1AB Flashcards
Population mean (๐)
๐ = (ฮฃ * X)/ N
The population mean is the sum of all values in the given data/population divided by a total number of values in the given data/population.
Population standard deviation (๐)
Wortel Sum (X-u) ^ 2 / N
X - the value in the data distribution
u - the population mean
N - the total number of observations
aka wortel (๐ 2) = wortel variance
The standard deviation is the variation between the values in the population
variance ๐ 2
Sum (X-u) ^ 2 / N
X - the value in the data distribution
u - the population mean
N - the total number of observations
the variance is the same as the standard deviation but for in the sample.
inferential statistics
is about making inferences about a population based on the sample that you examined
the null-hypothesis
the opposite of the alternative hypothesis and so usually states that an effect is absent
Itโs the opposite of what you want to know, so you test for the reverse. It indicates there is no relationship between what youโre testing and that the observed difference is due to chance
the alternative hypothesis
the hypothesis or prediction from your theory would normally be an effect will be present
p-value
will indicate the probability that you would draw a sample with an average X or lower, while the actual average X in the population is X >
P = > a; can not reject the H0
P = < a; we can reject the H0
How to test a hypothesis
- In order to test a hypothesis about a sample you need the p-value. This can be found in the t-test table after performing the t-test.
- You also need the degrees of freedom, which is n-k-1.
- If the p-value is higher than the common alpha/significance level of 0.05, you cannot reject the null-hypothesis
- If it is lower, you reject the null-hypothesis.
k is the amount of independent variables
confidence interval
- A confidence interval indicates all values of a null-hypothesis that would not be rejected by the observed sample mean.
- Always minus 1.96 times the SE and plus 1.96 times the SE
- For what population means would the probability of X still be greater than 5% (alpha = 0.05).
Mistake people make when interpreting the confidence interval
- In the example from the lecture the two values from the confidence interval meant that if the grade average is between those two values, it is still quite conceivable that you would draw a sample of 5 exams with an average of 5.0.
- Based on this you could technically assume that the average grade in the population is 3.8 and 6.2.
- This assumption gets made a lot in research, people interpret as if the confidence interval is true for the entire population when it doesnโt have to be.
3.8 and 6.2 are the confidence interval values from the example
Sample distribution
The sample distribution is the distribution of the entire sample.
Sampling distribution
- The sampling distribution is the distribution of all averages that you could find in all samples of a certain size you can draw from the original sample.
- The average here is the same as in the sample distribution, but the standard deviation is the standard error of the sample distribution.
Central limit theorem
The central limit theorem is the rule that with a sample size larger than 30, the sampling distribution will always follow the normal distribution.
