lecture 3 Flashcards
when are statistics needed in clinical experience
to quantify differences that are too small to recognize through clinical experience alone
what is the result when comparing the mean between 2 samples from the same population
they should have fairly similar means
what does it mean if the means from two samples are statistically different
likely to be drawn from 2 different populations, ie
they really are different
what does hypothesis testing involve
(3 steps)
Making an initial assumption;
Collecting evidence (data);
Based on available evidence (data), decide whether or not to reject the initial assumption.
EVERY hypothesis test includes these
what is the assumption made in statistics
always assume the null hypothesis is true/ null hypothesis is the initial hypothesis
what is the null hypothesis
H0. : the absence of a difference or an effect.
- no effect
- rejected if significance tests shows data doesn’t match H0
what is the alternative hypothesis
H’, H1, or HA.: the complement(equal opp) of the null hypothesis.
relate the clinical trial analgoy to statistics
In statistics, the data are the evidence.
if suff evidence exists beyond reasonable doubt the jury rejects H0 and deems the
defendant guilty.
If there is insufficient evidence, then the jury does not
reject H0.
making the decision reduces to
determining “likely” or “unlikely.”
what are the two ways to determine whether the evidence is likely or unlikley regarding the initial assumtption
- “critical value approach”- old textbooks
- “p-value approach”-research, journal articles, and
statistical software
define probability
A measure of the likelihood that a particular event
will happen.
- shown as a value between 0 and 1.
- the acc measurement is the rate in a group not just an event
- larger the p the more likley the event.
*
what is the conventional cut off point
if p is greater than 0.05 then the null hypothesis is greater as the result should only occur less than 5 times out of every 100 by chance
0.05 is completely arbitrary
what is p-value/statistical significance of a result
an estimate of the degree to which a result is true
probability of getting an e_vent at least as extreme_ as your result if the null hypothesis is true
What is power
probability of rejecting the null hypothesis.
- probability that youreject the null hypothesis when you should
(and thus avoid a Type II error). - varies according to underlying truth e.g. the actual difference betw/ pop means
- power increases with increased diff betw/ pop means
what is a type one
Rejecting the null hypothesis, when it is true
aka: α (alpha) which is also the power of the test when H0 is true
what is a type 2 error
occurs when we fail to reject the H0 when it is false.
probabilty of type 2 error is known as β (beta).
power is 1-β when H0 is false
when do type one errors often occur
whe nmany tests are done on the same data
if 100 tests are done 5 tests will inevitably fall into the rare 5 in a 100 so its dumb to say the one of those 5 is statistically significant if H0 is true
what does the choice of statistical test depend on
- Level of measurement for the dependent and independent variables
- Number of groups or dependent measures
- Number of units of observation
- Type of distribution
- The population parameter of interest (mean, variance, differences between means and/or variances)
define multiple comparison
two or more data sets, which should be analyzed
- repeated measurements made on the same individuals
- entirely independent samples
what is a degree of freedom
number of scores, items, or other units in the data set, which are free to vary
what are one and two tailed tests
- one-tailed test of significance used for directional
hypothesis - two-tailed tests in all other situations
what is a sample size
number of cases, on which data have been obtained
which characteristics of distribution are senstitive to SAMPLE SIZE
mean
SD
skewness
kurtosis
define the student t-test
Difference between the means divided by the pooled
standard error of the mean
what is a 1- sample t-test
Comparison of sample mean with a population mean
what is a 2 sample t test
comparison of means from two unrelated groups
types of t tests
independant sample t test
- independant samples & interval measures (parametric)
paired sample t-test
- related samples & interval measures (parametric
man-whitney u-test
- independant samples & ordinal/ non parametric
wilcoxon test
- related samples & ordinal/ non parametric
what is ANOVA
ANalysis Of VAriance
compares the differences in means between
groups but it uses the variance of data to “decide” if
means are different
F STATISTIC= Magnitude of the difference between the different
conditions
- the p-value associated with F is the probability that
differences between groups could occur by chance if
null-hypothesis is correct - post-hoc tests needed as ANOVA can tell you if
there is an effect but not where)
difference between parameteric and non parametric tests
Parametric test: estimate at least one population parameter from sample statistics
- variable is normally distro
- more reliable test
Non-parametric test: distribution free, no assumption
about the distribution of the variable in the population
