Bivariate stats and Hypothesis testing

Pearson’s rank correlation coefficient

Fill lists —> CALC (F2) —> REG (F3) —> X (F1) —> ax+b (F1)

r is the correlation coefficient

equation of regression line is y=ax+b

Spearman’s rank correlation coefficient

same instructions as pearson’s but use ranks instead of raw data

Null hypothesis

H0: μ =μ0

one tailed hypothesis

H1: μ > μ0 or H1: μ < μ0

two-tailed hypothesis

H1: μ ≠ μ0

test statistic

TEST (F3) —> t (F2) —> 1-SAMPLE (F1) —> execute

t is the test statistic

p-value

• lower p-value means less random

• high p-value means more random

students t-test

1. state null hypothesis and alternative hypothesis

2. calculate significance level

3. calculate value of test statistic

4. calculate p-value

5. reject H0 if p-value if ≤ a

two-sample t-test overview

null hypothesis is H0: μ1 = μ2

use ‘pooled’ on calculator

two-sample t-test instructions

TEST (F3) —> t (F2) —> 2-SAMPLE (F2)

if p-value < significance level (a), accept alternative hypothesis

X² goodness of fit test hypotheses

H0: stats fit (e.g. p1=1/6, p2=1/6 … p6=1/6)

H1: stats dont fit (e.g. p1, p2… p6 ≠ 1/6)

GOF test p-value

fill lists 1&2 TEST (F3) —> CHI (F3) —> GOF (F1)

if p-value is < a, reject H0 in favour of H1

GOF instructions

1. state null and alternative hypotheses

2. state significance level a

3. calculate test statistic

4. use technology to calculate p-value (using df = number of categories -1)

5. reject H0 if p-value ≤ a

GOF procedure with critical values

1. state null hypothesis and alt hypothesis

2. state significance level

3. calculate value of the test statistic

4. find critical value

5. reject H0 if test statistic ≥ critical value

X² test for independence hypothesis

H0: variables are dependent

H1: variables are independent

X² test for independence DF

df= (r-1)(c-1)

X² test for independence instructions

1. state null and alt hypotheses

2. state significance level a

3. calculate df

4. construct expected frequency table and calculate value of the test statistic

5. use technology to calculate p-value or find critical value

6. reject H0 if p-value ≤ a or test stat ≤ critical value