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Basics of Statistics: lecture notes

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A very digestible set of notes for people who are new to learn statistics. The language is very easy to understand as it was written by an international student in the UK.

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  • August 2, 2022
  • 40
  • 2021/2022
  • Class notes
  • Dr trevor sheldon
  • Week 5 to week 11
  • Unknown
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INFERENTIAL STATISTICS -

➔ Used to test hypothesis -
➔ Estimate disease burden (parameters)
➔ Each time the study is done, answer/hypothesis might be varied depending on the
sample you choose from the whole population THUS the estimate from a SINGLE study
may not be the the answer
➔ How to ensure this is the true result ?
➔ Even if you do the study 100 times and make it. Graph - it will be a normal bell shaped
curve
➔ And the results will lie in the 95% of the area
➔ Confidence interval : plausible range within which we are confident that the true value
lies
➔ If the CI does includes 1, then we are not confident about the groups being effective
against the other
➔ How do we prevent this uncertainty - INCREASE THE SAMPLE SIZE - smaller
confidence interval





➔ Bigger the sample, bigger the representation, can be generalised


,Sampling
➔ Selection bias - the sample won’t represent the entire population
➔ Larger and more random the sample, greater the inference /9applying the estimates
back to the population)
➔ Sampling frame - whole population whom you want to study
➔ Quantitative sampling techniques mein the calculations are done beforehand to estimate
the population ile you may need to get achieve significance - you do like a pilot
calculation to estimate the significance of your results
➔ Two types of sampling: Probability and Non probability sampling

Probability Sampling Types
➔ Simple random sampling - using a software to pick out people - like a lottery style bal
machines after the population is numbered
➔ Stratified sampling - first divide people based on age/gender and then conduct simple
random sampling in those 2 groups
➔ Cluster sampling - based on geographical location- people are divided into
clusters/groups and then random sampling from a few groups - Helps dealing with
subjects distributed geographically.
➔ Multi stage sampling - combining sampling methods - you may do cluster sampling -
followed by stratified - again Strat based on the groups you want to study, age, ethnic
group, gender - then simple sampling




◆ Non probability sampling - does not use random sampling methods - NO
GENERALISATION
◆ Convenience sampling - study population by asking for volunteers, people on the
road - used for small scale pilot study
◆ Quota sampling - they have a quota of 100 and just recruit people who may say
yes until 100 is reached - also might use proportional quota sampling

Types of errors

➔ Sample size calculation enough to give statistical power
➔ Type 1 error: researcher says result is significant but there is none; false positive.
➔ Probability of a type 1 error occurring - p
➔ P<0.05 - less than 5% probability of a type 1 Error occurring
➔ Null hypothesis means the opposite of your hypothesis
➔ Type 2 error: there is a genuine effect but researcher claim there isn’t: False negative
➔ Probability of a type II error : beta (power of a study)
➔ Occurs when the sample is too small
➔ Power of a study is 1-beta or 100-beta (if percent)

, ➔ Power of a study needs to be at least 80% meaning accepting a 20% probability of a
type II error

In hypothesis testing we always strive to test and reject the null hypothesis and therefore prove
the alternative hypothesis.

➔ StatsDirect, SPSS or STATA

P value

● P values indicates if the result you have gotten is due to a chance and not real
● P<0.05 - 5% likely that it is a chance finding
● P<0.01 - 1% “. “
● Recalls itself to the confidence interval - 95% we are sure, 5% we think it may be from
chance (why 5%? - arbitrary value you can choose any value for ex: p<0.02 - can be
your basis for a significnt study
● Greater the sample size, lesser the range of your CI - better the study

, ●

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