Comparing groups one Flashcards
What is the primary purpose of t-tests in statistical analysis?
To compare the means of two or more groups
What are the three main types of t-tests?
- One-sample t-test
- Independent samples t-test
- Paired samples t-test
What is a one-sample t-test used for?
To compare the sample mean to a known or hypothesized population mean
What are the null and alternative hypotheses for a one-sample t-test?
- Null hypothesis (H₀): µ = µ₀
- Alternative hypothesis (Hₐ): µ ≠ µ₀
In an independent samples t-test, what do the null and alternative hypotheses state?
- Null hypothesis (H₀): µₐ = µᵦ
- Alternative hypothesis (Hₐ): µₐ ≠ µᵦ
What is the paired samples t-test used for?
To compare means within the same group at different times
What are the null and alternative hypotheses for a paired samples t-test?
- Null hypothesis (H₀): µ₁ = µ₂
- Alternative hypothesis (Hₐ): µ₁ ≠ µ₂
What assumption must be met for conducting a t-test?
Data should be normally distributed
True or False: Independent samples t-tests require the groups to have equal variances.
True
What is the purpose of chi-square tests in statistical analysis?
To compare the proportions of categorical variables between groups
What are the three main types of chi-square tests?
- One-Sample Chi-Square Test
- Independent Samples Chi-Square Test
- Paired Samples Chi-Square Test
What is the null hypothesis for a one-sample chi-square test?
The proportion of a single categorical variable matches a known proportion
What is McNemar’s test used for?
To compare proportions in paired or matched samples
What is a key assumption for conducting chi-square tests?
Expected frequencies should be at least 5 in each cell
What is the interpretation if the p-value is less than 0.05 in a t-test?
Reject the null hypothesis
Fill in the blank: The one-sample t-test is used to determine if the mean of a sample differs significantly from a _______.
known population mean
What statistical software can be used to conduct t-tests?
SPSS
What conclusion can be drawn if the p-value is 0.07 in an independent samples t-test?
Fail to reject the null hypothesis
True or False: The paired samples t-test compares means from different groups.
False
What must be true about observations when conducting t-tests?
Observations must be independent
What does it mean if the p-value is less than 0.001 in an independent samples t-test?
There is a significant difference between the means of the two groups
What is an example of a scenario suitable for a one-sample t-test?
Testing if the average weight of individuals in a diet program is different from 66 kg
What is the correct interpretation of a headline stating ‘Half of the people who died were vaccinated’ without context?
It may mislead people about the effectiveness of the vaccine
How do you calculate the death rate for vaccinated individuals?
Divide the number of vaccinated deaths by the total vaccinated individuals
What is the main takeaway from the misinterpretation of COVID-19 vaccine benefits?
Understanding proportions and population sizes is crucial for accurate data interpretation
What test should be used to assess if the proportion of children with high ADHD is higher than 50%?
One-sample χ²-test
What test is appropriate for comparing proportions of boys and girls in ADHD classifications?
Pearson’s χ²-test
What is the alternative hypothesis for a one-sample chi-square test?
The proportion is significantly different from a specified value
What is one requirement for data when conducting a chi-square test?
The data should be categorical
What is the purpose of Pearson’s χ²-Test in the context of ADHD classification?
To compare the proportions of boys and girls in high and low ADHD categories
It checks if there is a significant difference in the distribution of ADHD classifications between boys and girls.
What is the null hypothesis (H₀) for Pearson’s χ²-Test regarding boys and girls in ADHD categories?
The proportions of boys and girls in high/low ADHD categories are the same
What is the alternative hypothesis (H₁) for Pearson’s χ²-Test regarding boys and girls in ADHD categories?
The proportions of boys and girls in high/low ADHD categories are different
What is the McNemar Test used for?
To compare paired data from mothers and fathers reporting on their child’s ADHD classification
In the McNemar Test scenario, how many families did Tom collect data from?
100 families
What does the McNemar Test focus on in the context of ADHD classification reports?
The discordant pairs of reports between mothers and fathers
What is the null hypothesis (H₀) for the McNemar Test regarding mothers’ and fathers’ reports?
There is no difference between mothers’ and fathers’ reports of ADHD classification
What is the alternative hypothesis (H₁) for the McNemar Test regarding mothers’ and fathers’ reports?
There is a difference between mothers’ and fathers’ reports of ADHD classification
What are the key components of the McNemar Test pair data?
Father’s report (High/Low) and Mother’s report (High/Low)
The paired data includes counts of agreements and disagreements in classification.
What is the One-Sample χ²-Test used for?
To compare one proportion to a specific value
Provide an example of a scenario for using the One-Sample χ²-Test.
Testing if more than 50% of children have high ADHD
What is the use case for Pearson’s χ²-Test?
Comparing proportions between two independent groups
Give an example of a scenario for using Pearson’s χ²-Test.
Comparing boys and girls in ADHD classification
What is the use case for the McNemar Test?
Comparing related proportions from paired data
Give an example of a scenario for using the McNemar Test.
Comparing mothers’ and fathers’ reports on the same child
