Data analysis lecture 1
Its about comparing means to each other
Assignment D is 20% of your total grade
Null hypothesis says the theory does not work → a researcher wants to reject the null,
because then something will work
Hypothesis testing = method of making statistical decisions about the population, based on
sample data
We make a decision about accepting or not accepting the null hypothesis:
The null hypothesis states:
- “equal to…”
- The same as…
- No change,
- No difference…
- No relationship…
The alternative hypothesis states:
- Not equal to…
- Not the same as…
- There is an increase,
- There is a difference,
- There is a relationship,
The test produces a P-value = the probability that data like this (or even more extreme)
could have occurred, if the null-model is correct
- If the P-value of the test is greater than a, we do not reject the null hypothesis
(outcome of the sample is not extreme different from the null hypothesis)
- If the P-value is less than a, we should reject the null hypothesis, and accept the
alternative as a plausible outcome (the outcome of the sample is extreme, the null
hypothesis can’t be true)
The criteria we need => alpha level (a)
,In general: if the P-value falls below a, we reject H0 -> then the outcome is statistically
significant
- Common alpha levels: 0.10 0.05 0.01
- If no information is given, we use a = .05(5%)
5 steps in performing a statistical test:
1. Rethink the problem
2. Formulate H0 and Ha and define a
3. Give the test statistic and the distribution of the test statistic (and investigate the
assumptions)
4. Calculate the test statistic, and carry out the test (using the P-value or critical value)
5. Draw a conclusion (short formal report plus interpretation)
,Two types of decisions rules:
Method 1: P-value: If the P-value is smaller than a, then the data are statistically significant.
(the outcome is rare given the null hypothesis => reject the null hypothesis)
Method 2: Critical value: if the test statistic is greater than the critical value (z*,t*,c*,….)
then the data are statistically significant (or if the statistic is negative:… smaller than the
critical value … significant)
,
Its about comparing means to each other
Assignment D is 20% of your total grade
Null hypothesis says the theory does not work → a researcher wants to reject the null,
because then something will work
Hypothesis testing = method of making statistical decisions about the population, based on
sample data
We make a decision about accepting or not accepting the null hypothesis:
The null hypothesis states:
- “equal to…”
- The same as…
- No change,
- No difference…
- No relationship…
The alternative hypothesis states:
- Not equal to…
- Not the same as…
- There is an increase,
- There is a difference,
- There is a relationship,
The test produces a P-value = the probability that data like this (or even more extreme)
could have occurred, if the null-model is correct
- If the P-value of the test is greater than a, we do not reject the null hypothesis
(outcome of the sample is not extreme different from the null hypothesis)
- If the P-value is less than a, we should reject the null hypothesis, and accept the
alternative as a plausible outcome (the outcome of the sample is extreme, the null
hypothesis can’t be true)
The criteria we need => alpha level (a)
,In general: if the P-value falls below a, we reject H0 -> then the outcome is statistically
significant
- Common alpha levels: 0.10 0.05 0.01
- If no information is given, we use a = .05(5%)
5 steps in performing a statistical test:
1. Rethink the problem
2. Formulate H0 and Ha and define a
3. Give the test statistic and the distribution of the test statistic (and investigate the
assumptions)
4. Calculate the test statistic, and carry out the test (using the P-value or critical value)
5. Draw a conclusion (short formal report plus interpretation)
,Two types of decisions rules:
Method 1: P-value: If the P-value is smaller than a, then the data are statistically significant.
(the outcome is rare given the null hypothesis => reject the null hypothesis)
Method 2: Critical value: if the test statistic is greater than the critical value (z*,t*,c*,….)
then the data are statistically significant (or if the statistic is negative:… smaller than the
critical value … significant)
,
