Lecture notes

Class + Reading notes Statistical Modelling for Communication Research (SMCR)(Communication Science) Y

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Module
774221002Y

Institution
Universiteit Van Amsterdam (UvA)

This includes 2 documents. The first is a summary of the chapters that are required readings (these can help score better in the weekly bonus tests!). It includes chapters 1-11 and each chapter has its own dictionary which summarizes all the new words that were mentioned (and are relevant for the e...

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Uploaded on November 3, 2022
Number of pages 12
Written in 2022/2023
Type Lecture notes
Professor(s) Wouter de nooy
Contains All classes

sampling distribution
spss
sample
observations
sample statistic
sampling space
expected value
probability density
random variable
confidence interval
population
sample
prbability models
bootstrapping

Institution
Universiteit van Amsterdam (UvA)
Education
Statistical Modelling for Communication Research
Module
774221002Y

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Chapter 1: Sampling Distribution; How different could my sample have been?

Overview
- Inferential statistics helps generalize conclusion about a) CI, b) p-value

1 sample = 1 observation

Chapter 1 DICTIONARY
1. Sampling distribution: many samples, all possible sample statistic values and their
probabilities/ probability densities

2. Sample statistic: (aka. Random variable) number describing a characteristic of the
sample (ex. Number of yellow candies)
3. Sampling statistics: (aka. Relative frequency); sampling space (value 0-1), probability .
proportion based, sample distribution = probability distribution
4. Sampling space:(all possible sample statistic values) sample statistic value present on x
axis of graph
5. Expected value: value drawn from population = mean of sampling distribution; mean of a
probability distribution such as a sample distribution
a. True population value = expected value
6. Probability density: a way of getting probability of a continuous random variable (like a
sample statistic) falls within a particular range
- Continuous variables! (range of values!) (ex. Bag with average candy weight of
AT LEAST 2.8 grams)
- Choose threshold/ range (ex. Between 2.70 grams to 2.85, and the
expected average is 2.8 grams)
- Probability density function: x-axis values for continuous probability
distribution (0-1)! NOT PROBABILITY!
- Right-hand probabilities: probabilities of values above (and
including) a threshold
- Left-hand probabilities: probabilities of values up to (and including)
a threshold value
7. Random variable: variable with values that depend on chance

, 8. Confidence interval: estivate possible range of values for sample statistic of a selected
population (compare sample drawn vs. expected value of population)
9. Population: large set of observations about which we want to make a statement
10. Sample: smaller set of observations about which we want to make a statement
11. Population statistic: parameter
12. Probability distribution: when we change frequency in sampling distribution into
proportions
- Tells us
- How many yellow candies to expect in bag of 10 candies
- Probability of specific outcome occurring

Population value: 1) draw 1000+ samples, 2) calculate mean of sampling distribution (of sample
statistic), 3) that number = population value
- To calculate population value accurately:
1. Random samples only
2. Unbiased estimated (used throughout course, and assumed in SPSS)
3. Continuous (probability density) vs. discrete (probability)
4. Impractical (time/resources)

Chapter 2: Probability models, sampling distribution

Mean of sampling distribution = expected value = true value in population

Sampling distribution construction from ONE SAMPLE
1. Bootstrapping (NON-CATEGORICAL VARIABLES)

Step 1) Calculate number of yellow candies (%) in original sample
Step 2) see if mean of bootstrap sample is the same = true sampling distribution

Sampling with replacement: bootstrap sample is different than original
- Pros: Creates meaningful sampling distribution
Sampling without replacement: proportion/ sample statistic of interest = identical to original
sample
- Con: Does not create meaningful sampling distribution
Sample statistic of interest: (ex. Proportion of yellow candies)

Cons of bootstrapping
1) Samples must be drawn randomly
2) Samples must be large

2. Exact approach (ONLY CATEGORICAL & DISCRETE VALUES!)
Aim: to calculate exact probabilities of all possible sample results

, Conditions
Pro Con

True sampling distribution Categorical & discrete variables only

Computer intensive

3. Theoretical approximation
Theoretical probability distribution: sampling distribution as math function
Normal distribution: larger amount of samples = more accurate (1000+ samples)

Conditions
- Probability of drawing a sample statistic X population size > 5

Con
- Does not fit sampling distribution for all kinds of data (can be skewed towards left/right
and therefore, it does not appear in the graph)
- Approximation of sampling distribution does not equal the true sampling distribution
- T-distribution: tests on means in small samples
- F-distribution: analysis of variance (ANOVA)
- Chi-squared: categorical variables

Chapter 3: Estimating a parameter; which population values are possible?

Confidence level/ probability: area under the curve which is not in the rejection area
Percision: width of interval (ex. 95% confidence interval)
Critical value: (z-value) where the CI ends/starts

- Population value does not have probability ( because its an exact. One value)
Z x SE =lower limit/ upper limit
exact distance between sample result and lowest plausible population value (lower limit)
*SE: Standard deviation of sampling distribution (calculated by SPSS)

To find lower and upper limit
- Set sample as mean, and apply Z x SE
- This leads to the conclusion that we are 95% confident that the average candy
weight in the population is between X gram and X
- Y grams.

Chapter 3 Dictionary
1. Point estimate: single guest for population value (based on sample)

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