Introduction to Data Analysis - Lecture 4: Standard Scores

These flashcards cover essential concepts from Lecture 4 of PSYC210, focusing on standard scores, z-scores, and their applications in data analysis.

What are standard scores?

Standard scores combine information about the center and spread of scores into one number.

What does a z-score indicate?

A z-score indicates how many standard deviations a score is from the mean.

How is a z-score calculated?

Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

What does a positive z-score mean?

A positive z-score indicates that the score is above the mean.

What does a negative z-score mean?

A negative z-score indicates that the score is below the mean.

What is the mean of a standard normal distribution?

The mean of a standard normal distribution is 0.

What is the standard deviation of a standard normal distribution?

The standard deviation of a standard normal distribution is 1.

What does the standard normal curve represent?

The standard normal curve represents the distribution of z-scores.

What is the significance of the 3-sigma rule?

The 3-sigma rule states that 34% of scores fall between the mean and +1 SD, 14% between +1 and +2 SDs, and 2% lie beyond 2+ SDs.

Why are z-scores useful?

Z-scores allow us to compare scores from different distributions.

What happens to a distribution when raw scores are converted to z-scores?

The shape of the distribution does not change.

What is a normal distribution?

A normal distribution is bell-shaped and symmetric about the mean.

How can we determine a score's probability?

Convert the score to a z-score and use the z-table to find its probability.

What is indicated by a z-score of +2?

A z-score of +2 indicates a score that is 2 standard deviations above the mean.

How does converting scores to z-scores impact comparability?

Converting to z-scores removes units of measurement, allowing comparability across different scales.

What is the first step to find probabilities using z-scores?

Convert the score to a z-score.

How does a z-table function?

A z-table shows the area under the curve for a given z-score.

What does a z-score of 0 represent?

A z-score of 0 represents a score that is exactly at the mean.

In a normal distribution, what proportion of scores fall below the mean?

50% of scores fall below the mean in a normal distribution.

What is the relationship between z-scores and percentile ranks?

Given a percentile rank, we can find the corresponding z-score.

What adjustments are made for IQ scores in relation to normal distributions?

IQ scores are typically standardized to a mean of 100 and a standard deviation of 15.

What does a z-score of -1 indicate?

A z-score of -1 indicates a score that is 1 standard deviation below the mean.

What properties characterize a normal distribution?

Bell-shaped, single peaked, symmetric about the mean.

How is a theoretical normal distribution defined?

By two numbers: the mean and the standard deviation.

What does an asymptotic property of a normal distribution imply?

The tails of the distribution approach but never touch the x-axis.

What visual aids can help in understanding z-scores?

Graphs showing the normal curve and shaded areas corresponding to probabilities.

What is the impact of sample size on the normality of distributions?

Larger samples tend to produce distributions that approximate normality.

What might a positively skewed distribution look like?

It has a longer tail on the right side, with more scores lower than the mean.

What is the formula for calculating z-scores?

Z = (X - μ) / σ.

Why is it essential to understand standard scores in data analysis?

They provide context for interpreting raw scores in relation to a distribution.

What is an example of a measurement that can be standardized?

Height, weight, or test scores can be standardized using z-scores.

How do transformations to z-scores preserve relationships in data?

They maintain the relative positions of scores within the distribution.

What tools can assist with converting raw scores to z-scores?

Use a calculator or a statistical software.

What is a common use of z-scores in research?

To compare mean scores across different groups.

What do you need to consider when interpreting z-scores?

The context of the data and the distribution from which it comes.

How can z-scores facilitate clearer communication in research findings?

They provide a universal metric for interpreting scores regardless of original scale.

What information could be derived from a standard normal table?

Probabilities and the area under the curve corresponding to specific z-scores.

Why is a live resource for formulas suggested in the lecture?

To help students easily access and consolidate information for exam preparation.

Which scoring methods were discussed in Lecture 3?

Mean, median, and mode.