Chapter 12: Descriptive Statistics

These flashcards cover the foundational concepts of descriptive statistics, including common notations, central tendency, variability, distribution shapes, outliers, and effect sizes as presented in the Chapter 12 lecture.

How does the focus of research methods differ from statistics?

Research methods focus on the tools, techniques, and strategies used to launch and run a study, while statistics focus on the results and the data approach obtained from the study.

What are descriptive statistics?

Analyses used to summarize and display data, such as describing distributions through central tendency, variability, percentages, and counts.

What is the primary goal of inferential statistics?

To take a sample and try to generalize the findings to a population.

In statistical notation, what do the symbols $s$ or $SD$ represent?

Sample standard deviation.

What does the lowercase Greek letter sigma (\text{\sigma}) represent in statistics?

Population standard deviation.

What are the symbols for the sample mean and the population mean?

The sample mean is represented by x-bar ($\bar{x}$) and the population mean is represented by mu ($\mu$).

What does the capital sigma ($\Sigma$) symbol indicate?

The sum of everything that follows.

In notation, what is the difference between lowercase $n$ and capital $N$?

Lowercase $n$ usually means sample size or a subset, while capital $N$ means the entire population or the total count in a study.

What are the three most common forms of central tendency?

The mean, the median, and the mode.

How is the arithmetic mean calculated and what is its main weakness?

It is the sum of scores divided by the count; its main weakness is that it is very sensitive to extreme scores or outliers.

When is it better to use the median instead of the mean?

When the data is skewed (leaning heavily in one direction), because the median is not as strongly influenced by extreme scores.

What is the definition of variability?

Dispersion, or how spread out the data points are from one another.

What is the conceptual definition of standard deviation?

The average amount that the scores in a distribution differ from the mean, calculated in original values.

What does a smaller standard deviation indicate about a group?

It indicates less variability, meaning the scores are closer together and the individuals in the group are more similar to one another.

What is a z-score?

A standardized score expressed in standard deviation units that tells you how many standard deviations a raw score is above or below the mean.

What is the mean of a scale once it has been converted to z-scores?

$$0$$

What z-score is commonly associated with being 'statistically significant'?

$$1.96$$

How can you distinguish between a positive skew and a negative skew using the 'slide' analogy?

If you climb to the peak and slide down toward the negative side (left), it is a negative skew; if you slide down toward the positive side (right), it is a positive skew.

What is the difference between a unimodal and a bimodal distribution?

A unimodal distribution has one single distinct peak, while a bimodal distribution has two peaks.

How does the lecturer define an outlier?

A data point that is extreme and far removed from the rest of the scores.

What are the two specific effect sizes mentioned for group differences and relationships?

Cohen's $d$ for group differences and Pearson's $r$ for relationships.

What is an effect size?

A measure of the magnitude of a difference or the strength of a relationship; essentially 'how strong' something is.

What is a meta-analysis?

A quantitative aggregate that combines effect sizes from multiple research studies to determine a summary or overall effect size.

Why does correlation not equal causation?

Correlations only indicate patterns, associations, direction, and strength; only a formal experiment can establish a causal statement.