Summary
Summary Advanced Statistics MAT/2022
- Course
- Institution
Full and well explained background of most statistical tests
[Show more]
Seller
Follow
sabinecaspers
Reviews received
Content preview
Advanced Statistics MAT20306,Symbols:
µ Population
y Response
H0 Null hypothesis
Hα Alternative hypothesis
σ Standard deviation
σ2 Variance
t Test statistic
df Degrees of freedom
CI Confidence interval
E Error margin
α Significance level / probability type I error
β Probability type II error
Δ Minimum relevant difference
π Proportion / probability
,Lecture 1: Confidence intervals and hypothesis testing
1.1 Two sample T-test
In the one sample T-test one random sample is taken, with an interest in a two population means.
1.1.1 Example
Researchers want to investigate the effectiveness of a new drug for tape worms in sheep. A random
sample of 24 sheep are randomly divided into two groups. One group receives the new drug, the
other group receives no treatment. After six months, the sheep are slaughtered and the worms are
counted.
1.1.2 Set up
The two groups/populations (µ) are compared to each other. The sheep are the experimental units.
The response is the number of tape worms. It is not possible to look at all 24 sheep, but a guess is
made about the difference between the population using one random sample of each population.
The population means are compared to each other; µ1 for the new drug, µ2 for no treatment. 6w2This
is the alternative hypothesis: Hα = µ1 - µ2 < 0. The null hypothesis will be H0 = µ1 - µ2 = 0. When H0 is
rejected, it is shown that the research hypothesis is true, i.e. we have shown that the number of tape
worms in the treated population is lower than the number of tape worms in the untreated
population.
1.1.3 Statistical model and assumptions
In the statistical model, a number of assumptions need to be made:
1. Normality
First off, it is assumed that the data comes from two normal distributions. This means that the data
follows a symmetrical graph, with an optimum.
2. Equal variance
, The variance (σ 2) is the variance of the data, differing from the mean. In the figure below, it can be
assumed that the first and second sample have unequal variance, and the second and third have an
equal variance.
The variance is the standard deviation (σ) squared. The standard deviation measures the amount of
variability, or dispersion, from the individual data values to the mean.
3. Independence
It is assumed that the responses from the 24 sheep are independent because it is a random sample
of sheep, which are randomly assigned to the groups and there is only one observation.
Because of these assumptions, we get the following statistical models:
y1 …y12~ N(µ1, σ 2) for sheep receiving the drug
y13 …y24~ N(µ2, σ 2) for sheep receiving no treatment
1.1.4 The test statistic
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller sabinecaspers. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.03. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53068 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now