Glossary and Practice Deck
This page collects the terms defined throughout the course. The glossary and flashcard deck update automatically when definition blocks in the lesson files change.
Practice with flashcards
Use the controls to study the terms. Select the card or the Reveal definition button to flip it.
Loading definitions…
Term
Select the card or press the reveal button to see the definition.
Full List of Terms and definitions
Lesson 0
- Statistics
-
The art and science of answering questions and exploring ideas through the processes of gathering data, describing data, and making inferences about a population on the basis of a smaller sample.
- Statistical literacy
-
“People’s ability to interpret and critically evaluate statistical information and data-based arguments appearing in diverse media channels, and their ability to discuss their opinions regarding such statistical information” (Gal, as cited by Rumsey, 2002)
Rumsey, D. J. (2002). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10(3). http://www.amstat.org/publications/jse/v10n3/rumsey2.html
Lesson 1
- Case
-
An experimental unit from which data are collected.
- Variable
-
Characteristic of cases that can take on different values (in other words, something that can vary).
- Constant
-
Characteristic that is the same for all cases in a study.
- Categorical variable
-
Names or labels (i.e., categories) with no logical order or with a logical order but inconsistent differences between groups (e.g., rankings), also known as qualitative.
- Quantitative variable
-
Numerical values with magnitudes that can be placed in a meaningful order with consistent intervals, also known as numerical.
- Explanatory Variable
-
Also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher
- Response Variable
-
Also known as the dependent or outcome variable, its value is predicted, or its variation is explained by the explanatory variable; in an experimental study, this is the outcome that is measured following manipulation of the explanatory variable
- Population
-
The entire set of possible cases.
- Sample
-
A subset of the population from which data are collected.
- Statistic
-
A measure concerning a sample (e.g., sample mean).
- Parameter
-
A measure concerning a population (e.g., population mean).
- Inferential Statistics
-
Statistical procedures that use data from an observed sample to make a conclusion about a population.
- Representative Sample
-
A subset of the population from which data are collected that accurately reflects the population.
- Bias
-
The systematic favoring of certain outcomes.
- Sampling Bias
-
Systematic favoring of certain outcomes due to the methods employed to obtain the sample.
- Simple Random Sampling
-
A method of obtaining a sample from a population in which every member of the population has an equal chance of being selected
- Convenience Sampling
-
A method of obtaining a sample from a population by ease of accessibility; such a sample is not random and may not be representative of the intended population.
- Non-Response Bias
-
Systematic favoring of certain outcomes that occurs when the individuals who choose to participate in a study differ from the individuals who choose to not participate
- Response Bias
-
Systematic favoring of certain outcomes that occurs when participants do not respond truthfully; they may do so to align with social norms or to appease the researcher
- Experimental Research Design
-
A study in which the researcher manipulates the treatments (i.e., level of the explanatory variable) received by subjects and collects data; also known as a scientific study
- Observational Research Design
-
A study in which the researcher collects data without performing any manipulations; also known as a non-experimental study
- Confounding Variable
-
Characteristic that varies between cases and is related to both the explanatory and response variables; also known as a lurking variable or a third variable.
- Randomization
-
The act of randomly assigning cases to different levels of the explanatory variable.
- Causation
-
Changes in one variable can be attributed to changes in a second variable.
- Association
-
A relationship between variables.
- Independent Groups
-
Cases in each group are unrelated to one another.
- Paired Groups
-
Cases in each group are meaningfully matched with one another; also known as dependent samples or matched pairs.
- Control Group
-
A level of the explanatory variable that does not receive an active treatment; they may receive no treatment or a placebo.
- Placebo Group
-
A group that receives what, to them, appears to be a treatment, but actually is neutral and does not contain any active treatment (e.g., a sugar pill in a medication study).
- Blinding
-
Procedure employed in research to prevent bias in which the participants and/or the researchers interacting with the participations do not know which treatment each case is receiving.
- Single-Blind Study
-
Research study in which the participants do not know the treatment group that they have been assigned to.
- Double-Blind Study
-
Research study in which neither the participants nor the researchers interacting with them know which cases have been assigned to which treatment groups.
Lesson 2
- Categorical
-
Names or labels (i.e., categories) with no logical order or with a logical order but inconsistent differences between groups, also known as qualitative.
- Quantitative
-
Numerical values with magnitudes that can be placed in a meaningful order with consistent intervals, also known as numerical.
- Die
-
A standard die has 6 sides: 1, 2, 3, 4, 5, 6.
- 52-Card Deck
-
A standard 52-card deck of playing cards has 13 Hearts, 13 Diamonds, 13 Spades, and 13 Clubs. Hearts (♥) and Diamonds (♦) are red suits. Spades (♠) and Clubs (♣) are black suits. For each suit, there is a 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. Jacks, Queens, and Kings are “face cards.”
- Risk
-
The probability that an event will occur. It may be written as a decimal, a fraction, or a percent.
- Odds
-
Express risk by comparing the likelihood of an event happening to the likelihood it does not happen.
- Symmetrical Distribution
-
A distribution that is similar on both sides of the center.
Fig 1 - Normal Distribution
-
One specific type of symmetrical distribution. This is also known as a bell-shaped distribution.
Fig 2 - Skewed
-
A distribution in which values are more spread out on one side of the center than on the other.
- Right Skewed
-
A distribution in which the higher values (towards the right on a number line) are more spread out than the lower values. This is also known as positively skewed.
Fig 3 - Left Skewed
-
A distribution in which the lower values (towards the left on a number line) are more spread out than the higher values. This is also known as negatively skewed.
Fig 4 - Mean
-
The numerical average; calculated as the sum of all the data values divided by the number of values.
The sample mean is represented as \(\bar{x}\) (“x-bar”) and the population mean is denoted as the Greek letter \(\mu\) (“mu”). The formula is the same for the sample mean and the population mean.
- Median
-
The middle of the distribution that has been ordered from smallest to largest; for distributions with an even number of values, this is the mean of the two middle values.
- Mode
-
The most frequently occurring value(s) in the distribution, may be used with quantitative or categorical variables.
- Empirical Rule
-
On a normal distribution about 68% of data will be within one standard deviation of the mean, about 95% will be within two standard deviations of the mean, and about 99.7% will be within three standard deviations of the mean
The normal curve showing the empirical rule.
Fig 5 - 95% Rule
-
On a normal distribution approximately 95% of data will fall within two standard deviations of the mean; this is an abbreviated form of the Empirical Rule
- z-score
-
Distance between an individual score and the mean in standard deviation units; also known as a standardized score.
- z-distribution
-
A bell-shaped distribution with a mean of 0 and standard deviation of 1, also known as the standard normal distribution.
Fig 6 - Percentile
-
Proportion of a distribution less than a given value.
- Range
-
The difference between the maximum and minimum values.
- Interquartile range (IQR)
-
The difference between the first and third quartiles.
Lesson 3
- Single Boxplot
-
Graph displaying data from one quantitative variable. Also known as a “box-and-whisker plot.” The box represents the middle 50% of observed values. The bottom of the box is the first quartile (25th percentile) and the top of the box is the third quartile (75th percentile). The line in the middle of the box is the median (50th percentile). The lines, also known as whiskers, extend to the lowest and highest values that are not outliers. Outliers are symbolized using asterisks or circles.
- Scatterplot
-
A graphical representation of two quantitative variables in which the explanatory variable is on the x-axis and the response variable is on the y-axis.
- Correlation
-
A measure of the direction and strength of the relationship between two variables.
- Residual
-
The difference between an observed y value and the predicted y value. In other words, \(y- \widehat y\). On a scatterplot, this is the vertical distance between the line of best fit and the observation. In a sample this may be denoted as \(e\) or \(\widehat \epsilon\) (“epsilon-hat”) and in a population this may be denoted as \(\epsilon\) (“epsilon”)
Lesson 4
- Confidence Interval
-
A range computed using sample statistics to estimate an unknown population parameter with a stated level of confidence.
- Sampling Distribution
-
Distribution of sample statistics with a mean approximately equal to the mean in the original distribution and a standard deviation known as the standard error.
- Standard Error
-
Standard deviation of a sampling distribution.
- Point Estimate
-
Sample statistic that serves as the best estimate for a population parameter.
- Margin of Error
-
Half of the width of a confidence interval; equal to the multiplier times the standard error.
- Bootstrapping
-
A resampling procedure for constructing a sampling distribution using data from a sample.
Lesson 5
- p-value
-
Given that the null hypothesis is true, the probability of obtaining a sample statistic as extreme or more extreme than the one in the observed sample, in the direction of the alternative hypothesis.
- Null Hypothesis
-
The statement that there is not a difference in the population(s), denoted as \(H_0\).
- Alternative Hypothesis
-
The statement that there is some difference in the population(s), denoted as \(H_a\) or \(H_1\).
Lesson 6
- Type I Error
-
Rejecting \(H_0\) when \(H_0\) is really true, denoted by \(\alpha\) (“alpha”) and commonly set at .05.
\[ \alpha=P(\text{Type I error}) \]
- Type II Error
-
Failing to reject \(H_0\) when \(H_0\) is really false, denoted by \(\beta\) (“beta”)
\[ \beta=P(\text{Type II error}) \]
Lesson 7
- z score
-
Distance between an individual score and the mean in standard deviation units; also known as a standardized score.
- Central Limit Theorem
-
If the sample size is sufficiently large, then the sampling distribution will be approximately normally distributed for many frequently tested statistics, including one sample mean, one sample proportion, difference in two means, difference in two proportions, the slope of a simple linear regression model, and Pearson’s r correlation.
Lesson 11
- Conditional Probability
-
The probability of one event occurring given that it is known that a second event has occurred. This is communicated using the symbol \(\mid\) which is read as “given.”
For example, \(P(A\mid B)\) is read as “Probability of A given B.”
- Independent Events
-
Unrelated events. The outcome of one event does not impact the outcome of the other event.
- Relative Risk
-
Relative risk compares the risk of a particular outcome in two different groups.
\[ \text{Relative Risk}=\dfrac{\text{Risk in Group 1}}{\text{Risk in Group 2}} \]
Lesson 12
- Simple linear regression
-
A method for predicting one response variable using one explanatory variable and a constant (i.e., the y-intercept).
- y-intercept
-
The point on the \(y\)-axis where a line crosses (i.e., value of \(y\) when \(x = 0\)); in regression, also known as the constant.
- Slope
-
A measure of the direction (positive or negative) and steepness of a line; for every one unit increase in \(x\), the change in \(y\). For every one unit increase in \(x\) the predicted value of \(y\) increases by the value of the slope.
- Least squares method
-
Method of constructing a regression line which makes the sum of squared residuals as small as possible for the given data.
- Predicted Value
-
Symbolized as \(\widehat y\) (“y-hat”) and also known as the “fitted value,” the expected value of y for a given value of x
- Sum of squared residuals
-
Also known as the sum of squared errors (“SSE”), the sum of all of the residuals squared: \(\sum (y-\widehat{y})^2\).