STATS 1123: PROBABILITY AND CHI-SQUARE

univariate data

• sinlge quantitative data

  • stemplot, histogram, boxplot

  • sample mean, standard deviation/ IQR

• categorical variable

  • pie chart, bar graph

  • sample proportion

bivariate data

• quantitative variables:

  • scatterplot

  • sample correlation coefficient

• categorical variables:

  • side-by-side bar graph

  • chi-square statistic

chi square analysis

• 2 categorical variables

• how independent the relationship between 2 variables is

• x²

two-way table

• columns x rows (frequency)

chi-square statistic formula

expected frequency formula

*The results of the chi-square analysis will not be accurate when one or
more of the expected frequencies are under five

*assume both variables are independent from eachother

steps to doing chi-square analysis

1. null hypothesis and alternative hypothesis

2. the X-variable and the Y-variable are independent to
   each other among all subjects in the population.
   • Alternative hypothesis: the X-variable and the Y-variable are
   not independent to each other among all subjects in the population

3. x² compared to DP using DF=(r-1)(c-1)

   • x² > DP → enough statistical evidence to reject null hypothesis and conclude that x and y are not significantly independent to e/o among all subjects in the population

   • x² < DP → do not have enough statistical evidence to reject null hypothesis and conclude that the two categorical variables are not significantly independent in the population

sample space

set of all possible outcomes for a random experiment

event

a subset of the sample space

event a formula

complement

event containing all outcomes not in A

P(A) = 1- P(Ac)

event A or event B

P(A|B) meaning

probability of A given B

P(A|B)=P(A) and vice versa if it’s independent

P(A and B)

P(A) x P(B) when A and B are independent

P(A and B) = 0 → mutually exclusive

mutually exclusive

P(A and B) = 0

P(A) x P(B) = 0

discrete and continuous random variable

• discrete: 1,2,3,4,5

• continuous: 1-10

expected value for discrete probability

E(X)= sum (x*f(x))

• when the experiment of (a scientific experiment) is repeated infinite # of times (long run), the average amount a person would gain/lose

standard deviation for discrete probability

sigma = sqrt(sum((x-u)² x f(x))