Complete overview and notes of the Introduction to Statistics course for year 1 sociology. It contains all the important information about the lectures and presentations, and the notes are a good overview of the entire course! I myself had a lot of trouble with statistics, so I made the notes as de...
Lecture 1 - 09/01
Expert in a dying field
On probability, z-scores and distributions
Types of variables
● Nominal
● Ordinal
● Interval
● Ratio
● Dichotomous
Describing data/variables
● Centrality (where is the centre of the variable?)
- Mode → most common value
- Median → middle value
- Mean → average value
● Dispersion
● Proportion → percentage/100
- For dichotomous variables the mean equals the proportion
● Standard deviation → sum of all squared distances to the mean
Distribution of data
● Bell-shaped empirical rule (standard normal distribution)
- In area of +y1 and -y1 standard deviation is 68% of all observations
- In area of +y2 and -y2 standard deviation is 95% of all observations
- In area of +y3 and -y3 standard deviation is 99,7% of all observations
● Standard normal distributions
- Mean equals 0, sd equals 1
● P-value equals .68 (or 68%) in above example
Probability
● Probability can be defined as z-scores
- Every position in a normal distribution has a z-score with corresponding
probability
- Using z-scores on data, we can calculator different probabilities and connect
probabilities to real scores on a variable
Lecture example: youngsters & ‘’ietsism’’ in De Pijp
● Z-score: value of observation, mean and standard deviation
- (value of observation - mean)/standard deviation
- (30-47,6)/18,2 = 0,97
● What p-value corresponds with z-score? → table A
- P = 1,660 (or 16,60%)
● What does this mean? The probability that a youngster believes in god is 16,60% or
0,1660
, Lecture 2 - 11/01
The pie
Sampling distributions and t-values
Important notes
● Any area under a distribution can be expressed as P
● We can find this P by using z-scores
● A z-score corresponds to P in tail
How do we draw conclusions about a population based on a sample?
Population (unknown) Sample (known)
Mean μ ^ ^
μ y
proportion π ^
π
Standard deviation σ S or ^
σ
Point estimation versus interval estimation
● Point estimation is based on a ‘’best guess’’
● Interval estimation
- Has a margin of error (uncertainty) around point of estimation
- Interval of which we’re quite certain that it will contain actual population value
- Confidence interval (CI)
How to obtain it? → sampling distribution
● Theoretical list of sampling statistic (such as a sample mean or sample proportion)
● Variables vary across different samples
● Point estimates vary across samples
But we only have one sample; how do we solve this?
● Sampling distribution is normally distributed and provides us with SE (standard error)
that we in turn can use to calculate confidence interval
● For an infinite number of samples, the sampling distribution follows normal
distribution with true proportion value in its centre
Difference sample and sampling distribution
● Sample is the distribution of a variable in a sample (eg. age); the sample is known
● Sampling distribution is theoretical, cannot be calculated (eg the mean); the mean
age varies across random samples, we cannot observe, we only have one sample
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