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Questions and Answers
What is the primary purpose of using a statistical model?
What is the primary purpose of using a statistical model?
- To represent real-world phenomena and simplify complex data. (correct)
- To ensure data conforms to pre-established biases.
- To make data more obscure and inaccessible to researchers.
- To complicate data analysis and introduce variability.
Why is assessing the 'fit' of a statistical model important?
Why is assessing the 'fit' of a statistical model important?
- It's irrelevant, as all models are equally valid.
- To ensure the model matches the researcher's preconceived notions.
- To make the model more complex and harder to interpret.
- To determine how well the model represents the observed data. (correct)
In the context of statistical modeling with the equation $Outcome_i = (Model) + error_i$, what does 'error' represent?
In the context of statistical modeling with the equation $Outcome_i = (Model) + error_i$, what does 'error' represent?
- The deviation between the model's prediction and the actual data. (correct)
- The degree to which the model perfectly fits the data.
- A pre-calculated, constant value used for standardization.
- A systematic bias intentionally introduced into the model.
Why is simply adding up the deviations when measuring the fit of a model insufficient?
Why is simply adding up the deviations when measuring the fit of a model insufficient?
What is the primary reason for squaring deviations in the calculation of the Sum of Squared Errors (SS)?
What is the primary reason for squaring deviations in the calculation of the Sum of Squared Errors (SS)?
Why do we use Mean Squared Error instead of Sum of Squared Errors to measure the accuracy of a model?
Why do we use Mean Squared Error instead of Sum of Squared Errors to measure the accuracy of a model?
How does the standard deviation relate to the shape of a distribution?
How does the standard deviation relate to the shape of a distribution?
What is the purpose of calculating the standard error?
What is the purpose of calculating the standard error?
What is a population in the context of statistical modeling?
What is a population in the context of statistical modeling?
What does a 'sample' represent in statistical analysis?
What does a 'sample' represent in statistical analysis?
In hypothesis testing, what is the null hypothesis ($H_0$)?
In hypothesis testing, what is the null hypothesis ($H_0$)?
What is the alternative hypothesis ($H_1$)?
What is the alternative hypothesis ($H_1$)?
What does the term 'degrees of freedom' refer to in statistics?
What does the term 'degrees of freedom' refer to in statistics?
What is the meaning of a 'test statistic'?
What is the meaning of a 'test statistic'?
What is a Type I error in hypothesis testing?
What is a Type I error in hypothesis testing?
A researcher sets their alpha level ($\alpha$) to 0.05. What does this signify?
A researcher sets their alpha level ($\alpha$) to 0.05. What does this signify?
How are confidence intervals useful in statistical analysis?
How are confidence intervals useful in statistical analysis?
Why is effect size important in statistical reporting?
Why is effect size important in statistical reporting?
A study examines sperm release in Japanese Quail, with a true mean of 15 million sperm. A sample mean is found to be 17 million sperm. Which interval estimate would not contain the true value?
A study examines sperm release in Japanese Quail, with a true mean of 15 million sperm. A sample mean is found to be 17 million sperm. Which interval estimate would not contain the true value?
In the context of statistical modeling, selecting a significance level involves:
In the context of statistical modeling, selecting a significance level involves:
What does 'power' refer to in the context of calculating sample size?
What does 'power' refer to in the context of calculating sample size?
If p is less than or equal to alpha, what should you do?
If p is less than or equal to alpha, what should you do?
If p is greater than alpha, what should you do?
If p is greater than alpha, what should you do?
In the research process, what is the role of generating predictions?
In the research process, what is the role of generating predictions?
What are the two types of tests in statistical analysis?
What are the two types of tests in statistical analysis?
Which of the following steps typically comes first in the research process?
Which of the following steps typically comes first in the research process?
Which of the following depicts the relationship between the good fit and the real world in the image?
Which of the following depicts the relationship between the good fit and the real world in the image?
Which of the following depicts the relationship between the moderate fit and the real world in the image?
Which of the following depicts the relationship between the moderate fit and the real world in the image?
In statistics, what does the term "fit" refer to?
In statistics, what does the term "fit" refer to?
In statistics, what is the purpose of statistical models?
In statistics, what is the purpose of statistical models?
What is the first step of the research process?
What is the first step of the research process?
Which of the follow is part of the Conceptual Domain phase?
Which of the follow is part of the Conceptual Domain phase?
Which of the follow is part of the Observable Domain phase?
Which of the follow is part of the Observable Domain phase?
What is the purpose of the mean?
What is the purpose of the mean?
Why is the mean considered a simple statistical model?
Why is the mean considered a simple statistical model?
Why should the final score of a sample be the value that makes the mean = 10?
Why should the final score of a sample be the value that makes the mean = 10?
Complete the missing text: 'reporting _____ and _____.'
Complete the missing text: 'reporting _____ and _____.'
Flashcards
Research Process
Research Process
The process of moving from data to initial observation, identifying variables, generating hypotheses, and then predictions.
Statistical Model
Statistical Model
A statistical model represents a simplification of the real world, attempting to capture essential patterns using mathematical equations.
Population
Population
The collection of units (people, things, etc.) to which we want to generalize a set of findings or a statistical model.
Sample
Sample
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The Mean
The Mean
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Model Fit
Model Fit
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Deviation
Deviation
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Sum of Squared Errors (SS)
Sum of Squared Errors (SS)
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Mean Squared Error
Mean Squared Error
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Degrees of Freedom
Degrees of Freedom
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Standard Error
Standard Error
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Standard Deviation
Standard Deviation
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Confidence Interval
Confidence Interval
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Null Hypothesis (H0)
Null Hypothesis (H0)
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Alternative Hypothesis (H1)
Alternative Hypothesis (H1)
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Test Statistic
Test Statistic
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Type II error
Type II error
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Type I error
Type I error
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Study Notes
- These notes cover key concepts in statistics, from understanding statistical models to hypothesis testing
Aims of Statistics
- Statistical models can be used to help us better understand data
- The 'fit' of a statistical model is important
- It is important to distinguish between models for samples and populations
- There are problems with Null Hypothesis Significance Testing (NHST) and modern approaches can provide solutions
- Confidence intervals and effect sizes are important to report
The Research Process
- Begins with an initial observation or research question
- Identifying variables and theories are part of the conceptual domain
- Hypotheses are generated
- Predictions are generated as part of the observable domain
- Measuring variables and collecting data to test predictions occurs
- Anaylsing data by graphing and fitting a model is essential
Statistical Models
- Statistical models are a simplification of the real world
- Building a useful model involves creating one with a good fit
Populations and Samples
- A population is the collection of units to which findings or a statistical model is to be generalized
- A sample is a smaller collection of units selected from a population, ideally representative
- Samples are used to determine truths about that population
Core Statistical Equation
- The fundamental equation in statistics is: Outcome = Model + Error
Statistical Models
- In statistics, fitting models to data is crucial for representing what's happening in the real world
- The mean is a hypothetical value and a simple statistical mode
The Mean
- The mean is the value from which the squared scores deviate the least
Calculating the 'Fit' of the Model
- The mean is a model for the typical score of your data
- Data doesn’t perfectly represent this model
- One question to address is how well the mean represents reality
Calculating Error
- A deviation, or error, is the difference between the mean and a data point
- Deviance = outcome - model
Total Error
- One can asses deviation by looking at the error between the mean and the data
- Deviations can be positive or negative
- Since the mean is the value from which the scores (squared) deviate least deviations cancel out
Sum of Squared Errors
- We can add the deviations to find out total error
- Deviations cancel each other out
- Square each deviation
- Adding the squared deviations gets the Sum of Squared Errors
Mean Squared Error
- The SS, sum of squares, allows you to measure the accuracy of your model
- The sum of squares does depend on the amount of data collected
- This can be overcome by using the Mean Squared Error
Degrees of Freedom
- Degrees of freedom account for constraints in parameter estimation
- In a sample of n numbers, the "degrees of freedom" are the number of values that are free to vary
- If the mean is fixed, then N-1 scores are still free to vary
- Once N-1 scores are known, the final score is also known
Standard Error
- Standard Deviation (SD) indicates how well the mean represents sample data
- To estimate population parameters, the standard error is needed
Samples and Populations
- Sample: mean and SD describe only the sample from which they were calculated
- Population: mean and SD are intended to describe the entire population (very rare in psychology)
- Sample to population: mean and SD are obtained from a sample, but are used to estimate the mean and SD of the population
Confidence Intervals
- Confidence intervals provide a range within which the true population mean is likely to fall
Types of Hypotheses
- Null Hypothesis (H0): there is no effect, often what we are trying to disprove
- Alternative Hypothesis (H1): AKA the experimental hypothesis
Hypothesis Testing
- Begin with alternative hypothesis
- Propose a "testable prediction"
- State a Null Hypothesis
- Specify a significance level with type 1 error rate
- Pick an appropriate sampling distribution, using power to calculate test statistics
- Randomly sample, and compute test statistic
- Compute the p value, if the probability is less than or equal to the alpha, reject the null
- Alpha is the chances that you will make a type 1 error
Test Statistics
- A statistic where the frequency of particular values is known.
- Observed values can be used to test hypotheses.
- Test statistic = signal/noise = variance explained by the model/variance not explained by the model = effect/error
One- and Two-Tailed Tests
- One-tailed tests assess the probability of the observed result occurring in a single direction
- Two-tailed tests consider the probability of the result occurring in either direction
Type I and Type II Errors
- Type I error: occurs when we believe that there is a genuine effect in our population, when in fact there isn't. (a-level 0.05)
- Type II error: occurs when we believe that there is no effect in the population when, in reality, there is. (ß-level often 0.2)
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