Standard scores (exam 1)

What is a standard score?

A score converted to a scale with a given mean and standard deviation.

Define a Z-score.

A raw score expressed in standard deviation units with a mean of 0 and SD of 1.

Formula for Z-score.

Z = (X - Mean) / SD

What does a positive Z-score indicate?

The score is above the mean.

What does a negative Z-score indicate?

The score is below the mean.

What percentage of data falls within ±1 SD in a normal curve?

68.26%

What percentage of data falls within ±2 SD in a normal curve?

95.44%

What percentage of data falls within ±3 SD in a normal curve?

99.74%

Define percentile.

A measure indicating the value below which a given percentage of observations fall.

How do you convert a Z-score to a percentile?

Use a Z-table to find the percentage, then add or subtract from 50 depending on sign.

Define T-score.

A standard score with a mean of 50 and SD of 10, based on a Z-score.

Formula to convert Z-score to T-score.

T = 50 + (10 × Z)

Define statistical inference.

The process of estimating population parameters based on sample statistics.

Define population in statistics.

A group of persons, places, or objects sharing at least one characteristic.

Define sample in statistics.

A subset of the population used to estimate population parameters.

Define parameter.

A characteristic of a population, such as the mean.

Define statistic.

An estimate of a parameter based on sample data.

Define statistical confidence.

A measure of how confident we are in our prediction about a population parameter.

List common levels of confidence and their Z-scores.

68% = 1.0, 90% = 1.65, 95% = 1.96, 99% = 2.58

Define sampling error.

The difference between a population parameter and a sample statistic.

Formula for confidence interval.

CI = Mean ± Z × SEM

Define SEM (Standard Error of the Mean).

SEM = SD / √N

Example of SEM calculation.

If SD = 25 and N = 50, SEM = 25 / √50 = 3.5

Interpret a 95% confidence interval.

We are 95% confident the true population mean lies within the interval calculated.

Why not always use a very high confidence level like 99%?

Higher confidence decreases precision of the estimate.

Which confidence level to use?

Depends on the consequences of being wrong; higher stakes require higher confidence.

What does a p-value represent?

The probability of making an error in rejecting the null hypothesis.

What is the typical alpha level used in science?

0.05 or 5%

Interpret a CI with no overlap between two groups.

There is likely a significant difference between the groups.

Interpret a CI with overlap between two groups.

There is likely no significant difference between the groups.

How is SPSS used for confidence intervals?

Use Analyze → Descriptive Statistics → Explore, then select Descriptives and specify CI level.