Week 2: Describing and Exploring Data

Flashcards covering key definitions, calculations, and concepts related to describing and exploring data, including SPSS introduction, measures of central tendency, and measures of variability.

What is SPSS?

A popular statistical package that allows users to analyze many types of data, including large and complex data sets from experimental, correlational, or other studies.

What are the two main views in the SPSS environment for data management?

'Data View' and 'Variable View'.

Why is it important to describe and explore data?

To simplify/summarize copious amounts of information, identify errors, and determine if data can be analyzed by planned statistical tests.

What are the three main measures of central tendency discussed?

The three main measures are Mode, Median, and Mean.

How is the Mode defined?

The value that occurs most often in a data set.

What term is used if there are two non-adjacent values with the same highest frequency?

The set is considered bimodal.

How is the Mode calculated if the two most frequently occurring values are adjacent?

As the average of those two adjacent values.

What is the Median?

The measure that divides the total number of scores in half, representing the 50th percentile.

When is the Median commonly used?

Data sets with extreme values, such as house prices or income.

How is the Median calculated for an odd number of scores?

For an odd number of scores, the single score in the middle is determined after ranking the scores from highest to lowest.

How is the Median calculated for an even number of scores?

For an even number of scores, the mean of the two middle scores is calculated after ranking them.

What is the formula for calculating the Mean of a sample?

The formula for the sample mean is X̄ = (Σ X) / n, where Σ X is the sum of all scores and n is the number of scores in the sample.

How is the Mean affected by extreme values compared to the Median and Mode?

A single extreme value (outlier) can dramatically change the Mean, but generally has no effect on the Mode and Median.

What are the measures of variability discussed?

Range, Interquartile Range (IQR), Variance, and Standard Deviation.

How is the Range calculated?

The highest score minus the lowest score.

What is a disadvantage of using the Range as a measure of variability?

It is easily influenced by a single extreme score.

What is the Interquartile Range (IQR)?

The difference between the lower quartile (Q1) and the upper quartile (Q3) comprises the middle 50% of the data.

How is an outlier detected using the IQR?

A data point is considered an outlier if it is below Q1 - (1.5 × IQR) or above Q3 + (1.5 × IQR).

When are Variance and Standard Deviation typically used?

Variance and Standard Deviation are used when the mean is the measure of central tendency.

What do Variance and Standard Deviation measure?

A measure of the standard, or average, distance from the mean, describes whether scores are clustered closely around the mean or widely scattered.

What is a deviation score?

The difference between an original score (X) and the mean (X̄), calculated as X - X̄.

Why are deviation scores squared when calculating Variance?

Deviation scores are squared to get rid of negative values, resulting in the sum of squares (SS).

What is the formula for calculating population variance (σ²)?

The formula for population variance is σ² = SS / N, where SS is the sum of squared deviations and N is the number of scores in the population.

What is the formula for calculating sample variance (s²)?

The formula for sample variance is s² = SS / (n - 1), where SS is the sum of squared deviations and n is the number of scores in the sample.

How is the Sample Standard Deviation (s or SD) derived from the sample variance?

The Sample Standard Deviation is obtained by taking the square root of the sample variance (s = √s²).

What is the general rule for rounding final answers in statistical calculations?

Final answers should generally be rounded to one more decimal place than in the original data.