inferential statistics
what is a CI
a quantitative measure of how certain we can be that a specific interval contains the true parameter
what is an interval
a range of values around a point estimate made on a sample
The best inference of a population mean is? what about a population SD
a sample mean. a sample SD
Inferential statistical procedures are used to
make inductive inferences of population parameters using sample statistics
Probability of observed effect being due to sampling variation (chance) alone is too high to rule out Ho
then fail to reject and results are not significantly significant
whats the purpose of a hypothesis test
to decide which of at least two hypotheses are correct
Interval estimates quantify
level of uncertainty regarding true value of a parameter
types of effects
--Response magnitude to experimental manipulation --Degree of correlation between variables (strength of a trend) --Difference between statistics (eg means being compared)
5 concepts of an inference
1. parameters(point& interval) 2. uncertainty(margin of error and CI's) 3. effect size 4. stat significance(p value) 5. power
most common CI
95%
why is There is always uncertainty about how close a sample statistic is to the unknown population parameter.
A point estimate, by itself, provides no information on the degree of uncertainty. Due to sampling error we can only infer from samples to population parameters.
what does an interval measure
CI and margin of error
p value is close to what
CI, they work together and you cant have one without the other
what is the presumption of innocence
Defendant may be innocent or guilty but is presumed innocent until proven guilty. The Ho assumes innocence = default position.
false negative solution?
Making an incorrect decision that a person is not sick when they are -increase test power
false positive solution?
Making an incorrect decision that a person is sick when they are not -use more restrictive p values
Must a statistically significant result be of biological or scientific importance?
No. There is a difference between concepts of statistical significance and biological or scientific importance
the length of CI is
a measure of our level of uncertainty about a parameter ------ *precision of inference*
what does statistically significant effect mean
an effect is unlikely if Ho is really true
a powerful test provides evidence to do what to a false Ho
be able to reject the false Ho
an H test is like a
criminal trial-- innocent(Ho) until proven guilty(Ha)
Less sample variance means
easier it is to show that a null hypothesis is false///reduces the p value
the bigger the CI the
more uncertainty and less precise inference
statistically significant result is
one with a p value of .05 or less
types of estimation
point(mean, variance, SD and proportions) and interval(CI and margin of error)
probability can be used to quantify
quantify how sure (or unsure) one is about the truth of a proposition or statement.
Interval estimation is a
range of values around a point estimate that, with a specified level of certainty or probability, enclose the true parameter.
All probabilities are
ratios. It is essential to define both the numerator (particular event occurs) and denominator (number of all possible events, given conditions).
what is probability
the chance that an event will happen relative to all possible events that could happen - under defined conditions.
the smaller CI is
the less uncertainty and more percise our inference
the greater the power,
the more reliable a decision to reject of not we can make
define p value
the probability of results assuming Ho is true
what does heterogeneity mean
variation, scatter
what is power
decision reliability---the probability of rejecting a false Ho
steps of H test
define problem define testable hypothesis design test test it, collect data, analyze decide to reject or fail to reject
statistical significance does not equal
effect size
ways we use inferential statistics
estimation and hypothesis testing
Using inferential statistics, you are trying to reach a conclusion that
extends beyond immediate data alone - to make inductive inferences about population parameters based on probability.
test power helps to make
good decisions
the less a p value is, the
greater chance Ho is not true
what is margin of error
interval length of that portion of the 95% CI on either side of a point estimate.
larger sample size means what about uncertainty
less uncertainty and more precise
Less random variation (smaller sample SD) means
less uncertainty of inference = better precision.
why are inferential statistics necessary
only when a quantitative inductive inference about population parameter(s) needs to be made
five concepts we are seeking in a test of a null hypothesis
parameter estimates precision effect size p value of Ho power
inferential statistics is what type of inference
probabilistically-based inductive inference
why are descriptive statistics necessary
whenever simple quantitative description is required
what is an effect size
= the quantitative magnitude or "strength" of an observed effect, or a relationship of two variables, or the difference in values of statistics between groups being compared
what is a point estimate
A single value for a sample summary statistic representing the "best guess" value of a parameter.
what is a model
All probability statements are based on a set of assumptions or conditions ex-under these conditions, the prob of x is y%
The p-value is a
a measure of the strength of evidence against a Ho.
Assuming Ho, the probability of observed effect occurring by chance alone is low (≤ 5%).
reject null and results are statistically significant
what is a hypothesis test
research to evaluate probable truth of a null hypothesis
a ________ is a point estimate of the ________ which is also called______
sample mean population mean parameter
what does CI length depend on
sample size (want this to be big) and random variation(SD)(want this to be small)
what can affect the p value
sample size, random variation and effect size
SD measures
scatter in data(dispersion)
whats general form of hypothesis testing
to reject of fail to reject Ho
