Kvant flashcards lecture 2-3
Confidence interval
a range in which the true parameter value is likely to be found with a certain probability (95%)
Sample mean +- margin of error
Margin of error
the maximum expected difference between the true parameter and the estimate.
Calculated by multiplying the Z-score by the standard error.
Provides the range within the which the true parameter is likely to lie, given a certain confidence level
z-score
Gives an idea of how far from the mean a data point is (standard deviation)
Positive z-score: Value is above the mean.
Negative z-score: Value is below the mean.
Z-score of 0: Value equals the mean.
Chi-squared test
Used for categorical data to test relationships between variables
A Chi-squared test is a statistical test used to compare observed and expected frequencies in categorical data to determine whether the difference is due to random variation or a real relationship.
Two types:
- Goodness of fit test: Checks if sample data matches a population.
- Test of Independence: Checks for association between two categorical variables
Law of large numbers:
The Law of Large Numbers (LLN) states that as the sample size increases, the sample mean approaches the population mean.
Null hypothesis (H0):
Assumes no effect or no difference.
Alternative hypothesis (H1):
Represents a claim contradicting H0. There is an affect or difference.
Type I error
Rejecting the H₀ when it is actually true (false positive).
Type II error
Failing to reject H₀ when H₁ is true (false negative).
Significance level (α)
Is a measure of the strength of the evidence that must be present in the sample before rejecting the null hypothesis
p-value
The probability of obtaining a result at least as extreme as the one observed, assuming h0 is true.
The smallest significance level at which H0 would be rejected.
Critical value:
Defines the upper and lower bounds of a confidence interval
Example:
confidence interval: 95%
Critical Value (Two-Tailed): From the z-table, The critical values: −1.96 and +1.96.
If your z-score is outside: −1.96 and +1.96., reject H0
Z-test
Used when the population variance is known, and sample size is large (n > 30).
compares the sample mean to the population mean
T-test (student’s t-test)
Used when the population variance is unknown, and sample size is small (n ≤ 30).
One-sample t-test: compares sample mean to population mean
Two-sample t-test: Compares means between two groups (independent or paired).
Ekstra: Variance unknown, but sample size is large, z or t-test?
T-test. u may use the sample variance as an estimate of the population variance
Chi-squared test
Used for categorical data to test relationships between variables
A Chi-squared test is a statistical test used to compare observed and expected frequencies in categorical data to determine whether the difference is due to random variation or a real relationship.
Two types:
- Goodness of fit test: Checks if sample data matches a population.
- Test of Independence: Checks for association between two categorical variables.
