mathe Flashcards
types of variables
categorical ->describes categories
qualitative-> describes magnitude
discrete-> counted
continous -> measured
level of measurement
nom numeric
- nominal: describe categories
- ordinal: describe differences but not to which degree
numeric:
- interval: freely chosen 0 point, describe differences and to what degree
- ratio: fixed 0 point, differences, degree, ratios
frequency distribution
nominal scaled
metric scaled: how often a value k is not exceeded
measurement of central tendency
mean : average
median: divides set into two halfs
mode: the value that occurs most frequently
measurment of dispursion
deviation: how observation differs from mean
variance
standard deviation: typical distance from mean
range: distance between largest and smallest observation
bivariate frequency distributions
describe observed frequencies of two variables at a time and their relationship
contingency table:
-describe joint distribution of variables
correlation and coveriance
coveriance shows positive association between variables
correlation shows direction if association (-1-1)
spearman rank correlation coefficient if at least on ordinal
methods of estimation
ordinary leadt square regression
- difference between observed and estimated value is residual
- OLS shows line with minimum squared distances
probability theory
value between 0 and 1 describing the possibility and event will occur
probability distribution: function that relates value to its probability (e.g binomial how often occurs head when thrown 6 times)
probability distribution of continuous random variables
with increasing n it becomes a binomial distribtuon and when n approaches infinity this becomes a normal distribution
no talk about the probability being in a intervall
sampling distribution
how close the sample mean is to population mean
central limit theorem
-sampling distribution can be approximated with normal distribution with larger sample size
confidence interval
the interval of which you are confident that it will contain the population mean
hypothesis test use and steps
test if a claim about a population is correct or not
- assumption
- hypothesis (null or alternative null)
- level of significance (allowing max prob of error)
- test statistics (two tailed - it is or not, one tailed- above or below)
- p value
one sample t test
tests the distance between sample mean and a value in nr of standard errors
independent samples t test
differences of population means