Unit 5 Flashcards
What is the purpose of descriptive statistics?
they provide conclusions about a sample, such as position, central tendency, and variability. They summarize the data for easier interpretation
What is the purpose of inferential statistics?
they provide conclusions about the population. They use sample data to make generalizations or predictions about a larger group
What is the difference between statistics and parameters?
Statistics (^ø) are estimated based on a sample
Parameters (ø) are values that describe the entire population
-> statistics are used as estimators of parameters
What is the role of probability theory in statistics?
It is the foundation for inferential statistics.
-> helps estimate the likelihood of obtaining specific results and assists in making conclusions based on random or deterministic phenomena
What is a conceptual hypothesis?
a broad statement predicting a relationship between two variables
-> e.g.: “Class attendance is related to academic performance.” It guides the research and sets the foundation for further testing
What is an operative (statistical) hypothesis?
a specific, testable prediction that can be confirmed or refuted with data.
-> e.g.: “The average grade of students with more than 60% attendance will be higher than that of students with less than 60% attendance.” (H: μ1 > μ2)
What does the hypothesis “H: µ1 > µ2” represent in this hypothesis: The average grade of students with more than 60% attendance will be higher than that of students with less than 60% attendance
it predicts that the average grade of students with more than 60% attendance (μ1) will be higher than the average grade of students with less than 60% attendance (μ2)
What is the conceptual hypothesis?
it is a direct statement and easy to understand
what is the operational hypothesis?
quantifiable, measurable and ultimately analyzable terms
-> inform how the concepts or variables will be measured
-> is about quantifying, to be able to compare and verify the stated relationship in an objective way
in what terms do we use statistical hypothesis?
in terms of statistics or parameters
What are statistical hypotheses formulated with?
the population in mind, not the sample
What is the purpose of an operative/statistical hypothesis?
An operative/statistical hypothesis is used to quantify and compare the stated relationship in an objective way, allowing for verification of the claim
What is the null hypothesis (H0)?
it always states equality, meaning there is no effect, difference, or association. It assumes no relationship between variables.
-> e.g.: “There is no effect, the difference is 0.
What is the alternative hypothesis (H1)?
it is the opposite of the null hypothesis. It states that there is an effect, difference, or association. It is based on the research hypothesis.
-> e.g.: “The effect is not equal to 0 (Effect ≠ 0)
How do we test hypotheses?
by checking whether our claim can be supported by evidence from the population. We compare the null hypothesis (H₀) with the alternative hypothesis (H₁) using data
What does a directional hypothesis predict?
it predicts a particular direction of difference between population
What is an example for Directional hypothesis regarding this hypothesis: The air-conditioned (AC) group will get better final marks than the non-air-conditioned (SA) group
H0: 𝜇AC ≤ 𝜇SA
H1: 𝜇AC > 𝜇SA
What is an example for Nondirectional hypothesis regarding this hypothesis: Extroverted people will show different mean self-esteem scores than introverted people
H0: 𝜇E = 𝜇I
H1: 𝜇E ≠ 𝜇I
What does a Nondirectional hypothesis predict?
It does not predict a particular direction of difference
Do a hypothesis testing for this:
Operational hypothesis: University students who experience high levels of academic stress show a worse academic performance compared to those with low levels of stress.
It is..
Directional (One-tailed)
H1: µHS < µLS
H0: µHS ≥ µLS
How are directional and nondirectional hypotheses tested in inferential statistics?
Directional and nondirectional hypotheses are tested using the same general process, but the predictions differ:
Directional hypothesis: Predicts a specific direction of the difference.
Nondirectional hypothesis: Does not predict a specific direction of the difference
How is a hypothesis tested in inferential statistics?
statistics rely on probabilities to determine the likelihood of a certain effect, assuming the null hypothesis is true.
-> helps us assess if the evidence supports the alternative hypothesis
What does the probability in hypothesis testing represent?
how likely it is that a certain effect will occur, assuming the null hypothesis is true.
-> helps determine whether the observed data is consistent with the null hypothesis
Why do we use samples and statistics to test hypotheses?
to test hypotheses and generalize the results to the population, as it’s often impractical to test the entire population
How is a statistic from a sample related to a population?
it is analogous to a direct score from the population, but with the limitation that it might not be identical due to measurement error
Why do different samples show different statistics?
due to measurement error
What is assumed about the distribution of scores and statistics?
that scores and statistics follow a certain distribution, typically the normal distribution, which is key for hypothesis testing
What does the Central Limit Theorem state?
if a random variable (X) is normally distributed in the population, and we take infinite random samples of size N and calculate their means, the resulting distribution of sample means will approximate a normal distribution
When can we predict probabilities?
if the variable’s distribution is normal
What are Parametric tests?
those that make assumptions about the parameters of the population
distribution from which the sample is drawn
-> This is often the assumption that the population data are normally distributed
What Non-parametric tests?
they are “distribution-free” and, as such, can be used for non-normal variables.
What is the formula to calculate a Z-Score for a sample mean?
z = (ˉx - µ) : (σ:√n)
What is the p-value?
Probability associated to the statistics.
How likely is to find that statistic by chance
-> if probability is really low, probability of H0 being true is reduced
When do we accept or reject H0 and H1?
p ≤ 𝛂
p ≤ 0.05 = Reject H0, Accept H1
p > 𝛂
p > 0.05 = Accept H0, Reject H1
What is a two-tailed (nondirectional) hypothesis test, and how is it represented?
A two-tailed (nondirectional) hypothesis test tests for the possibility of an effect in two directions (either positive or negative). The alternative hypothesis (H1) does not predict a direction, just that there is a difference
- Null Hypothesis (H₀): 𝜇 = μ0
(Population mean equals a specific value)
- Alternative Hypothesis (H1): µ ≠ µ0
(Population mean is not equal to the specified value)
What is a left-tailed (directional) hypothesis test, and how is it represented?
A left-tailed (directional) hypothesis test tests whether the sample mean is significantly less than the population mean.
- Null Hypothesis (H₀): µ ≥ µ0
(Population mean is greater than or equal to a specified value) - Alternative Hypothesis (H₁): µ < µ0
(Population mean is less than the specified value)
What is a right-tailed (directional) hypothesis test, and how is it represented?
A right-tailed (directional) hypothesis test tests whether the sample mean is significantly greater than the population mean.
- Null Hypothesis (H₀): µ ≤ µ0
(Population mean is less than or equal to a specified value) - Alternative Hypothesis (H₁): µ > µ0
(Population mean is greater than the specified value)
What are the statistical decisions made when performing a hypothesis test?
- The null hypothesis (H0) is either accepted or rejected based on the results of the test.
- If the p-value is less than the significance level (α), the null hypothesis is rejected.
- If the p-value is greater than the significance level (α), the null hypothesis is not rejected (it is accepted).
What are right decisions in Type I and Type II Errors?
- The null hypothesis (H0) is true and it is accepted.
- The null hypothesis (H0) is false and it is rejected.
What are wrong decisions in Type I and Type II Errors?
- The null hypothesis (H0) is true and it is rejected.
- The null hypothesis (H0) is false and it is accepted.
What is Confidence Interval estimation?
Estimate a range of values (symmetrical with respect to the mean) among
which the true value can be found, with a high and known probability
What 2 values are there in confidence interval?
Upper limit (UL)
Lower limit (LL)
What is the procedure in Confidence interval?
- find out standard error of statistic
- find the maximum sampling error (Emax)
- find the lower limit, subtract the Emax from the statistic
- find the upper limit, add the Emax to the statistic
