Hypothesis testing and chi squared Flashcards
(26 cards)
What is a hypothesis?
An informed statement, supposition, speculation, or expectation about reality that can be tested or falsified.
Hypothesis must be informed, testable, and an expectation.
What is the Null Hypothesis (H₀)?
A default assumption that states ‘no effect’, ‘no difference’, or ‘no relationship’ which we try to prove false.
The burden of proof is on the alternative hypothesis (H₁).
What does the alternative hypothesis (H₁) state?
That there is an effect, a difference, or a relationship in the population.
The hypotheses are about the population, not the sample.
How does Karl Popper’s idea of falsification relate to hypothesis testing?
We can never definitively prove a hypothesis; we can only reject a hypothesis based on evidence.
Progress is made by rejecting hypotheses and formulating better explanations.
True or False: Failing to reject the null hypothesis proves it true.
False.
Failing to reject indicates insufficient evidence to reject it, not proof of its truth.
What is the significance level (α) in statistical testing?
The probability of rejecting the null hypothesis when it is actually true, typically set at 0.05.
This level indicates the risk of a Type I error.
What is a Type I error?
Rejecting the null hypothesis when it is true (False Positive).
It occurs when the significance level is set too high.
What does a p-value indicate?
The probability of observing test results as extreme as ours assuming the null hypothesis is true.
A low p-value suggests that the observed data is unlikely under H₀.
What is the conventional significance level in social sciences?
0.05 (5%).
Researchers may also use 0.10 or 0.01 depending on the study.
What are the steps in conducting a Chi-Squared Test?
- Formulate the H₀ and H₁
- Collect sample data
- Decide the significance level
- Calculate the χ² test statistic
- Compare the test statistic to the critical value.
Each step is crucial for testing the association between categorical variables.
What does the Chi-Squared Test evaluate?
Whether the frequency distributions of two nominal or ordinal variables are independent or depend on each other.
It assesses the association between categorical variables.
Fill in the blank: The Chi-Squared Test is used to determine whether there is a significant _______ between two categorical variables.
[association].
What is the formula for calculating expected counts in a Chi-Squared Test?
E = (Row Total * Column Total) / Grand Total.
Expected counts assume independence of the variables.
What does a significant level of α < 0.05 indicate?
It indicates a trade-off between a weaker but easier-to-detect result and a stronger but harder-to-detect result.
This level is commonly accepted in hypothesis testing.
What is the purpose of setting a significance level in hypothesis testing?
To define how much risk we are willing to take in rejecting the null hypothesis incorrectly.
It guides the interpretation of test results.
What does SPSS do regarding calculations?
SPSS will do these calculations for you!
However, you will need to do these calculations in the Exam.
What is the significance level (α) set at in the Chi-Squared Test example?
0.05
This corresponds to a 5% probability.
What is the formula to calculate degrees of freedom (df) in the Chi-Squared Test?
(rows - 1) * (columns - 1)
In the example, it is (2-1) * (2-1) = 1 degree of freedom.
What is the critical value of χ² for α = 0.05 and df = 1?
3.841
What happens if the sample value of χ² is larger than the critical value?
We can reject the null hypothesis.
What is indicated if the χ² test statistic is smaller than the critical value?
We fail to reject the null hypothesis.
What does the significance level represent in the Chi-Squared Test?
The probability of obtaining a value of χ² or larger assuming the null hypothesis is true.
What are the steps of Statistical Hypothesis Testing? List them.
- Step 1: Formulate the null (and alternative) hypothesis
- Step 2: Collect the sample data
- Step 3: Decide the significance level
- Step 4: Calculate the test statistic
- Step 5: Compare the test statistic to the critical value
What must the p-value be to reject the null hypothesis (H0)?
Smaller than 0.05
