Normal Distribution Flashcards
What does the z-score tells you?
What is the formula for the z-score
The z score tells you how many standard deviations from the mean your score is (score is x, which could pe an iq)
- it allows researchers to calculate the probability of a score occurring within a standard normal distribution;
- enables to compare two scores that are from different samples (which may have different means and standard deviations).
Formula:
Z= X-Xmean / Standard Deviation
What is the STANDARD ERROR OF THE MEAN in a Z SCORE FORMULA good for.
You have several samples. Each sample has a mean. The STANDARD ERROR OF THE MEAN will tell you how many standard errors there are between the sample mean and the population mean μ.
CHEBYSHEV’S THEOREM
- what does it tell you?
- Requirement?
- Formula?
- Solve: the average check at a local restaurant is 36.42 with a standard deviation of 8.15. What is the minimum percenttage of checks between 15.23 and 57.61?
tells you how much data falls into the given interval(its k amount of standard deviations)
Mean has to be in the middle of the interval. so, pe the mean hast to be 30$ if the average pay is 20$ to 40$
1-(1/k²) # k is the number of standard deviations. How to calculate k? Limit-mean/standard deviation # limit is start or nd point of the interval
solution: 85,2% (https://www.youtube.com/watch?v=9BnsxXe5SdA)
CENTRAL LIMIT THEOREM says?
you take several samplings of the data and calculate their means. These means will be a normal distribution for the data.
If the number of samples is high, there will be a normal distribution around the mean. The mean for any roll is (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5, thus the normal distribution will be around the mean 3,5.
How to get a stratified random sample?
Stratified means, in layers. Divide the population in good groups, p.e. 20-29 years, 30-39 …. Take the amount of people you want for a sample, divide it by the size of the population and multiply it with the amount of all people who are in one group. The results off all groups have to add up to the size of the sample.
What is a sampling frame ?
the population size / the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, p.e. all trauma hospitals in the US.
HOW TO PERFORM SIMPLE RANDOM SAMPLING?
most basic sampling in statistics
- make a sampling frame(list all trauma hospitals in the US and assign numbers to them.
- decide what your sample size will be.
- Use a random number generator to select the sample, using your sampling frame and your sample size. If your sample size is 50 and your population is 500, generate 50 random numbers between 1 and 500.
HOW TO PERFORM SYSTEMATIC SAMPLING?
And what is Repeated Systematic Sampling
method of choosing the nth member , p.e. every 10th.
- shuffle the list, otherwise it could be male/female/m/f/m/f…
- assign numbert to elements
- decide sample size
- Divide the population by your sample size. This is your “nth” sampling digit
With Repeated Systematic Sampling you are doing you nth steps to a certain point and then change to an other point. P.e. you are doing 10th steps up to 50, then go to 61, going over to 71 … and so on.
3 steps of hypothesis testing?
- Stating the hypothesis
- Calculate a test statistic (depending on distribution and sample size.)
- Convert the test statistic into a P-Value and use this value to decide to support or reject the null hypothesis
What are p-value and alpha values used for?
A P-value (probability value) tells you if your hypothesis statement is probably true or not. It is the evidence against a null hypothesis. Calculate z score and put in table, this is p-value.
You get an alpha level by subtracting your confidence interval from 100%. For example, if you want to be 98 percent confident in your research, the alpha level would be 2% (100% – 98%)
Compare P and Alpha values: A small p-value (≤ 0.05), reject the null hypothesis. This is strong evidence
that the null hypothesis is invalid. A large p-value (> 0.05) means the alternate hypothesis is weak, so you do not reject the null hypothesis.
What is a T-score?
Formula?
Simliar to p-values, but T-scores are generally used when you don’t know the population standard deviation or the sample size is less than 30.
T = (Z x 10) + 50.
A t-score of over 50 means above average; below 50 means below average.
When is an F Test used?
The test compares the ratio of two variances.
If you had two data sets with a sample 1 variance of 10 and a sample 2 variance of 10, the ratio would be 10/10 = 1. You always assume that the
population variances are equal when running an F Test.
What is a chi-squared test used for?
To test whether distributions of categorical variables differ from each another.
A very small chi square test statistic means that your observed data fits your expected data extremely well.
A very large chi square test statistic means that the data does not fit very well. If the chi-square value is large, you reject the null hypothesis.
