Hypothesis testing confidence and significance Flashcards
What is a hypothesis in research?
A testable statement explaining beliefs about observed phenomena
Hypotheses can be formulated based on observations of trends or phenomena.
What is the Null Hypothesis (H₀)?
There is no effect or difference
In an exercise example, H₀ would state that the population mean hours of exercise are zero.
What is the Alternative Hypothesis (Hₐ)?
There is an effect or a difference
In an exercise example, Hₐ would suggest that the population mean hours of exercise are not zero.
What happens if we reject the Null Hypothesis (H₀)?
We accept the Alternative Hypothesis (Hₐ)
Rejecting H₀ indicates that the sample data provides sufficient evidence against it.
What is a Type I Error?
False positive; rejecting H₀ when it is true
Example: Concluding smoking affects lung cancer when it doesn’t.
What is a Type II Error?
False negative; failing to reject H₀ when it is false
Example: Not detecting a relationship between smoking and lung cancer when one exists.
What does the term ‘Power’ refer to in hypothesis testing?
The probability of correctly rejecting a false null hypothesis
Researchers typically aim for a power of 0.80.
What factors affect the chances of committing Type I or Type II errors?
- Sample Size
- Effect Size
A larger sample size increases the chance of detecting a true effect.
What is the purpose of Power Analysis?
To determine the necessary sample size or evaluate the statistical power of a test
Power Analysis can be conducted a-priori or a-posteriori.
What are the two types of Power Analysis?
- A-Priori Power Analysis
- A-Posterior Power Analysis
A-Priori is done before the study, while A-Posterior is done after.
What is the role of the p-value in hypothesis testing?
Quantifies the strength of evidence against H₀
If p-value ≤ 0.05, we reject H₀; otherwise, we fail to reject H₀.
Fill in the blank: The Null Hypothesis (H₀) assumes _______.
[no effect or difference]
Fill in the blank: The Alternative Hypothesis (Hₐ) suggests _______.
[there is an effect or a difference]
In hypothesis testing, what does a sample mean falling in the rejection area indicate?
We reject the Null Hypothesis (H₀)
The rejection area is defined by the significance level (e.g., α = 0.05).
What is the significance level commonly set at for hypothesis testing?
0.05 (5%)
This level determines the threshold for rejecting the null hypothesis.
What is the purpose of formulating hypotheses in research?
To establish a basis for testing and making inferences about a population parameter
Hypotheses guide the research direction and statistical testing.
What is the first step in hypothesis testing?
State the Hypotheses
This includes defining both the null and alternative hypotheses.
What type of test is used to evaluate whether the population mean is equal to a specific value?
One-Sample t-Test
This test compares the sample mean against a known population mean.
What does the sample standard deviation reflect in hypothesis testing?
The variability of the sample data
It is crucial for calculating the test statistic.
What is a common method used to perform hypothesis testing in statistical software?
SPSS
SPSS provides various statistical tests, including t-tests and chi-square tests.
What is the significance of the degrees of freedom (df) in hypothesis testing?
It affects the shape of the t-distribution used in tests
Degrees of freedom are typically calculated based on sample size.
What does SPSS provide for descriptive statistics?
Mean, standard deviation, standard error
These statistics help summarize the central tendency and variability of data.
What is the test statistic (t) in the given SPSS output?
-24.106
This value indicates the calculated t-value for the hypothesis test.
What is the degrees of freedom (df) in the SPSS output?
99
Degrees of freedom are a parameter used in various statistical tests.
What conclusion can be drawn if the p-value is <0.001?
Reject H₀
This indicates that the result is statistically significant.
What is the null hypothesis (H₀) in the one-sample chi-square test example?
π = 0.5
This hypothesis states that the observed proportion equals the hypothesized proportion.
What is the alternative hypothesis (Hₐ) in the one-sample chi-square test example?
π ≠ 0.5
This hypothesis states that the observed proportion is different from the hypothesized proportion.
What is the test statistic (χ²) in the one-sample chi-square SPSS output?
40.091
This value reflects the calculated chi-square statistic for the hypothesis test.
What is the p-value in the one-sample chi-square SPSS output?
<0.001
A p-value this low indicates strong evidence against the null hypothesis.
What conclusion can be drawn if p < 0.05 in the chi-square test?
Reject H₀
This indicates that the observed proportion is significantly different from 50%.
What are the structured steps in hypothesis testing in SPSS?
Formulating hypotheses, testing with sample data, interpreting p-values
These steps guide the analysis of scientific data.
What is the significance of understanding statistical tests like the t-test and chi-square test?
Helps draw meaningful conclusions in various fields
Knowledge of these tests is essential for data analysis.
