Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
78 Cards in this Set
- Front
- Back
|
Descriptive Statistics
|
Collecting, summarizing, and describing data
|
|
|
Inferential Statistics
|
Drawing conclusions and/or making decisions concerning a population based only on sample data
|
|
|
VARIABLE
|
A variable is a characteristic of an item or individual
|
|
|
DATA
|
Data are the different values associated with a variable
|
|
|
OPERATIONAL DEFINITIONS
|
Data values are meaningless unless their variables have operational definitions, universally accepted meanings that are clear to all associated with an analysis
|
|
|
POPULATION
|
A population consists of all the items or individuals about which you want to draw a conclusion.
|
|
|
SAMPLE
|
A sample is the portion of a population selected for analysis.
|
|
|
PARAMETER
|
A parameter is a numerical measure that describes a characteristic of a population.
|
|
|
STATISTIC
|
A statistic is a numerical measure that describes a characteristic of a sample.
|
|
|
Primary Sources
|
The data collector is the one using the data for analysis
|
|
|
Secondary Sources
|
The person performing data analysis is not the data collector
|
|
|
Categorical (qualitative)
|
variables have values that can only be placed into categories, such as “yes” and “no.”
|
|
|
Numerical (quantitative)
|
variables have values that represent quantities.
|
|
|
Types of Date
|
|
|
|
Categorical Data
|
|
|
|
Summary Table
|
indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories.
|
|
|
bar chart
|
a bar shows each category, the length of which represents the amount, frequency or percentage of values falling into a category.
|
|
|
pie chart
|
The pie chart is a circle broken up into slices that represent categories. The size of each slice of the pie varies according to the percentage in each category
|
|
|
Pareto Chart
|
Used to portray categorical data (nominal scale)
A vertical bar chart, where categories are shown in descending order of frequency A cumulative polygon is shown in the same graph Used to separate the “vital few” from the “trivial many” |
|
|
Numerical Data Charts
|
|
|
|
ordered array
|
An ordered array is a sequence of data, in rank order, from the smallest value to the largest value.
Shows range (minimum value to maximum value) May help identify outliers (unusual observations) |
|
|
stem-and-leaf display
|
A stem-and-leaf display organizes data into groups (called stems) so that the values within each group (the leaves) branch out to the right on each row.
|
|
|
frequency distribution
|
The frequency distribution is a summary table in which the data are arranged into numerically ordered classes.
You must give attention to selecting the appropriate number of class groupings for the table, determining a suitable width of a class grouping, and establishing the boundaries of each class grouping to avoid overlapping. The number of classes depends on the number of values in the data. With a larger number of values, typically there are more classes. In general, a frequency distribution should have at least 5 but no more than 15 classes. To determine the width of a class interval, you divide the range (Highest value–Lowest value) of the data by the number of class groupings desired. It condenses the raw data into a more useful form It allows for a quick visual interpretation of the data It enables the determination of the major characteristics of the data set including where the data are concentrated / clustered Different class boundaries may provide different pictures for the same data (especially for smaller data sets) Shifts in data concentration may show up when different class boundaries are chosen As the size of the data set increases, the impact of alterations in the selection of class boundaries is greatly reduced When comparing two or more groups with different sample sizes, you must use either a relative frequency or a percentage distribution |
|
|
histogram
|
A vertical bar chart of the data in a frequency distribution is called a histogram.
In a histogram there are no gaps between adjacent bars. The class boundaries (or class midpoints) are shown on the horizontal axis. The vertical axis is either frequency, relative frequency, or percentage. The height of the bars represent the frequency, relative frequency, or percentage. |
|
|
histogram
|
A vertical bar chart of the data in a frequency distribution is called a histogram.
In a histogram there are no gaps between adjacent bars. The class boundaries (or class midpoints) are shown on the horizontal axis. The vertical axis is either frequency, relative frequency, or percentage. The height of the bars represent the frequency, relative frequency, or percentage. |
|
|
percentage polygon
|
A percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.
|
|
|
cumulative percentage polygon, or ogive
|
The cumulative percentage polygon, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.
Useful when there are two or more groups to compare. |
|
|
The Contingency Table
|
A cross-classification (or contingency) table presents the results of two categorical variables. The joint responses are classified so that the categories of one variable are located in the rows and the categories of the other variable are located in the columns.
The cell is the intersection of the row and column and the value in the cell represents the data corresponding to that specific pairing of row and column categories. |
|
|
Scatter Plots
|
Scatter plots are used for numerical data consisting of paired observations taken from two numerical variables
One variable is measured on the vertical axis and the other variable is measured on the horizontal axis Scatter plots are used to examine possible relationships between two numerical variables |
|
|
Time Series Plot
|
A Time Series Plot is used to study patterns in the values of a numeric variable over time
The Time Series Plot: Numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis |
|
|
central tendency
|
the extent to which all the data values group around a typical or central value.
|
|
|
variation
|
the amount of dispersion, or scattering, of values
|
|
|
shape
|
the pattern of the distribution of values from the lowest value to the highest value.
|
|
|
Measures of Central Tendency: The Mean
|
The most common measure of central tendency
Mean = sum of values divided by the number of values Affected by extreme values (outliers) |
|
|
Measures of Central Tendency: The Median
|
|
|
|
Measures of Central Tendency: The Mode
|
|
|
|
Measures of Central Tendency: Which Measure to Choose?
|
The mean is generally used, unless extreme values (outliers) exist.
The median is often used, since the median is not sensitive to extreme values. For example, median home prices may be reported for a region; it is less sensitive to outliers. In some situations it makes sense to report both the mean and the median. |
|
|
Range
|
Range = Xlargest – Xsmallest
Simplest measure of variation Difference between the largest and the smallest values: Ignores the way in which data are distributed |
|
|
Variance of a sample
|
|
|
|
Standard deviation of a sample
|
Steps for Computing Standard Deviation
1. Compute the difference between each value and the mean. 2. Square each difference. 3. Add the squared differences. 4. Divide this total by n-1 to get the sample variance. 5. Take the square root of the sample variance to get the sample standard deviation. |
|
|
Summary of Variations
|
The more the data are spread out, the greater the range, variance, and standard deviation.
The more the data are concentrated, the smaller the range, variance, and standard deviation. If the values are all the same (no variation), all these measures will be zero. None of these measures are ever negative. |
|
|
The Coefficient of Variation
|
|
|
|
Z-score
|
To compute the Z-score of a data value, subtract the mean and divide by the standard deviation.
The Z-score is the number of standard deviations a data value is from the mean. A data value is considered an extreme outlier if its Z-score is less than -3.0 or greater than +3.0. The larger the absolute value of the Z-score, the farther the data value is from the mean. |
|
|
Shape of a Distribution
|
|
|
|
population mean
|
|
|
|
Population Variance
|
|
|
|
Population: standard Deviation
|
|
|
|
The Empirical Rule
|
68% of all test takers scored between 410 and 590 (500 ± 90).
95% of all test takers scored between 320 and 680 (500 ± 180). 99.7% of all test takers scored between 230 and 770 (500 ± 270). |
|
|
Chebyshev Rule
|
|
|
|
Quartile
|
Find a quartile by determining the value in the appropriate position in the ranked data, where
First quartile position: Q1 = (n+1)/4 ranked value Second quartile position: Q2 = (n+1)/2 ranked value Third quartile position: Q3 = 3(n+1)/4 ranked value where n is the number of observed values When calculating the ranked position use the following rules If the result is a whole number then it is the ranked position to use If the result is a fractional half (e.g. 2.5, 7.5, 8.5, etc.) then average the two corresponding data values. If the result is not a whole number or a fractional half then round the result to the nearest integer to find the ranked position. |
|
|
Quartile Measures: The Interquartile Range (IQR
|
The IQR is Q3 – Q1 and measures the spread in the middle 50% of the data
The IQR is also called the midspread because it covers the middle 50% of the data The IQR is a measure of variability that is not influenced by outliers or extreme values Measures like Q1, Q3, and IQR that are not influenced by outliers are called resistant measures |
|
|
The Five Number Summary
|
The five numbers that help describe the center, spread and shape of data are:
Xsmallest First Quartile (Q1) Median (Q2) Third Quartile (Q3) Xlargest |
|
|
Relationships among the five-number summary and distribution shape
|
|
|
|
The Boxplot
|
|
|
|
Distribution Shape and The Boxplot
|
|
|
|
Boxplot example showing an outlier
|
|
|
|
The Covariance
|
Covariance between two variables:
cov(X,Y) > 0 X and Y tend to move in the same direction cov(X,Y) < 0 X and Y tend to move in opposite directions cov(X,Y) = 0 X and Y are independent The covariance has a major flaw: It is not possible to determine the relative strength of the relationship from the size of the covariance |
|
|
Coefficient of Correlation
|
The population coefficient of correlation is referred as ρ.
The sample coefficient of correlation is referred to as r. Either ρ or r have the following features: Unit free Ranges between –1 and 1 The closer to –1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker the linear relationship |
|
|
Basic Probability Concepts
|
Probability – the chance that an uncertain event will occur (always between 0 and 1)
Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) |
|
|
Assessing Probability
|
|
|
|
Events
|
Simple event
An event described by a single characteristic e.g., A red card from a deck of cards Joint event An event described by two or more characteristics e.g., An ace that is also red from a deck of cards Complement of an event A (denoted A’) All events that are not part of event A e.g., All cards that are not diamonds |
|
|
Sample Space
|
The Sample Space is the collection of all possible events
e.g. All 6 faces of a die: |
|
|
Visualizing Events
|
|
|
|
Definitions Simple vs. Joint Probability
|
Simple Probability refers to the probability of a simple event.
ex. P(King) ex. P(Spade) Joint Probability refers to the probability of an occurrence of two or more events (joint event). ex. P(King and Spade) |
|
|
Mutually Exclusive Events
|
Mutually exclusive events
Events that cannot occur simultaneously Example: Drawing one card from a deck of cards A = queen of diamonds; B = queen of clubs Events A and B are mutually exclusive |
|
|
Collectively Exhaustive Events
|
Collectively exhaustive events
One of the events must occur The set of events covers the entire sample space example: A = aces; B = black cards; C = diamonds; D = hearts Events A, B, C and D are collectively exhaustive (but not mutually exclusive – an ace may also be a heart) Events B, C and D are collectively exhaustive and also mutually exclusive |
|
|
Computing Joint and Marginal Probabilities
|
|
|
|
Joint Probability Example
|
|
|
|
Marginal Probability Example
|
|
|
|
Marginal & Joint Probabilities In A Contingency Table
|
|
|
|
Probability Summary
|
|
|
|
General Addition Rule
|
|
|
|
General Addition Rule Example
|
|
|
|
Computing Conditional Probabilities
|
|
|
|
Conditional Probability Example
|
Of the cars on a used car lot, 70% have air conditioning (AC) and 40% have a CD player (CD). 20% of the cars have both
What is the probability that a car has a CD player, given that it has AC ? |
|
|
Independence
|
|
|
|
Multiplication Rules
|
|
|
|
Marginal Probability
|
|
