Chapter 2 - Summarizing And Comparing Distributions (Lecture Slides) Flashcards
What are descriptive statistics?
Quantitatively describes or
summarizes features from data in a compact, easily understood fashion.
What is a distribution?
Describes the concentration of different
score values on the same variable.
We can use graphs, tables, or mathematical functions to describe how likely to observe each score.
A graph, table, or mathematical
function describing the frequency of each score.
There are both discrete variables &
continuous variables
What do discrete variables measure?
Frequency = count
What do continuous variables measure?
Density
What is a normal distribution?
A theoretical function that describes many physical, physiological, and
psychological traits.
What is the anatomy of a normal distribution? What does it look like?
This is a bell shape
Whatever value is at the very peak of the bell shape is called the “center.”
The far left side is considered “low” / “lower tail.”
The far right side is considered “high” / “upper tail.”
The further up you go on the Y-axis the more often/likely it is to occur
The further down you go on the Y-axis the less often/likely is it to occur
What does the center of a distribution represent?
A common or typical score value.
A distribution’s center is often where scores are highly concentrated (e.g., at the typical value).
The center of the distribution is often used as the basis for comparison because it represents a “typical” individual in each group.
What does the distribution’s spread capture?
The degree to which scores are similar or different.
The variability or dissimilarity of scores.
High spread (variability) indicates greater score differences among individuals and will look like a longer/lower/more spread out bell shape.
Low spread indicates similarity among the scores and will look like a shorter/taller/less spread out bell shape.
What does the distribution shape describe?
The symmetry or asymmetry of scores.
Distribution shape characterizes the concentration of scores at different values.
Distributions can be symmetric or asymmetric (skewed).
Shape is a useful descriptive tool that conveys a picture of the data.
Describe a symmetric distribution
The left side of the distribution mirrors the right side (e.g., normal distribution).
Everything is the same on both sides. You can think of a perfect bell curve for example.
Describe a uniform distribution
This is also considered a symmetric
distribution and looks like a flat line all the way across.
All scores are equally likely, no single score occurs more frequently than others. It’s the same at 1 as it is at 2, 3, 4, 5, and so on.
Describe a positively skewed distribution (AKA right-skewed distribution)
Most scores are in the low range (far left side where you’ll find the peak of the bell curve) and higher scores in the upper tail (far right side) are less frequent.
It is also called right-skewed
distribution - the tail is the longest on the right side.
Describe a negatively skewed distribution (AKA left-skewed distribution)
Most scores are in the high range (the far right side where you’ll find the peak of the bell curve) and lower scores are in the lower
tail (far left side) are less frequent.
It is also called left-skewed distribution - the tail is the longest on the left side.
What is a bar plot (bar chart)?
A bar plot (bar chart) uses bar height to represent the frequency or count of responses in each bin (category).
You’ve seen this many times, it’s just a graph with bars (with breaks in the horizontal axis).
It shows the relationship between a numeric and a categoric variable. Each entity of the categoric variable is represented as a bar. The size of the bar represents its numeric value.
It presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.
The ordering of categories in nominal variables (marital status) is arbitrary in the bar chart, you can put them in any order on the chart.
The ordering of categories in ordinal variables (home value) is NOT arbitrary! They must go in order.
I believe it is used in nominal and ordinal variables - double-check this!
What is a frequency distribution?
A frequency distribution is a tabular display of the information from the bar graph.
The table includes a column of scores and their corresponding counts and percentages.
It’s a visual display that organizes and presents frequency counts so that the information can be interpreted more easily.
It looks like a table.
I believe it is used in nominal and ordinal variables - double-check this!
