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Questions and Answers
What does a Z-score of 0 indicate about a specific value in relation to the mean?
In the example provided, what is the Z-score calculated for Ahmet's family's income of 15,230 TL?
You receive a Z-score of -1.5. What can you infer about the data value?
What percentage of people earn more than Ahmet's family based on the calculated Z-score?
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What is the first step in calculating a Z-score?
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Which of the following is true regarding the Z-score table?
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If a variable has a Z-score of 2.5, what does this imply?
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What is an important consideration when using Z-scores in non-normal distributions?
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Study Notes
Statistics in Psychology PSYC 241 - Week 6
- Course: Statistics in Psychology PSYC 241
- Week: 6
- Instructor: Demet Kara, PhD
- Semester: Fall 2024
- Topics: Standard units in statistics and introduction to SPSS
Z-scores
- Definition: An indication of how many standard deviations a value is away from the mean.
- Formula: z = (x - μ) / σ
- μ = Mean
- σ = Standard Deviation
- Applicability: Equally applicable to any variable (e.g., time, anxiety, depression, height).
- Importance: Provides a universal scale for measurement.
Z-scores and the Standard Normal Distribution
- Z-score of 0: Represents the mean.
- Z-score of 1: Represents 1 standard deviation above the mean.
- Z-score of -1: Represents 1 standard deviation below the mean.
- Bell Curve: The Standard Normal Distribution visually depicted as a bell curve.
- Percentages: Specific percentages of the distribution are associated with specific z-score intervals.
Normal Distribution & Z-scores
- Normal Curve: The distribution follows a bell-shaped curve; also known as the "bell curve".
- Z-scores: Used to identify the location of individual data points within the distribution.
Z-score Table
- Application: Provides probabilities for specific z-score values.
- Usage: To determine the percentage of data points falling within a given interval.
- Interpretation: Requires both first and second decimal places
Exercises
- Exercise Example (Turkish Income): A Turkish family's income, the average income in Turkey, and the standard deviation of household income are provided; students need to calculate the percentage of people who earn more than Ahmed's family.
- Example Formula (Turkish Income): z=(15230-11500)/2200 = 1.70
Where does Ahmet's family income fall?
- Distribution: The average income in Turkey and Ahmet's family income are positioned on the normal distribution graph.
- Percentage: The percentage of people who earn more than Ahmed's family is approximately 4%
Relative Age Example (Senate/House Leaders' Ages & Related Concepts)
- Leaders: The Senate and House of Representatives minority leaders' ages are provided in a context.
- Concept: The ages are compared relative to the mean ages of their respective groups to determine which leader was older.
- Conclusion: The Senator was older in relation to the House representative.
Relative Time Example (Marathon/Half-Marathon Times)
- Times: The average time for both races, Rex's full marathon time, and Lisa's half-marathon time are provided.
- Concept: Comparing Rex's and Lisa's times relative to the average for their respective races determines who finished faster.
- Conclusion: The person finishing a half-marathon in 100 minutes would have finished faster relative to their specific race.
Important Questions about Z-score
- Applicability: Z-score tables only apply to normal distributions.
- Non-normal Distributions: Percentiles of a z-score are uncertain in non-normal distributions.
SPSS Functionality
- Tool: A software application, SPSS
- Usage: Used to perform statistical analyses.
- 'Analyze' Menu: All functions and tasks of analyses needed when using SPSS are accessed via the 'Analyze' menu
Descriptive Statistics in SPSS
- Function: Used for calculating counts, percentages, means, modes, medians, and standard deviations.
- Frequencies: For counts and percentages.
- Descriptives: For means, modes, medians, and standard deviations.
Producing Charts/Graphs in SPSS
- Graphs: Histograms can show whether a data distribution is normal.
- Tools: Charts are built and produced with various tools in SPSS.
Checking for Normality
- Method: Statistical methods available in SPSS to check for normal distributions
- Procedure: Steps to follow in SPSS for checking normality.
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Description
This quiz covers week 6 of Statistics in Psychology PSYC 241, focusing on standard units in statistics and an introduction to SPSS. Topics include z-scores, their formula, and the relationship with the standard normal distribution. Test your understanding of these fundamental concepts in psychology statistics.
