Week 3 Flashcards
What is Chebyshevs theorem?
For any set of observations, the proportion of values that lie within k standard deviations of the mean is at least:
1-(1/k^2) given k>1
What does sd measure?
Dispersion with respect to mean
What is a probability?
A value between 1 and 0 describing relative possibility of an event occurring
What is a random variable?
Quantity resulting from an experiment that can assume different values
What is a probability distribution?
Shows all possible outcomes of a test and the probabilities associated to each outcome
6 characteristics of a normal distribution?
Bell shaped Area under curve = 1 Asymptotic to X axis Symmetrical about the mean Mean=median=mode Peak in centre
2 measures of distributions?
Skewness
Kurtosis
What is Kurtosis?
How peaked it is (normal dist. = 3)
What is leptokurtic Kurtosis?
Kurtosis >3
What is platykurtic Kurtosis?
Kurtosis <3
Kurtosis equation?
Kurtosis = (Σ(Xi-μ)^4)/((Σ(Xi-μ)^2)^2)
What is a standard normal probability distribution?
Mean = 0 Sd = 1
What does the z-score tell us?
The number of sd’s a score lies above or below the mean
What is a probability sample?
Each item in sample has a known probability of being included in the sample
4 ways to produce a probability sample?
1) simple random sampling
2) systematic random sampling
3) stratified random sampling
4) cluster sampling
What is cluster sampling?
Population is divided into primary units (clusters), individual clusters are randomly selected then a random sample is taken from each selected cluster
What is sampling error?
The difference between sample statistic and its corresponding population parameter
What is a sampling distribution?
Probability distribution of a statistic for all possible samples of a certain size N
What is empirical sampling distribution?
Take the whole population, split into many samples of equal size and look at distribution formed
Characteristics of empirical sampling distribution? (3)
Mean pop = mean of distribution of sample means
Spread of pop>spread of dist. of sample means
Dist. Sample means is similar/can be approximated by normal distribution
Standard deviation of a sample = ?
σ/(N)^0.5
What is the central limit theorem?
Sampling distribution of the mean of any independent random variable will be normal or nearly normal
When is an estimator of the mean unbiased?
When μ (sample) = μ (population)
What is bias proportional to?
Error
What determines if a sampling distribution is efficient?
If σ is small it is efficient
Increasing N increases efficiency
