stats 5 Flashcards
hypothesis
a testable statement predicting a relationship or effect between variables, often framed as an expectation of what will happen
null hypothesis
a specific type of hypothesis that assumes no effect or no difference between variables and serves as a baseline to test against
The null hypothesis gives a
counterfactual
Counterfactual
an alternative scenario or condition that contrasts with the proposed effect or relationship in the hypothesis, effectively serving as the null hypothesis which assumes no effect or difference
Researchers need a null hypothesis to provide a
baseline or default position that allows us to test and determine whether observed data provides sufficient evidence to support a proposed effect or relationship
it is important to develop a corresponding - for each
hypothesis for purposes of -
null hypothesis, hypothesis testing
Hypothesis testing
a statistical method used to determine whether there is enough evidence in a sample of data to support a specific claim or hypothesis about a population
Hypothesis testing determines if your sample data provides enough evidence to
reject a null hypothesis in favor of an
alternative hypothesis
first step of hypothesis testing
state the null hypothesis (e.g., no difference between the sample mean and a population mean) and the
alternative hypothesis (e.g., a difference exists)
second step of hypothesis testing
set a critical value
Critical value
a predetermined threshold derived from a particular statistical distribution used to conduct a statistical test
Each critical value has an associated
significance level
Significance level
the probability of rejecting the null hypothesis when its actually true, representing the threshold for statistical significance.
third step of hypothesis testing
calculate a test statistic from your sample data
Test statistic
a value calculated by:
* identifying the sample statistic (e.g., the mean),
* determining its standard error (e.g. standard error of the mean),
and
* using a specific formula to assess how far the sample result
deviates from the null hypothesis
Different hypothesis tests are interested in different sample statistics.
For example:
- the t-Test sample statistic is the sample mean,
- the Chi-Squared test sample statistic is the observed frequency in
a contingency table, and - the ANOVA sample statistic is the sample mean squares.
fourth step of hypothesis testing
After calculating the test statistic from your sample data, you compare it to the critical value.
fifth step of hypothesis testing
You then find the p-value of your data.
p-value
the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true
p-values are a probability, so they range from
0 to 1 (0-100%)
sixth step of hypothesis testing
compare p value of your data to the critical values significance level (a) to determine whether the result is statistically significant.
a p val that is smaller than the significance value (a) suggests that such a result is unlikely under the
null hypothesis, leading you to reject it in favor of the alternative hypothesis
a p val that is larger than the significance value (a) suggests that such a result is likely under the
null hypothesis, leading you to reject it in favor of the alternative hypothesis
In the social sciences, the standard p-value threshold is
p = 0.05.
When the p-value is adequately small (e.g., p < 0.05), the findings are considered
statistically significant
Statistical significance
an indication that an observed effect or relationship in the data is unlikely to have occurred by random chance alone. (assuming the null hypothesis is true and the study is repeated an infinite number of times by drawing random samples from the same population, less than 5% of these results will be more extreme than the current result.)
When a result is statistically significant, that does not mean that
the alternative hypothesis is proven to be true. It just means you can reject the null hypothesis
Statistical significance really just means that
we are not likely to
see the relationship between our variables by chance alone
Chi-squared test of tabular association
a statistical test that
evaluates whether observed categorical data align with the expected frequencies based on a specific hypothesis
Bivariate analysis
the analysis or examination of the relationship between two variables, such as an independent variable and a dependent variable
Categorical variable
a type of variable that represents distinct categories or groups without any inherent numerical value or order, such as gender, color, or type of car. (have 2 or more categories. * Categorical variables with 2 categories are often called binary, dummy, or dichotomous variables.)
- To define your null hypothesis, first define your
research question
To define your null hypothesis,
write out both your null and
alternative hypotheses
To define your null hypothesis,
think about what hypothesis
test you need
To define your null hypothesis, next making a
contingency table (The independent variable should go in the columns.
* The dependent variable should go in the rows.)
Contingency table
a matrix that displays the frequency distribution of two categorical variables, showing how their values intersect
To define your null hypothesis, next think about
what the data
would look like if the null hypothesis were to be true, If the null hypothesis is true, we would expect there to be no difference in turnout by party affiliation
Define your null hypotheses
there is no relationship between partisan affiliation and voter turnout.
next, identify the
critical value
we need 2 pieces of information to define a critical value in a chi-squared test of tabular association
- a value for alpha (a) and - the degrees of freedom (df)
Degrees of freedom
the number of independent values or quantities that
can vary in a statistical calculation, typically indicating the number of values that are free to vary after certain constraints are applied
The shape of the Chi-square
distribution depends on the
degrees of freedom!
- Calculate a test statistic from the
sample data
- compare test statistic from your sample data to the
critical value
- Find the - of the data
p-value
