Summary - Statistical Modelling for Communication Research

fWEEK 1


~ 2.1 VIDEO PREPARATION (EMPIRICAL CYCLE)
~ E-BOOK Preparation
Chapter 1->
- SMCR Session 1
● without a sampling distribution we cannot generalize from the sample to the
distribution (it is the connection point)
● start with candy example
- the distribution is not the same (your sample might have equal red and yellow
candies while it might be different)
- that's why we need a sampling distribution (we focus on samples)
SAMPLING DISTRIBUTION :
1. includes the COUNT of the candies and
2. THE NUMBER of the candie
3. it's about the PROBABILITY


-> the EXPECTED VALUE= the mean of the sampling distribution


COMPLICATIONS
1. the sample must be a random sample
2. the sample statistic must be an unbiased estimator of the population
3. sampling distribution if the sample statistic is continuous = if it can take number
with an endless amount of decimals
- probability density VS probability
4. it is impractical




IF we want to have a informed decision about our conclusion then we need to compare
the characteristic of the sample that we have to -> the characteristics of the sample
that we could have drawn (= the sampling distribution)
- SD= are the central element in estimation

,INFERENTIAL STATISTICS->
making about large set of observations (= the POPULATION) from a smaller set of
observations (= the SAMPLE)


- The sampling space is also considered a variable


*= an example of a discrete probability distribution is:




EXPECTED VALUE of a random variable:
- the average of the sampling distribution of a random variable (number of yellow
candies in t=a sample
- also called EXPECTATION of a probability distribution


UNBIASED ESTIMATOR
: a sample statistic
- of the population statistic IF the expected value (mean) is equal = to the
population statistic


PROBABILITY DENSITIES
- Left-hand probability -> the probability of values ur to (and including) a
threshold value
- Right-hand probability -> the probability of values above (and including) a
threshold value

, ● THESE are used to calculate p values


!HOME POINTS!
1. The sampling distribution of a sample statistic tells us the probability of
drawing a sample with a particular value of the sample statistic
2. If a sample statistic is an unbiased estimator of a parameter, the parameter
value equals the average of the sampling distribution, which is called the
expected value or expectation.
3. For discrete sample statistics, the sampling distribution tells us the probability
of individual sample outcomes. For continuous sample statistics, it tells us the
probability density, which gives us the probability of drawing a sample with an
outcome that is at least or at most a particular value



TUTORIAL- 1ST
1. .Discrete distribution (the outcome space is fixed) VS continuous distribution (
you get any number in the space)
2. Continuous



WEEK 2
Chapter 2->
3 WAYS OF SAMPLING DISTRIBUTION W ONE SAM[LE
1. Bootstrapping
- the bootstrap sample should be as large as the original sample
- sample with replacement
- it is different from the original
- only correct if the original sample is representative of the population :
for it to be effective


2. The exact approach
- exact probability with all results
- the original variable should be categorical
- computer intensive -> true sampling distribution


3. Theoretical approximate
- normal distribution as a function
- approximation is not the true sampling distribution

, - poor approximation if the conditions have not been met


IN GENERAL -
1. For each bootstrap sample, we calculate the sample statistic of interest and we
collect these as our sampling distribution.
2. WITHOUT replacement the bootstrap sample is the same as the original


BOOTSTRAPPING LIMITATIONS
1. MAIN: the variables that we are interested in need to be distributed more or
less as in the population -> or the sampling distribution gives a distorted view of
the true sampling distribution
- it is more likely to be representative if the sample is large or truly
random


ADVANTAGES
1. The sampling distribution is just the collection of the sample statistics
calculated for all bootstrap samples
2. the only way to get a sample median


SPSS
Analyze-> Comparative Means -> Independent Samples t-test-> test variable (what i
want to compare)-> define the groups -> Bootstrap -> Perform-> Number : 5000->
PASTE


INTERPRET
● see t-test statistic -> mean is their value in average -> lower and upper is the
space they are supposed to be within
● independent test -> value above 5 = the population variances are equal


EXACT APPROACH
-> not possible for an unlimited of categories
- it uses a binomial probability formula
- available for the association between two categorical variables in a contingency table.
- The fisher-exact test is an example of an exact approach to the sampling distribution
of the association between two categorical variables.
- they are computer intensive



SPSS