Final exam revision Flashcards
What is an alpha level?
Also known as a significance level
Probability of rejecting the null hypothesis when it is true.
The alpha level is typically set at 0.05, which means that there is a 5% chance of incorrectly rejecting the null hypothesis
A lower alpha level indicates a more stringent test, meaning that there is a lower chance of a Type I error (a false positive). However, a lower alpha level also means that there is a lower chance of detecting a real difference or relationship (a Type II error).
What is a type I error?
False-positive: occurs if an investigator rejects a null hypothesis that is actually true in the population.
What is a type II error?
False-negative: This occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
What’s the difference between one-sided and two-sided tests?
One-sided has a direction in which we expect the data to go, while a two-sided test does not specify a direct of difference.
For example, if we were testing a new drug to see if it was effective in reducing blood pressure, we might only be interested in detecting a difference in the mean blood pressure if it was lower in the group that took the drug. In this case, we would use a one-sided test to reduce the risk of a Type I error.
What is a measurement unit?
The units in which data is measured.
For example, height can be measured in centimetres or inches, weight can be measured in kilograms or pounds, and time can be measured in seconds, minutes, or hours.
What is an experimental unit?
The individuals or objects that are studied in an experiment.
For example, if you are conducting an experiment to test the effects of a new fertilizer on plant growth, the experimental units would be the plants.
Write down a linear regression model
y = b0 + b1x + e
where:
y is the dependent variable
b0 is the intercept
b1 is the slope
x is the independent variable
e is the error
How do you reduce type II error
False-negative
1. Increasing the sample size. A larger sample size will increase the
power of the test, which is the probability of rejecting the null
hypothesis when it is false.
2. Increasing the effect size. A larger effect size will also increase the
power of the test.
3. Using a more sensitive test. There are a number of different
statistical tests that can be used to compare two groups. Some tests
are more sensitive to differences between the groups than others.
4. Reducing the variability in the data. Variability in the data can reduce
the power of the test. This can be done by controlling for
confounding variables or by using a more precise measurement
instrument.
How do you reduce type I error
What is the effect size in statistics
A measure of the strength of the relationship between two variables.
How do you increase effect size in statistics
Generally, effect size is calculated by taking the difference between the two groups (e.g., the mean of treatment group minus the mean of the control group) and dividing it by the standard deviation of one of the groups.
So lowering the standard deviation would end up with a higher effect size
Define t-student distribution
Test to compare the means of two groups.
It is a bell-shaped distribution, but it has heavier tails than the normal distribution.
The t-distribution is a family of distributions, and the shape of the distribution depends on the degrees of freedom.
What’s degrees of freedom?
The degrees of freedom are a measure of the variability of the data. The larger the degrees of freedom, the more closely the t-distribution resembles the normal distribution.
What is an absolute value of a critical value?
The absolute value of a critical value is the distance from the mean of a distribution to the point at which the probability of observing a value at least as extreme is equal to the significance level. In other words, it is the point at which the null hypothesis can be rejected.
For example, if the significance level is 0.05, then the critical value for a two-tailed test is 1.96. This means that if the absolute value of the test statistic is greater than 1.96, then the null hypothesis can be rejected with a 95% confidence level.
What are the linear model assumptions?
Linearity: The relationship between the independent and dependent variables is linear. This means that the data points should form a straight line when plotted on a scatter plot.
Homoscedasticity: The variance of the residuals is constant across all values of the independent variable. This means that the spread of the data points around the regression line should be the same for all values of the independent variable.
Normality: The residuals are normally distributed. This means that the residuals should follow a bell-shaped curve.
Independence: The residuals are independent of each other. This means that the value of one residual should not be related to the value of any other residual.
Multicollinearity: There is no multicollinearity among the independent variables. This means that the independent variables are not perfectly correlated with each other.
