Z-scores
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What are some examples of different scales used to measure the same variable?
• 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)
Why does measurement context matter in comparisons?
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.
How does the cost of beer in the UK compare to Slovakia when taking volume and currency into account?
• 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).**
How does the cost of beer compare relative to average monthly wages in the UK and Slovakia?
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.
What types of things are measured in psychology?
Direct biological responses like heart rate and reaction times. Complex concepts like well-being, anxiety, depression, creativity, etc.
How are psychological constructs usually measured?
• 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.
Why are there so many different scales for the same psychological concepts?
• 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.
What are some examples of well-being scales in psychology?
• WHO-5 Well-Being Index (5 items, 1-6) • Ryff’s Psychological Well-Being Scales (42 items, 1-6) • Satisfaction with Life Scale (5 items, 1-7) • Warwick-Edinburgh Mental Well-being Scale (14 items, 1-5) • Flourishing Scale (8 items, 1-7) • Positive and Negative Affect Schedule (30 items, 1-5)
What are some examples of depression scales in psychology?
• 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)
What is the issue with using different anxiety scales in research?
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.
How does the scale of measurement affect interpreting results?
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.
What is the difference between extroversion and introversion?
• 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.
How can two different measures of extroversion lead to conflicting results?
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.
How do Z-scores standardize different measurements?
• 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.
How is a Z-score calculated?
Formula: Z = (X - μ) / σ * X = score * μ = mean of the sample * σ = standard deviation of the sample
What do positive and negative Z-scores indicate?
• Positive Z-scores: The score is above the mean. • Negative Z-scores: The score is below the mean
How do Z-scores help in comparing two different distributions?
Z-scores standardize scores, allowing us to compare them across different distributions, even if they have different scales.
What are the key characteristics of a normal distribution in terms of Z-scores?
~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.
What Z-score range is considered to represent extreme or outlier values?
Z-scores greater than |3.29| are considered extreme and are often flagged as potential outliers (occur in less than 0.1% of cases).
What is the caution when using Z-scores to identify outliers?
• 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.
Why does context matter when using Z-scores to compare distributions?
Z-scores assume identical circumstances for collecting data. If distributions are from different contexts (e.g., different populations), the comparison may be misleading.
How do Z-scores relate to normal distributions?
• 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.
What proportion of data falls within 1, 2, and 3 standard deviations in a normal distribution?
~68% within ±1 SD ~95% within ±2 SD ~99% within ±3 SD
How do Z-scores help identify outliers in data?
• 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.**