MAS183 Glossary
A)
addition rule: For any events A and B: P(A or B) = P(A) + P(B) - P(A and B)
For mutually exclusive events A and B: P(A or B) = P(A) + P(B)
asymptotic: as you move further from the mean, the
probability density gets closer and closer to 0, but never
quite gets there
B)
bias in sampling: when some cases are more or less likely to be included in the sample than others
binary data: each outcome can be only one of two distinct possibilities - yes/no, success/fail
binomial conditions:
- a definite number of trials, n
- each trial has only two possible outcomes, arbitrarily called 'success' and 'failure'
- the probability of success, p, is the same for each trial
- trials succeed or fail independently of each other
- the variable under consideration, X, is the number of successes out of the n trials
binomial random variable: random variable that meets all five binomial conditions
bivariate data: data in which each case includes two measurements
C)
categorical/qualitative data: expressing a label or quality, e.g., male/female,
unsatisfactory/satisfactory, unit code
central limit theorem: For samples of size n drawn from a population with any distribution, the sampling distribution of means approaches a Normal distribution as n increases.
coefficient of determination: r2 - the percent of variation in the y variable that can be explained by the variation in the x variable
complementary event (A'): the event that A does NOT occur
conditional probabilities P(A|B): the chance of something occurring when something else occurs, and we talk about "the chance that A will occur when B occurs" or, more compactly, "the chance of A given B". Note that the given condition changes the denominator of the fraction we use to calculate a probability
confidence interval: provides an interval estimate of a population parameter
confidence level: the estimated probability that a population parameter lies within a given confidence interval
continuous numerical data: able to take any values within an allowable range (may be finite or infinite)
continuous random variables: for continuous RVs the probability of getting any
particular exact value is zero
convenience bias: parts of a population that may be harder to observe are excluded
convenience sample: easily obtained but potentially biased samples
correlation: a measure of linear relationship between numerical variables
cumulative probability: the probability that RV takes a value less than or equal to a - accumulates the individual probabilities
D)
describing relationship from a scatterplot: direction, shape, strength of the trend
difference between samples and populations: the sample mean, std deviation and proportion estimate the population mean, std deviation and proportion
direction of a trend: positive or negative
discrete data: able to take only certain distinct values within an allowable range.
The allowable range may be finite or infinite
discrete random variable: if X is the number of kangaroos seen in an area on any day, then X will take discrete values (counting numbers) and it will be a discrete random variable.
E)
event (A): a particular outcome in a sample space
event "A or B": This is an event comprising either or both of event A and event B. event A or B occurs if we draw either of those events
explanatory / predictor variable: a variable that 'explains' another and allows us to predict it in some way.
x variable factor: a categorical variable used to define groups of cases
F)
five-number summary / order statistics:
minimum
lower quartile
median
upper quartile
maximum
H)
how to define the probability distribution of an RV:
- Enumerate all possible values and probabilities - state the chance that each possible value might occur
- Tabulate all values and probabilities (into table)
- Give the formula for P(X=x)
- Give its name and parameters in standard notation (if mathematical form)
how to find sample variance:
divide the sum of squared deviations by one less than the sample size
how to find the standard deviation: square root of the variance
how to interpret R2: if R2 is close to 100% then knowing x will tell us nearly everything about y - a 'good' prediction and vice versa
how to measure spread with std deviation: if there is variation, s will be positive, the larger it is = more spread out data
I)
independent events: A set of events are independent if the occurrence of one of them has no effect on the chance that other
events in the set will occur.
individual probabilities: the chance that RV will take a particular value
investigator intervention: humans are bad at picking an 'average group'
joint event "A and B"
An event comprising both event A and event B happening (or being considered) together.
50
If event A is "the student is enrolled in MAS183" and event B is "the student enrolled through the School
of Veterinary and Life Sciences", then event "A and B" occurs if the student is both enrolled in MAS183
and did so through the School of Veterinary and Life Sciences.
IQR:
L)
least-squares estimation: measures the closeness of the line to data points by the sum of the squares estimation errors
M)
main features of Normal distributions:
- bell shaped
- symmetric around the mean
- mean and median equal
- asymptotic
measurement level: reflects the amount of information conveyed by data. The lowest
measurement level is nominal, then ordinal, then interval, then ratio
measures of location: median, mean, mode and quartiles
measures of shape: symmetric or skewed
peaked or flat - multimodal?
measures of spread: IQR, range, std deviation, variance
multiplication rule: For any events A and B: P(A and B) = P(A) × P(B | A)
For independent events A and B: P(A and B) = P(A) × P(B)
multistage sampling: the area containing population is divided into regions and a random sample of regions is taken - creates a cluster effect
mutually exclusive events: events that can't occur together. Events A and B are mutually exclusive if P(A and B) = 0.
N)
nominal categorical data: labels that are not intrinsically ordered, e.g., male/female (sex), blue/brown (eye colour)
non-response bias: people who refuse to participate or drop out from a study systematically differ from those who take part
numerical data: expressing a quantity, whether by counting (1, 2, 3,...) or by measurement (54.87 kg, 2.54 ml/mol, etc).
O)
ordinal categorical data: labels that are intrinsically ordered, e.g., primary/secondary/tertiary (educational attainment).
outlier: an observation that stands out from the overall pattern of the data
P)
point estimate: single value that serves as an estimate of a population parameter
population mean: mean of all the measurements in a population
population parameter example: Pollsters are interested in how the entire voting public will vote on election day. The population here is the set of all those eligible to vote in the election. We are interested in the percentage that will vote for one of the parties. This percentage is a population parameter.
population parameters: characteristics of a population that are inferred from characteristics of a sample
population proportion: ratio of members of a population with a particular characteristic to the total members of the population
probability density curve: represents a continuous distribution
probability of an event P(A): The probability of an event is the chance that it will occur. The notation for "the probability that A will occur" is P(A).
proportion of outcomes P(A):
A proportion is a fraction of some larger whole and it can take values from 0 to 1 inclusive, just as probabilities do. The probability of an event is often taken to equal the proportion of outcomes corresponding to the event. Thus, when rolling a die we would
say that the probability of rolling a number less than 4 = 3/6 or 0.5 because that is the proportion of the outcomes that match the event "less than 4" and we implicitly assume all outcomes are equally likely.
p-value: the chance of getting a result as least as extreme as what we observed
R)
random variable: a number that takes varying values in different samples, individuals, cases, etc. We don't know the value yet but whose possible values will follow some distribution
regression: investigation of relationship between numerical variables
relation between bias and representation: bias is a property of the sampling process, representation concerns the result of the process and how it compares to the population
response variable: a variable that is explained or predicted by an explanatory variable
S)
sample space (S): The set of all possible outcomes for a process whose outcomes are not determined in advance. For example, when rolling a six-sided die, S = {1, 2, 3, 4, 5, 6}.
sample variance: average of the squared deviations of the observations from the mean
self-selection bias: over represents people with strong opinions
shape of a trend: linear or curved
simple random sample: every case in the population has the same chance of being included in the sample; every possible sample from the population has the same chance of being selected
slope of a line: the change in y when x increases by 1
standard normal distribution: set of probabilities for the easiest distribution of mean=0, std dev.=1
stratified random sampling: accounts for a particular characteristic affecting the variable of interest --> if x% of population is in socio-economic group A, we take x% of sample from that group
strength of a trend: amount of scatter or spread around the trend
systematic sampling: Every (x)th item in the target population is selected (e.g. every 3rd, 4th)
T)
types of bias: self-selection bias, investigator intervention, convenience, non-response bias, investigator intervention
types of categorical data: (all is discrete), nominal or ordinal
types of numerical data: discrete or continuous
V)
values for probabilities: numerical values from 0 to 1 inclusive. That is, events cannot be less unlikely than impossible (probability = 0) and they cannot be more likely than certain (probability = 1).
Y)
y-intercept: value of y when x=0
Z)
z score: tells us how far X is from the mean, in std deviations