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Types of Hypotheses
Scientific hypotheses are tentative explanations for observations. Statistical hypotheses include null (H0) and alternative (Ha) hypotheses.
Null Hypothesis
States no difference between compared groups. Example: H0 - No difference in feather pigmentation between flamingos supplemented with crustaceans versus those that are not.
Alternative Hypothesis
States a difference between compared groups. Example: Ha - Difference in feather pigmentation between flamingos supplemented with crustaceans versus those that are not.
Two-tailed Hypothesis
Considers differences in both directions. Example: Ha - Difference in feather pigmentation across diets.
One-tailed Hypothesis
Considers differences in one direction. Example: Ha - Flamingos fed a crustacean diet express more feather pigments than those fed a fish diet.
Predictions
Statements about expected outcomes in an experiment. Example: Expect to see a difference in color pigmentation based on diet.
Test with Experiment/Study
Conducting experiments to test predictions and hypotheses, ensuring controls, replicates, and randomization.
Collect the Data
Gathering data on dependent and independent variables to analyze.
Descriptive Statistics
Stats like the mean that describe data but cannot be generalized beyond the dataset.
Inferential Statistics
Stats like t-tests that allow making inferences about populations beyond the data.
Two-sample t-test
Used to determine if the mean scores are different across groups, involving t-calculated and critical t-value calculations.
Degrees of Freedom (df)
Calculated as n1 + n2 - 2, where n1 and n2 are sample sizes.
Critical t-value
A value from a table used to determine significance in a t-test.
Student's t Distribution
Distribution used in t-tests, where choosing an alpha of 5% leads to a 5% chance of rejecting H0 due to chance alone.
Type I error (false positive)
Probability of rejecting the null hypothesis although it is true
Scientific method in action
ask a question, integrate and synthesize info, establish hypothesis, articulate predictions, test, collect and organize data, analyze, interpret, communicate findings
One-sample t-test
Statistical test comparing the mean of a single sample to a known value or mean
Dependent variable
Variable whose value depends on another variable
Independent variable
Variable that stands alone and is not changed by the other variables you are trying to measure
p-value
Probability of obtaining test results at least as extreme as the results observed during the test, assuming that the null hypothesis is correct
Critical value (alpha)
The threshold value used to determine whether the null hypothesis is rejected
Type II error
Probability of not rejecting the null hypothesis although it is false
Scientific hypothesis
A proposed explanation for a phenomenon based on observations and scientific knowledge
Statistical hypothesis
A statement about the relationship between two or more variables in a population
Null hypothesis
A general statement that there is no relationship between two measured phenomena
Alternative hypothesis
A hypothesis that states there is a significant difference or relationship between two variables
One-tailed t-test
A statistical test in which the critical area of a distribution is one-sided
Two-tailed t-test
A statistical test in which the critical area of a distribution is two-sided and tests for differences in both directions
Dependent vs. Independent variable
Dependent variable changes in response to the independent variable, which is not influenced by other variables
t-statistic
A measure that quantifies the difference between the sample mean and the null hypothesis mean in terms of the sample standard deviation
Variance
A measure of the dispersion of a set of data points around their mean value
Standard deviation
A measure of the amount of variation or dispersion of a set of values
experimental design components
randomization, control, and replication
a
when a = 0.05 there is a 5% chance of rejecting a true null hypothesis
level of significance
the max probability of committing a type 1 error and is symbolized by a
d = 1-B
power of the test statistic
