Chapter 8: Hypothesis Testing Flashcards
Define hypothesis:
A: A concrete and proven statement that accurately reflects the true value of a population parameter, providing a definitive answer to a research question.
B: A prediction. For example, we don’t know the true value of the population mean, so we replace its unknown value with a hypothesis. We then use the sample mean (an estimate) to infer the population mean (a parameter).
C: A random guess or assumption made without any basis or prior information, often used in research to see if the data supports this arbitrary idea.
B: A prediction. For example, we don’t know the true value of the population mean, so we replace its unknown value with a hypothesis. We then use the sample mean (an estimate) to infer the population mean (a parameter).
To test a hypothesis we can:
> Look at the p-value and confidence interval in order to refute/reject or accept/support a hypothesis
Define “specify a hypothesis:”
A: Creating a statement that is deliberately vague and ambiguous, allowing for various interpretations to see which one fits the data best.
B: Make a prediction that provides a meaningful value for the unknown population mean.
C: Choosing a random value for the population mean without considering any relevance or connection to the research question, as the goal is merely to generate an arbitrary prediction.
B: Make a prediction that provides a meaningful value for the unknown population mean.
True or false: 95% of all samples we could work with will have means that fall within approximately ± 2 standard errors (± the margin of error) of the true population mean.
A: True
B: False
False: It’s not 3, it’s 1.96 👇🏽
95% of all samples we could work with will have means that fall within approximately ± 1.96 standard errors (± the margin of error) of the true population mean.
True or false: If we use a normal distribution, the critical
value is 1.96. If we use a t distribution, the critical value depends on the sample size.
A: True
B: False
A: True
> And we calculate a t distribution critical value in Jamovi
What is the formula for Margin of Error if we’re using a NORMAL distribution:
A: 1.96 x critical value
B: 1.96 x sample standard deviation
C: 1.96 x standard error
C: 1.96 x standard error
> Answer is in standard error units
What are “Common” Estimates:
A: Estimates that fall within the margin of error of the hypothesized population mean are “common” if the hypothesis is true. This kind of estimate (sample mean) supports our hypothesis.
B: Values that are significantly different from the hypothesized population mean, indicating a more accurate representation of the true parameter.
C: Those that consistently fall outside the margin of error, providing stronger evidence against the hypothesis and suggesting a need for revision.
A: Estimates that fall within the margin of error of the hypothesized population mean are “common” if the hypothesis is true. This kind of estimate (sample mean) supports our hypothesis.
What does it mean if the estimates are “similar” to the hypothesis?
A: It means there is a lack of reliability in the data, as the margin of error is too wide, making the estimates inconclusive.
B: It suggests a failure to gather diverse data, and the results are biased in favor of the hypothesis, potentially overlooking important variations in the population.
C: It means the estimates fall within the margin of error and the sample means support the hypothesis
C: It means the estimates fall within the margin of error and the sample means support the hypothesis
> This is the same for both normal distributions and t distributions (C.V. x standard error)
> PUT THIS ON YOUR CHEAT SHEET!!! Similar = likely = inside margin of error/ t distribution = estimates support null hypothesis = non-significant = fail to reject the hypothesis = plausible that the null hypothesis is true = p > .05
What does it mean if the estimates are “different” from the hypothesis?
A: It means it falls outside of the margin of error and does not support your hypothesis. It means your sample mean refutes your hypothesis.
B: It means there was an error in the data collection process, and the results should be discarded as outliers.
C: It implies a lack of statistical significance, and the hypothesis should be revised to better align with the observed data for more accurate conclusions.
A: It means it falls outside of the margin of error and does not support your hypothesis. It is unlikely and means your sample means refute your hypothesis.
> Estimates outside the margin of error are unlikely (i.e., occur in less than 5% of all samples we could work with) if the hypothesis is true. This kind of estimate (sample mean) REFUTES our hypothesis.
> This is the same for both normal distributions and t distributions (C.V. x standard error)
> PUT THIS ON YOUR CHEAT SHEET!!! Different = unlikely = outside margin of error/ t distribution = estimates refute null hypothesis = statistically significant = reject the null hypothesis =
p < .05
The critical value is not always 1.96. When the sample size is larger, the critical value is _____ 1.96
A. Closer to
B. Further away from
A. Closer to
Fill in the Significance Testing Flowchart:
A: Step 1: Compare the sample estimate to the hypothesis.
Step 2: Consult an expert opinion: Seek the opinion of an expert in the field to confirm the validity of the hypothesis based on their experience.
Step 3: Accept or reject the hypothesis based on personal judgment: Use personal judgment to decide whether the hypothesis is valid without relying on statistical analysis.
Step 4: Dismiss alternative explanations: Reject alternative explanations for the observed data, insisting that the hypothesis is the only valid interpretation.
B: Step 1 - Specify hypotheses: Propose a value for the
true population parameter.
Step 2 - Design study and collect sample data: Sample data will be used to evaluate the hypothesis.
Step 3: Assess the similarity of data and hypothesis: Compare sample estimate to hypothesis.
Step 4: Make a judgment about the hypothesis: The estimate is either similar to or different from the hypothesis
C: Step 1: Compare the sample estimate to the hypothesis.
Step 2: Choose the hypothesis that seems more plausible: Select the hypothesis that appears more reasonable based on subjective judgment rather than statistical evidence.
Step 3: Disregard statistical significance: Ignore statistical tests and significance levels, and accept the hypothesis that aligns with preconceived notions or expectations.
Step 4: Avoid peer review: Skip the peer-review process and immediately accept the hypothesis, disregarding external input and critique.
B: Step 1 - Specify hypotheses: Propose a value for the
true population parameter.
Step 2 - Design study and collect sample data: Sample data will be used to evaluate the hypothesis.
Step 3: Assess the similarity of data and hypothesis: Compare sample estimate to hypothesis.
Step 4: Make a judgment about the hypothesis: The estimate is either similar to or different from the hypothesis
If you determine that the results are “non-significant” what does it mean?
A: It indicates a flaw in the research methodology, and the data should be dismissed as unreliable. The hypothesis is likely incorrect due to these methodological issues.
B: It suggests that the study lacked statistical power, and repeating the experiment with a larger sample size would likely yield significant results, confirming the hypothesis.
C: The hypothesized population could have produced the data
C: The hypothesized population could have produced the data
> You fail to reject the hypothesis
If you determine that the results are “statistically significant” what does it mean?
A: It suggests a flaw in the experimental design, and further investigation is needed to identify and correct the sources of bias. The hypothesis may be valid with adjustments.
B: The hypothesized population is unlikely to have produced the data
C: It indicates that the study may have unintentionally manipulated the data, and the findings should be considered dubious. The hypothesis might be accurate, but caution is warranted due to potential biases.
B: The hypothesized population is unlikely to have produced the data
> You reject the hypothesis
What is an “alternate hypothesis?”
A: The alternate (alternative) hypothesis is a prediction that often aligns with the idea that “something is happening”.
B: The alternate hypothesis is a statement suggesting that the observed results are due to chance or random fluctuations in the data, rather than indicating a real effect.
C: An alternate hypothesis is a conjecture proposing that the experimental conditions have no impact on the outcome, and any observed effects are merely coincidental or irrelevant to the study
A: The alternate (alternative) hypothesis about the population mean that reflects the researcher’s interests or beliefs. A prediction that often aligns with the idea that “something is happening”.
> Ha = alternate/alternative hypothesis
What is a One-Tailed Alternate Hypotheses?
A: Used when researchers anticipate ambiguous or unpredictable outcomes, allowing for the possibility of both an increase and a decrease in the observed results.
B: Researchers make predictions about the expected results in both directions, assuming that the outcome could either increase or decrease, depending on various factors.
C: Researchers specify one-tailed hypotheses when the expected results can only go in one direction (an increase or a decrease, not both)
C: An alternate hypothesis where the researcher expects or predicts an increase or a decrease, but not both. Researchers specify one-tailed hypotheses when the expected results can only go in one direction (an increase or a decrease, not both).
> Example: If the study goal is to examine whether people tend to maintain a humorous perspective even in the face of stress or adversity, the alternate hypothesis is that the population mean rating should be greater than “sometimes true.”
I use a one-tailed hypothesis because I expect that the
population mean can be higher than 3 but not lower than 3
Ha : μ > 3
OR: The alternate hypothesis also can be that the population mean rating should be smaller than
“sometimes true.”
Ha : μ < 3
What is a Two-Tailed Alternate Hypotheses?
A: Applied when researchers expect a precise and specific outcome, either an increase or a decrease, and want to cover all possible scenarios.
B: Researchers focus on predicting only one direction of the results, either an increase or a decrease, excluding the possibility of an outcome in the opposite direction.
C: Researchers use two-tailed hypotheses when the results can reasonably go in either direction (scores can increase or decrease).
C: An alternate hypothesis where the researcher expects or predicts that either an increase or a decrease are possible. Researchers use two-tailed hypotheses when the results can reasonably go in either direction (scores can increase or decrease).
> Example: Suppose the study aims to explore whether
people tend to maintain either a humorous perspective or a humorless perspective.
The true mean rating in the population could be greater than or less than “sometimes true.”
Ha : μ > 3 or μ < 3 OR: Ha : μ ≠ 3
> While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.
What is a Null Hypothesis?
A: The null hypothesis is a prediction that aligns with the researcher’s expectations and supports the idea that a significant effect or change is occurring in the study.
B: The null hypothesis is a value opposite of what
the researcher expects. A value that often aligns
with the idea that “nothing is happening”
C: In a null hypothesis, researchers propose a value that is in line with their anticipated outcomes, indicating that the experimental conditions are likely to produce a noticeable effect.
B: The null hypothesis about the population mean is a value opposite of what the researcher expects. A value that often aligns with the idea that “nothing is happening.”
> Example: The true population mean rating is “sometimes true.”
H0 : μ = 3
> Our goal is ALWAYS to prove that the null hypothesis is not true. We want to reject the hypothesis!
> The goal of a hypothesis test is to show that the null
hypothesis is probably false.
> The null hypothesis is innocent until proven guilty.
> We also cannot prove the null hypothesis is true (you can NEVER accept the null hypothesis) (perhaps we fail to reject the null hypothesis due to the small sample size). We only can state that the null hypothesis is PLAUSIBLE (remember the alien example she gave in class).
> While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.
What role does the sample mean (estimates) play in hypothesis testing?
A: The sample mean will be used to determine whether the data can refute the null
B: The sample mean serves as an absolute confirmation of the null hypothesis, providing direct evidence that the expected outcome has occurred as predicted.
C: The sample mean acts as an independent measure, separate from the null hypothesis, and is not relevant in assessing the validity of the null hypothesis.
A: The sample mean will be used to determine
whether the data can refute the null
Standard Error Revisited: What is standard error?
A: The standard error is the standard deviation of
estimates from many different random samples
B: The standard error represents the average difference between the estimated value and the true population parameter, providing a measure of accuracy in the data.
C: Standard error is a measure of variability within a single sample, indicating the spread of data points around the sample mean, rather than across multiple random samples.
A: The standard error is the standard deviation of
estimates from many different random samples
