Module 8 Flashcards
product of hypothesis testing via various statistical tests and is claimed to be significant (i.e. not due to chance) most commonly when the value is 0.05 or less
It cannot provide information about what size of an effect is or what the effect size is likely to be on the total population
Value 0.05 is arbitrary; simply a convention amongst statistician that this value is deemed the cutoff level for significance
P-value
can be anything from 0.80 (80%) to 0.99 (99%) depending on requirements to avoid too many subjects being recruited for a study
Drawback in the calculations do not take variation of data into account
Power
aka “False Positive”
Error of rejecting the null hypothesis when it is actually true
Error of accepting an alternative hypothesis (real hypothesis of interest) when the results can be attributed to chance
Occurs when we are observing a difference when in truth there is none (or there is no statistically significant difference)
TYPE I ERROR
aka “False Negative”
Error of NOT rejecting the null hypothesis when the alternative hypothesis is the true state of nature
Error of failing to accept an alternative
hypothesis when you don’t have adequate power
Occurs when we are failing to observe a difference when in truth there is one
TYPE II ERROR
measure of the researchers’ uncertainty in the sample statistic as an estimate of the population parameter, if less than the whole population is studied usually set at 95% by convention
CONFIDENCE INTERVAL
Shrink with increasing sample size, the researcher should be seeking to reach an optimal size, rather than the maximal sample size
STANDARD ERROR
i.e. standard deviation, effect of being studied e the less variability in the sample, the more precise the estimate in the population and therefore a narrower range
THE MEAN AND THE VARIABILITY
The more confident someone wants to be in the obtained results, the higher the confidence interval needs to be.
Conversely, in a 90% confidence interval is considered sufficient then the range of data required will be narrower, and hence the required sample size will be smaller
DEGREE OF CONFIDENCE
any process of generating a set of data or observations that can be repeated under basically the same conditions, which lead to well-defined outcomes.
Random experiment
set all possible outcomes of an experiment
o usually denoted by S
Sample space
element of the sample space; an outcome
Sample point
any subset of the sample space
Event
a subset of the sample space that contains no elements
o Denoted by the symbol f
Null space (Empty Space)
– event which contains only
one element of the sample space
Simple event
event that can be expressed as the union of simple events; contains more than one sample point
Compound event
two events A and B are mutually exclusive which means that A and B have no elements in common
Mutually exclusive events
empty space can be viewed as an event that will never happen
Impossible event
the sample space S, as an event always occurs
o Also referred to as certain
Sure event
shows intersection of events A and B
o Event that both A and B occur
A ∩ B
– shows union of events A and B
o Event that A or B or both occur
A ∪ B
shows complement of an event A with respect to S
o Contains all elements of S that are
not in A and is the event that A does
not occur
A^1 or A^c
Determined even before the experiment is performed using the following rule:
If an experiment can result in any N different equally likely outcomes, and if exactly n of these outcomes corresponds to event A, then the probability of event A is
Priori (Classical Probability)
Determined by repeating the
experiment a large number of times
Posteriori (Relative Frequency/ Empirical Probability)
Probability is determined by the use of intuition, personal beliefs, and other indirect information
Subjective Probability
An arrangement or ordering of all or part of a set of objects.
Permutation
selection of r objects from n without regard to order
Combination
The probability of an event B occurring
when it is known that some event A has
occurred
It is defined by the equation
P(B | A) = “P(A∩B)” /”P(A)” if P (A) > 0
Conditional Probability
P (B | A) is read as
“probability of B given A”
Function whose value is a real number determined by each element in the sample space
Concept of Random Variable
If a sample space contains a finite number of possibilities or an unending sequence with as many elements as there are whole numbers
Discrete sample space
Random variable defined over a discrete
sample space
Discrete random variable
Table or formula listing all possible values that a discrete random variable can take on, along with the associated probabilities
The probabilities associated with all possible values of a discrete random variable must sum to 1
Discrete Probability Distribution
sample space contains an infinite number of possibilities equal to the number of points on a line segment
Continuous sample space
Random variable defined over a continuous sample space
Continuous random variable