1, 2, and 3 standard deviations in a normal distribution?

Answer 23

~68% within ±1 SD
~95% within ±2 SD
~99% within ±3 SD

Question 24

How do Z-scores help identify outliers in data?

Answer 24

• Scores with Z-scores above |3.29| are likely outliers (occur with less than 0.1% probability).
• Scores above |2.58| are rare but not necessarily outliers and should be examined.**

Question 25

What should you avoid when handling outliers in data?

Answer 25

• Avoid automatically removing outliers based on Z-scores, as this can lead to biased analysis.
• Outliers should be carefully investigated to ensure they are not data entry errors.

Question 26

what is a Z-score

Answer 26

a standardized score that indicates how many standard deviations a particular data point is away from the mean of its distribution. It allows us to compare scores from different distributions on a common scale.

Question 27

what does a Z-score tell you ?

Answer 27

A positive Z-score means the score is above the mean of the distribution.
A negative Z-score means the score is below the mean.
The absolute value of the Z-score tells you how far the score is from the mean in terms of standard deviations.