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A veterinarian is comparing weight gain in underweight cats using three different diets (A, B, C). What is the most appropriate null hypothesis for this analysis?
A veterinarian is comparing weight gain in underweight cats using three different diets (A, B, C). What is the most appropriate null hypothesis for this analysis?
- Each diet will produce statistically different weight gains.
- Diet A results in a greater average weight gain than Diets B and C.
- The average weight gain will be different for each individual cat.
- The average weight gain is the same for all cats, regardless of diet. (correct)
In an ANOVA comparing cat diets, the assumption of constant variance is assessed using descriptive statistics. Given the standard deviations for diets A, B, and C are 2.506, 2.983, and 4.690 respectively, which statement best describes the validity of this assumption?
In an ANOVA comparing cat diets, the assumption of constant variance is assessed using descriptive statistics. Given the standard deviations for diets A, B, and C are 2.506, 2.983, and 4.690 respectively, which statement best describes the validity of this assumption?
- The assumption is likely violated because the standard deviation of diet C is almost twice as large as diet A's. (correct)
- The assumption is valid if the means of each group are also similar.
- The assumption is valid because the standard deviations are nearly identical.
- The assumption cannot be assessed using only standard deviations.
A political party uses a bar graph to display election results, exaggerating the y-axis scale. What statistical principle is most directly violated by this visualization technique?
A political party uses a bar graph to display election results, exaggerating the y-axis scale. What statistical principle is most directly violated by this visualization technique?
- Accurate representation of data (correct)
- Regression to the Mean
- Central Limit Theorem
- Principle of Parsimony
A researcher measures the body temperature of 20 Norwegian Lundehund dogs and obtains a mean of 38.5965 degrees Celsius with a standard deviation of 0.2285026. A one-sample t-test is performed to test if the true mean is 38.5 degrees Celsius. Given the t-statistic is 1.8886 and degrees of freedom are 19, what is the most appropriate next step?
A researcher measures the body temperature of 20 Norwegian Lundehund dogs and obtains a mean of 38.5965 degrees Celsius with a standard deviation of 0.2285026. A one-sample t-test is performed to test if the true mean is 38.5 degrees Celsius. Given the t-statistic is 1.8886 and degrees of freedom are 19, what is the most appropriate next step?
Based on the Norwegian Lundehund body temperature data, a 95% confidence interval is calculated. Given the t-value for 19 degrees of freedom at a 95% confidence level is 2.093, which calculation will correctly determine the upper bound of the confidence interval?
Based on the Norwegian Lundehund body temperature data, a 95% confidence interval is calculated. Given the t-value for 19 degrees of freedom at a 95% confidence level is 2.093, which calculation will correctly determine the upper bound of the confidence interval?
A study measures blood pressure in horses before and after administering medication. Which statistical test is most appropriate for analyzing the data?
A study measures blood pressure in horses before and after administering medication. Which statistical test is most appropriate for analyzing the data?
In the horse blood pressure study, if the horses were randomly assigned to different doses of medication (20mg and 40mg), what type of variable is 'medication dose'?
In the horse blood pressure study, if the horses were randomly assigned to different doses of medication (20mg and 40mg), what type of variable is 'medication dose'?
In a study using the National Eye Institute Visual Functioning Questionnaire before and after cataract surgery, why is it appropriate to analyze this data using a paired t-test?
In a study using the National Eye Institute Visual Functioning Questionnaire before and after cataract surgery, why is it appropriate to analyze this data using a paired t-test?
When analyzing data from the National Eye Institute Visual Functioning Questionnaire, given that each individual has two readings (pre- and post-surgery), which assumption of the paired t-test is potentially violated?
When analyzing data from the National Eye Institute Visual Functioning Questionnaire, given that each individual has two readings (pre- and post-surgery), which assumption of the paired t-test is potentially violated?
In the confidence interval equation $x̄ ± k * SE$, which variable is directly influenced by the choice between a 90% and 95% confidence level?
In the confidence interval equation $x̄ ± k * SE$, which variable is directly influenced by the choice between a 90% and 95% confidence level?
Which confidence interval will be wider, a 90% confidence interval or a 95% confidence interval, assuming all other factors remain constant?
Which confidence interval will be wider, a 90% confidence interval or a 95% confidence interval, assuming all other factors remain constant?
When would you use ANOVA/Regression with a categorical variable with three or more levels?
When would you use ANOVA/Regression with a categorical variable with three or more levels?
Select the correct statement regarding p-values and significance levels.
Select the correct statement regarding p-values and significance levels.
What does a 95% confidence interval represent?
What does a 95% confidence interval represent?
In regression analysis, which of the following is NOT a typical assumption that must be satisfied?
In regression analysis, which of the following is NOT a typical assumption that must be satisfied?
A research team is developing a new diabetes medication and measures triglyceride levels in participants. Based on the boxplot in the material, which of the following best describes the distribution of triglyceride levels in the control group?
A research team is developing a new diabetes medication and measures triglyceride levels in participants. Based on the boxplot in the material, which of the following best describes the distribution of triglyceride levels in the control group?
If a one-way ANOVA on the triglyceride data produces a p-value of <0.001, what can be scientifically concluded at the 5% significance level?
If a one-way ANOVA on the triglyceride data produces a p-value of <0.001, what can be scientifically concluded at the 5% significance level?
Consider the monarch caterpillar question. If the monarch caterpillar takes, on average, 35 days from birth to emerge as a butterfly, with a standard deviation of 1 day, approximately what proportion of caterpillars have emerged after 37 days (assuming a normal distribution)?
Consider the monarch caterpillar question. If the monarch caterpillar takes, on average, 35 days from birth to emerge as a butterfly, with a standard deviation of 1 day, approximately what proportion of caterpillars have emerged after 37 days (assuming a normal distribution)?
What type of graph is the "Student Grades" plot?
What type of graph is the "Student Grades" plot?
Which statistical test is most appropriate for comparing the mean Interferon Gamma levels in coffee versus tea drinkers, given the study design, assumptions, and data provided?
Which statistical test is most appropriate for comparing the mean Interferon Gamma levels in coffee versus tea drinkers, given the study design, assumptions, and data provided?
Flashcards
What is the null hypothesis?
What is the null hypothesis?
A statement assumed to be true for the purpose of argument or investigation.
What is the alternative hypothesis?
What is the alternative hypothesis?
Alternative to the null hypothesis; what the researcher wants to prove.
What is a Type I error?
What is a Type I error?
The error of rejecting a true null hypothesis.
What is a Type II error?
What is a Type II error?
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What is the p-value?
What is the p-value?
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What is a confidence interval?
What is a confidence interval?
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What is Standard Error?
What is Standard Error?
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What is a Two Sample t-test?
What is a Two Sample t-test?
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Regression Assumptions
Regression Assumptions
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What is a paired t-test?
What is a paired t-test?
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What is ANOVA?
What is ANOVA?
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Study Notes
- The average weight gain significance can be determined with the use of various diet plans for underweight cats in an animal shelter
Hypothesis Statements
- H₀: µₐ = µв = µc represents the idea that the population mean lean mass gain is consistent across exercise programs A, B, and C
- H₁: Indicates that there is a difference among at least one of the population means
Constant Variance
- Constant variance is achieved as the highest standard deviation (4.69) stays within the constraint of being less than double the lowest standard deviation (2.506)
Misleading Visualizations
- It occurs in visualizations when the presented information implies candidate B got significantly more votes than candidate A
- This is due to the y-axis scaling and bar chart placement
Visualization Improvement
- Adjusting the figure involves setting the y-axis to include zero
- Ensuring similar bar heights accurately reflect the actual data
- While it is acceptable changing the subtitle isn't directly relevant
Test Statistic
- Test statistic value determined with t = (x̄ - μ₀) / (s / √n)
- The values x̄ = 38.5965, μ₀ = 38.5, s = 0.2285026, and n = 20
- The t is approximately 1.89 when calculated by hand
Confidence Interval
- k is derived from a t-distribution
- Degrees of freedom = n-1 = 20-1=19
- Cumulative probability is at 0.975 for a 95% CI
Confidence Interval Interpretation
- Indicating dogs in a confidence interval study vs specifically Norwegian Lundehund dogs in the population is unsuitable
Medication Study Design
- A study on blood pressure of horses that uses two doses utilizes a two-sample independent t-test
- This is due to each horse receiving just one type of medication from the sample
Variables
- Blood pressure is a numerical data type that is continuous
- Medication is a categorical and ordinal data type
Questionnaire Analysis
- Utilizing pre-cataract and post-cataract measurements conducted on the same subject calls for paired-samples analysis
Questionnaire Independence
- A single mean t-test conducted on all the differences between pre and post surgery ensures that any difference is independent
Changes In Confidence Intervals
- The 'k' value will vary across confidence intervals
- A higher cumulative probability results in an increased 'k' value
Interval Width
- Given the larger value of 'k' it is accepted that the 95% confidence interval is indeed higher
ANOVA
- ANOVA is used to compares the means of 3 or more groups when samples are of numerical values and the groups are categorical data
T-Test
- Utilized to comparing means of two groups when the samples are numerical values and the group's data is categorical
- Each has a sole measurement that corresponds to only one group
Paired T-Test
- Utilized for comparing the difference in means in numerical values within 2 categorical groups
- Each subject has recordings for both categories
- OR, can tests the mean of those differences against if it is zero
Regression
- Analyzes relationships between numerical values
- Can compare the mean difference between numerical values across two or more groups
P Value
- Depends on the set significance level
Significance Level
- Should be set before you collect your data
- Data analysis plan should be written prior to data collection
Sample Data
- Equal sample sizes provide ANOVA with robustness against slight deviation from the assumptions, however unequal group sizes may still be analysed
Confidence Interval
- Confidence interval is how the degree of trust the population mean will fall
- Should fall between 2 values
Regression Assumptions
- The observations must be independent
Linearity
- A must have to guarantee a linear relationship between Y and X variables
- Can be seen in a scatterplot of the raw data
Residuals
- Standardized must be centered around 0 while following a normal curve distribution
Constant Variance of Residuals
- A standardization where 95% lies between -2 and 2 with an even spread from left to right
Independence
- Observations must be independent of each other
- Should be no influence of measurement on one another
Location With Control Group
- Median approximates to 144 mg per dL
Spread With Control Group
- A small scale when compared to other groups
- Ranging from approximately 143 to 147.5 mg per dL
Comparing Control Groups
- It is appropriate to compare with an independent/ two-sample t-test
- Or, conduct a regression test with two levels of categorical values
Data Classification
- Group is data is of a categorical, nominal type
- Triglycerides are of a numerical and continuous data type
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