Hypothesis Testing 2 Flashcards
what is analysis of variance (ANOVA)?
Most effective way of analysing data
Multiple variations
possible to use wrong analysis of variance
Inaccurate conclusions result
What equation is used to compare more than two poulation means
To compare more than two population means.
Ho: 𝜇1= 𝜇2= 𝜇3= 𝜇4= … … 𝜇n ;n= population
Ha : At least one mean differs from others.
What are the 2 types of ANOVA tests?
One-Way ANOVA (F-test)
- Only on independent variable tested
N-way ANOVA
- Two independent variables tested
Analysis of Covariance (ANCOVA)
- if independent variables are all categorical, some of the independent variables are categorical and some are continuous ANCOVA will be more appropriate
What is a post-hoc test used for?
used after statistically significant results are found and where the differences came from
What are the different types of post-hoc tests?
Methods
fisher PLSD
Student-newman-keuls (SNK)
Duncans multiple range test
Scheffé’s test
Dunnett’s test
Bonferroni
for more info go to slide 7 lect 8
What are the 3 assumptions of analysis of variance ?
Normally distributed data
- natural variability of measurement is normally distributed
Homogeneity of variance
- although means may vary from group to group the variance is relatively constant in all treatment groups
Treatment effects are additive
- effect of treatment is assumed to have a quantity either positive or negative to the control
What is the kruskal-Wallistest?
Nonparametric test.
Allows to compare more than two population
Null Hypothesis
What is the Friedman’s test?
Nonparametric Test
Three or more measures or experimental conditions.
Can be used in repeated measures.
Nonparametric version of two-way ANOVA
need random sample
need 1 independent and 1 dependant variable
minimum of 12 participants
what does larger sample sizes mean and what value does p need to be to reject a null hypothesis?
Larger sample size leads to accurate estimates.
P< 0.05 – Null hypothesis is rejected.
How do you calculate the sample size tests?
Unpaired t-test
N = (Zα + Zβ)^2 2σ^2/d^2
Where:
N = required sample size
d = size of difference to be detected
Zα= z value corresponding to chosen alpha level
* Obtained from z tables
* For example, z = 1.96 for alpha = 0.05 and 2-tailed test
* Recall that alpha defines protection against type I errors
Zβ= z value corresponding to chosen beta level
* Obtained from z tables
* For example, z = 0.84 for beta = 0.20 and 2-tailed test
* Recall that beta defines protection against type II errors
* Power is 0.8 (80%) when beta = 0.20
σ = population standard deviation
* usually estimated from previous experiments
How do you calculate the power of a statistical test?
Zβ = (√ N.d/ √ 2. σ) – Zα
Where:
N = actual sample size
d = difference actually detected
Zα = z value corresponding to chosen alpha level
Obtained from z tables as previously described
Zβ = z value corresponding to actual beta level
σ = actual standard deviation
Beta is then the probability read from z tables
Power (%) = 100 (1 – Beta)
What is the purpose of correlation?
To determine whether the relationship between two variables is
statistically significant.
To determine whether the relationship is positive or negative.
To determine what proportion of the variability in one variable can be accounted for by the other
how are variables named and how are correlations established?
Correlations establish whether two variables have a linear relationship
Variables:
Y = dependent, outcome or response variable
X = independent, predictor or explanatory variable
X1, X2 = no clear
dependent or independent
variable Convention used in this chapter:
Upper case letter = variable
Lower case letter = individual measurements
what is pearsons parametric correlation coefficient?
Product moment correlation coefficient
r = ∑xy/√(∑x^2∑y^2)
Where:
∑x^2 is the sums of squares of the X values
∑y^2 is the sums of squares of the Y values
∑^xy is the sum of products of the individual
pairs of X and Y values
r = 1 for perfect linear relationship
how do you interpret pearsons correlation coefficient?
r ranges from -1, through 0, to 1
r = +1
line from bottom left corner to top right corner on graph
strong positive correlation
r= -1
line from top left to bottom right on graph
strong negative correlation
r= +0.59
less scatter than 0 more that -1 and +1
weak positive correlation
r=0
lots of scatter no correlation
