Week 5: Hypothesis

The basic methodology used in the pursuit of knowledge is to

Formulate hypothesis

Gather data

Examine wether the data supports the hypothesis

Steps for hypothesis testing

  1. Formulate null (H0) and alternative (H1) hypothesis
  1. Chose the significance level (alpha)

Null Hypothesis is where things go as expected, alternative hypothesis is the unexpected

Legend

Miu

Population parameter

In statistics, a population parameter is a number that describes something about an entire group or population

X_

Sample mean

Alpha

Significance level

Usually 0.05 and set by the researcher

Usually 0.05

  1. Calculate the test statistic and critical value

n

Sample size

Sx

Sample Standard Deviation

t-stat

Test statistic

Compares your data with what is expected under the null statistic

We use this formula to calculate the t-stat

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Critical Value

Df

Degrees of freedom

n-1 when calculating 1 parameter

Obtained from the T distribution

For critical value we use excel and use

For two sided tests = t.inv.2t (significance level, degrees of freedom)

  1. Make a decision

If critical value > than the t-stat (absolute value) there is no sufficient evidence to reject the null hypothesis

Types of tests

Two Sided (tailed) tests

Alternative hypothesis = Population parameter is not equal to the hypothezised value

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One sided test

Greater than

Lesser than

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For one sided tests = t.inv (significance level, degrees of freedom)

Errors in hypothesis testing

Type 1 error

Rejecting null hypothesis who its true

Type 2 error

Not rejecting the null hypothesis when it is false

Probability of a type 1 error = significance level

By reducing the significance levels we reduce the probability of committing a type 1 error but we increase the probability of committing a type 2

For lineal regression models we use

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n-2 when calculating 2 parameters

P -value approach

P value

Probability that a sample deviates an x amount from the population mean given that the null hypothesis is true

If p value is less than alpha or significance level then we reject null hypothesis

If p value is greater or equal we do not reject null hypothesis, but not necessarily reject

Reject null hypothesis if p value is less than alpha in two tailed

P value divided by two for one tailed tests

Based on the sample tested compared to true population