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
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 JunaSTDY. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.55. You're not tied to anything after your purchase.