me myself and I lecture 2- chi-square test Flashcards
what is a sample?
a sample is usually only a [very small] subset of the total population
what is the population?
The population is all members of a defined group
Repeating experiments gives more insight into reliability of results.
what is sampling error?
sampling error is the random variation introduced into a data set as a function of only sampling a subset of the total population.
It is important to always consider sampling error when analysing and interpreting data. Repeating experiments can increase the reliability of our results.
what is a statistical hypothesis?
A statistical hypothesis is a statement or assumption about the characteristics of a population or the relationship between variables that is subject to statistical testing.
It is formulated based on the research question and serves as a framework for conducting statistical analyses and drawing conclusions.
what is the null hypothesis?
H0 is the default expectation that categorical outcomes are all equally likely, that there is no relationship between two measured phenomena, or that there is no association between groups.
H0 is the default expectation if there is no experimental/biological effect
what is the alternate hypothesis?
H1 is the expectation that categorical outcomes are not all equally likely, that there is a relationship between two measured phenomena, or an association among groups
how do you find out if the alternate or null hypothesis are statistically significant?
Once the null and alternative hypotheses are defined, statistical tests are conducted to assess the evidence in the data and determine if there is enough support to reject the null hypothesis in favor of the alternative hypothesis.
examples of hypothesis…
H0 = the ratio of males to females = 1 : 1
H1 = the ratio of males to females ≠ 1 : 1
* this is a two-sided test
- H2 = there are more females than males
- this is a one-sided test
- H3 = there are more males than females
- this is a one-sided test
what is a 2 sided test?
In statistics, a two-sided test is a type of hypothesis test that considers deviations from the null hypothesis in both directions. It is used when the researcher is interested in determining if there is a significant difference or effect, regardless of the direction of that difference.
what is a chi squared test?
the chi-squared test (𝜲2) can be used where the observations are assigned into mutually exclusive classes
it is essentially a quantification of how far our data deviates from the expected numbers. It takes into account how many observations we had. Smaller the difference between the observed and expected, the smaller the chi-squared value.
the number of observations in each class are compared to those expected under the null hypothesis
Assumes:
Variables are categorical
Observations are independent
Observations are mutually exclusive
Most of theexpected values are greater than 5.
what is the chi-squared formula?
the chi-squared formula = 𝜲2 = ∑(d2/e)
*where: d (difference) = o (observed) – e (expected)
∑ = sum of
how do you find the degrees of freedom?
-unless no. columns = 1, then d.o.f. = no. rows – 1
- degrees of freedom = (no. rows – 1) x (no. columns – 1)
In statistics, degrees of freedom refers to the number of values in a calculation or analysis that are free to vary. The degrees of freedom are determined by the number of independent pieces of information available in a sample or data set. Minimum number must be 1.
