Hypothesis Testing Flashcards
What is a null hypothesis?
Supported if chance finding
Not statistically significant
H0
What is an alternative hypothesis?
Supported when the null hypothesis is rejected
so not a chance finding (real event rep)
Statistically significant
HA
What is a false-positive error (type 1 or alpha)
null hypothesis rejected in error
protection against this type of error provided by:
- setting alpha level,
- usually 0.05 (i.e. only 5% risk)
Whats a false-negative error?
null hypothesis accepted in error
protection against this type of error provided by:
- beta level is rarely set
What is the p-value ?(probability)
Measured probability of finding occurring by chance
If p > alpha level
- the null hypothesis is
supported
- finding not statistically
significant
If p < alpha level
- null hypothesis is rejected
- so, alternative hypothesis
is supported
- finding is statistically
significant
How do you check if you data is normally distributed?
Chi-square (x^2) goodness of fit
Explain Chi-square (x^2) goodness of fit
Chi-square distribution is positively skewed with values between 0 and ∞.
Chi-square distribution are labelled based on degree of freedom (df ).
Mean and variance of the chi-square distribution are given by
𝜇 = df and 𝜎^2 = 2df.
What is the Kolmogorov-smirnov one-sample test?
Is used to test whether a sample comes from a specific distribution.
Determine whether a sample comes from a
population that is normally distributed
What is a one tailed test?
One-tailed test - alternative hypothesis states that one group mean is
higher or lower than another
only one tail of normal distribution considered
- e.g. if z = 1.96 then p = 0.025
What is a two tailed test?
Two-tailed test - alternative hypothesis states that two group means are
different
- both tails of normal distribution
considered
- e.g. if z = 1.96 then p = 0.05
Parametric tests: Difference between pairs of sample means (look at lect 7, slide 10)
Lect 7 slide 10
What is the equation for the unpaired T-test?
shows degree of variation between 2 means
Equation for t = C- T / s√ (1/n1 + 1/n2)
Where:
- C* = Mean of control group
- T* = Mean of treated group
- s = Estimate of the standard deviation
based on both
samples
- n1 = Number of observation in group 1
- n2 = Number of observations in group 2
How is the T value judged as significantly significant?
Value taken to a statistical table of the T distribution for comparison.
t-distribution graph (look at lect 7 slide 12)
F(t) = Frequency of ‘t’ values
DF = Degrees of freedom
What is the equation for the paired t-test?
Equation for paired design, t = d*/ (sd/√n)
Where:
d* = mean of the differences between each paired
observation
Sd = standard deviation of the differences between each paired observation
Enter t table with n – 1 degrees of freedom, where n = number of pairs of subjects
Give advantages of the paired design
A paired design is often employed to reduce the effect
of subject variability
Pairing subjects will often reduce the standard error
Pairing should only be considered when a logical
method of pairing is present
What are the assumption of t-test?
Individual measurements, the treatment
means, or the differences between the means are normally distributed
What is data transformation?
sometimes data collected needs to be transformed to make it close to a normal distribution
one method is o convert or transform the original measurements so they are expressed on a new scale which is closer to a normal distribution than the original scale
The usual parametric test can then be carried out on the transformed values
if the data is in the form of percentages the data can be transformed into angular or arcsine scale using :
Angle = sin-1 √(%/100)
transformation for small whole numbers (x) or quantities with
limited scales
- √ x
- √ x + 1 (if many zeroes are present)
transformation for data (x) that lack homogeneity of variance
- Log(x)
Name 3 other statistical tests
Mann-Whitney U Test
Wilcoxon Matched-Pairs Signed-Ranks Test
Kruskal-Wallis Test
