Podcast
Questions and Answers
Two dice are rolled. What is the probability of rolling a sum of 5?
Two dice are rolled. What is the probability of rolling a sum of 5?
- 1/36
- 1/9 (correct)
- 1/12
- 1/6
What is the probability of not rolling a 5 or 6 on a standard six-sided die?
What is the probability of not rolling a 5 or 6 on a standard six-sided die?
- 1/6
- 5/6
- 1/3
- 2/3 (correct)
A coin is tossed 5 times, and each time it lands on heads. According to the gambler's fallacy, what is most likely to happen on the next toss?
A coin is tossed 5 times, and each time it lands on heads. According to the gambler's fallacy, what is most likely to happen on the next toss?
- The probability of tossing tails is higher than heads on the next toss.
- The coin is biased, so heads is still more likely.
- The probability of tossing heads or tails is still 50/50. (correct)
- The probability of tossing heads is higher than tails on the next toss.
Which of the of the following best describes Gambler's Fallacy?
Which of the of the following best describes Gambler's Fallacy?
Which cognitive bias leads to an inaccurate judgment due to overvaluing a recent event or information?
Which cognitive bias leads to an inaccurate judgment due to overvaluing a recent event or information?
In empirical probability determination, why is it important to analyze probabilities within their specific context?
In empirical probability determination, why is it important to analyze probabilities within their specific context?
In an archaeological survey, 15 test pits are dug in a lowland area and 5 contain artifacts, while 10 test pits are dug in a highland area and 6 contain artifacts. What is the probability of finding archaeological materials in a test pit in the highland area?
In an archaeological survey, 15 test pits are dug in a lowland area and 5 contain artifacts, while 10 test pits are dug in a highland area and 6 contain artifacts. What is the probability of finding archaeological materials in a test pit in the highland area?
What does empirical determination of probability involve when compared to calculating probability with known finite spaces?
What does empirical determination of probability involve when compared to calculating probability with known finite spaces?
A researcher is evaluating the effectiveness of a new drug. According to probability theory, what does a p-value of 0.01 (1%) indicate regarding the likelihood of the observed results if the drug has no effect?
A researcher is evaluating the effectiveness of a new drug. According to probability theory, what does a p-value of 0.01 (1%) indicate regarding the likelihood of the observed results if the drug has no effect?
Which of the following statements best describes the Law of Large Numbers?
Which of the following statements best describes the Law of Large Numbers?
A standard six-sided die is rolled twice. What finite probability space represents all the possible outcomes of this experiment?
A standard six-sided die is rolled twice. What finite probability space represents all the possible outcomes of this experiment?
Events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is the probability of either A or B occurring?
Events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is the probability of either A or B occurring?
A bag contains 5 red balls and 3 blue balls. What is the probability of randomly drawing a red ball, followed by a blue ball, assuming the first ball is NOT replaced before drawing the second ball?
A bag contains 5 red balls and 3 blue balls. What is the probability of randomly drawing a red ball, followed by a blue ball, assuming the first ball is NOT replaced before drawing the second ball?
A researcher wants to ensure their findings are highly representative of the population. How should they use the Law of Large Numbers in their study design?
A researcher wants to ensure their findings are highly representative of the population. How should they use the Law of Large Numbers in their study design?
A weather forecast states that the probability of rain tomorrow is 30%. Which of the following interpretations is most accurate?
A weather forecast states that the probability of rain tomorrow is 30%. Which of the following interpretations is most accurate?
What is the probability of rolling a 6 on a standard six-sided die, and then flipping a coin and getting heads?
What is the probability of rolling a 6 on a standard six-sided die, and then flipping a coin and getting heads?
When deciding whether to visualize data, what primary consideration should guide the decision?
When deciding whether to visualize data, what primary consideration should guide the decision?
What is the most important guiding principle when using colors and symbols in a graph?
What is the most important guiding principle when using colors and symbols in a graph?
Before creating a graph, what is the FIRST question one should ask?
Before creating a graph, what is the FIRST question one should ask?
In addition to the graph itself, what accompanying element is essential for effectively communicating the data's meaning?
In addition to the graph itself, what accompanying element is essential for effectively communicating the data's meaning?
What is the primary consideration when choosing the appropriate type of graph for a particular dataset?
What is the primary consideration when choosing the appropriate type of graph for a particular dataset?
When constructing a bar graph, what effect does starting the axis scale at a value significantly higher than zero typically have on the visual representation of the data?
When constructing a bar graph, what effect does starting the axis scale at a value significantly higher than zero typically have on the visual representation of the data?
What is a primary reason why pie charts are generally discouraged for data visualization?
What is a primary reason why pie charts are generally discouraged for data visualization?
A study examines the relationship between two continuous variables, and the researcher wants to visually represent this relationship. Which type of graph would be most appropriate?
A study examines the relationship between two continuous variables, and the researcher wants to visually represent this relationship. Which type of graph would be most appropriate?
In the context of data visualization, what is the main purpose of a box plot?
In the context of data visualization, what is the main purpose of a box plot?
When should a line graph include zero on the Y axis?
When should a line graph include zero on the Y axis?
What critical information should always be included in a figure caption to ensure the graph is properly understood?
What critical information should always be included in a figure caption to ensure the graph is properly understood?
In a histogram displaying class test scores, what does the size of the bins (width of each bar) represent?
In a histogram displaying class test scores, what does the size of the bins (width of each bar) represent?
A researcher is creating a bar graph to compare the average income across three different cities. To avoid misleading interpretations, what is the MOST important guideline they should follow regarding the axis?
A researcher is creating a bar graph to compare the average income across three different cities. To avoid misleading interpretations, what is the MOST important guideline they should follow regarding the axis?
If a study finds a relative risk of 0.7 for developing a certain condition in an exposed group compared to a control group, how should this be interpreted?
If a study finds a relative risk of 0.7 for developing a certain condition in an exposed group compared to a control group, how should this be interpreted?
In a study comparing smokers to non-smokers regarding the development of lung cancer, what does a relative risk of 2.5 imply?
In a study comparing smokers to non-smokers regarding the development of lung cancer, what does a relative risk of 2.5 imply?
In a study assessing the impact of a new medication on disease incidence, the absolute risk in the treatment group is 5% and in the control group is 8%. What does this indicate about the medication's effect?
In a study assessing the impact of a new medication on disease incidence, the absolute risk in the treatment group is 5% and in the control group is 8%. What does this indicate about the medication's effect?
What does a relative risk of 1.0 suggest regarding the difference in risk between two groups?
What does a relative risk of 1.0 suggest regarding the difference in risk between two groups?
If the absolute risk of developing a disease over a 5-year period is 10%, what does this metric primarily describe?
If the absolute risk of developing a disease over a 5-year period is 10%, what does this metric primarily describe?
Suppose the absolute risk of a certain event is 20% in group A and 10% in group B. Which calculation would determine the relative risk?
Suppose the absolute risk of a certain event is 20% in group A and 10% in group B. Which calculation would determine the relative risk?
In comparing the risks between two groups, what key piece of information does relative risk provide that absolute risk does not?
In comparing the risks between two groups, what key piece of information does relative risk provide that absolute risk does not?
If the relative risk of developing a condition for an exposed group is 1.0, and the absolute risk in the unexposed group is known to be 5%, what is the absolute risk in the exposed group?
If the relative risk of developing a condition for an exposed group is 1.0, and the absolute risk in the unexposed group is known to be 5%, what is the absolute risk in the exposed group?
In the context of Null Hypothesis Significance Testing (NHST), what is the primary purpose of setting a significance threshold (e.g., p < 0.05)?
In the context of Null Hypothesis Significance Testing (NHST), what is the primary purpose of setting a significance threshold (e.g., p < 0.05)?
A researcher conducts a study and obtains a p-value of 0.03. Assuming a significance level of α = 0.05, what is the correct interpretation of this result?
A researcher conducts a study and obtains a p-value of 0.03. Assuming a significance level of α = 0.05, what is the correct interpretation of this result?
What is the fundamental question that Null Hypothesis Significance Testing (NHST) aims to address?
What is the fundamental question that Null Hypothesis Significance Testing (NHST) aims to address?
In hypothesis testing, what does failing to reject the null hypothesis imply?
In hypothesis testing, what does failing to reject the null hypothesis imply?
A researcher sets their significance level (alpha) to 0.01 instead of the conventional 0.05. What is the consequence of this choice?
A researcher sets their significance level (alpha) to 0.01 instead of the conventional 0.05. What is the consequence of this choice?
A dataset contains the following values: 5, 7, 7, 9, 11, 13. Which of the following statements is true regarding the mean and median of this dataset?
A dataset contains the following values: 5, 7, 7, 9, 11, 13. Which of the following statements is true regarding the mean and median of this dataset?
In a dataset with several extreme outliers, which measure of central tendency would be the MOST reliable indicator of the 'typical' value?
In a dataset with several extreme outliers, which measure of central tendency would be the MOST reliable indicator of the 'typical' value?
A researcher is analyzing income data for a city and discovers that the distribution is heavily skewed to the right. Which measure of central tendency would BEST represent the 'center' of the income distribution?
A researcher is analyzing income data for a city and discovers that the distribution is heavily skewed to the right. Which measure of central tendency would BEST represent the 'center' of the income distribution?
Which of the following is the MOST accurate definition of 'mode'?
Which of the following is the MOST accurate definition of 'mode'?
A real estate company wants to determine the 'typical' home price in a neighborhood. They have data on the prices of all homes sold in the last year, but the dataset includes a few multi-million dollar mansions. Which measure of central tendency would provide the MOST representative value for a typical home in this scenario?
A real estate company wants to determine the 'typical' home price in a neighborhood. They have data on the prices of all homes sold in the last year, but the dataset includes a few multi-million dollar mansions. Which measure of central tendency would provide the MOST representative value for a typical home in this scenario?
What is a key characteristic of an asymmetrical distribution?
What is a key characteristic of an asymmetrical distribution?
Why is the mode typically less useful for continuous data compared to discrete data?
Why is the mode typically less useful for continuous data compared to discrete data?
Which measure of dispersion is most sensitive to extreme values in a dataset?
Which measure of dispersion is most sensitive to extreme values in a dataset?
What does the interquartile range (IQR) primarily describe?
What does the interquartile range (IQR) primarily describe?
What is the primary reason for squaring the deviations from the mean when calculating variance?
What is the primary reason for squaring the deviations from the mean when calculating variance?
If the variance of a dataset is 25, what is the standard deviation?
If the variance of a dataset is 25, what is the standard deviation?
Why is the standard deviation a more intuitive measure of dispersion than variance?
Why is the standard deviation a more intuitive measure of dispersion than variance?
Under what circumstances is the coefficient of variation (CV) most useful?
Under what circumstances is the coefficient of variation (CV) most useful?
Which of the following measures is least affected by outliers in a dataset?
Which of the following measures is least affected by outliers in a dataset?
A researcher finds that the standard deviation of plant heights in a sample is 5 cm. However, the researcher wants to compare this variability to another sample where the average height is significantly different. What would be the most appropriate measure to use?
A researcher finds that the standard deviation of plant heights in a sample is 5 cm. However, the researcher wants to compare this variability to another sample where the average height is significantly different. What would be the most appropriate measure to use?
In statistical analysis, how does the term 'significant' differ from its everyday usage?
In statistical analysis, how does the term 'significant' differ from its everyday usage?
Which statistical measure is most commonly used to determine statistical significance?
Which statistical measure is most commonly used to determine statistical significance?
A researcher obtains a statistically significant result (p < 0.05) in a study. What is the most accurate interpretation of this finding?
A researcher obtains a statistically significant result (p < 0.05) in a study. What is the most accurate interpretation of this finding?
What is a key limitation of relying solely on statistical significance (p-value) in research?
What is a key limitation of relying solely on statistical significance (p-value) in research?
In the context of statistical hypothesis testing, what does a higher p-value (e.g., p = 0.40) suggest?
In the context of statistical hypothesis testing, what does a higher p-value (e.g., p = 0.40) suggest?
When using graphs for data analysis, which of the following is a primary purpose during the analysis phase?
When using graphs for data analysis, which of the following is a primary purpose during the analysis phase?
A researcher notices extreme values in their dataset. What should be their initial consideration regarding these outliers?
A researcher notices extreme values in their dataset. What should be their initial consideration regarding these outliers?
In which scenario is a bar graph most appropriate?
In which scenario is a bar graph most appropriate?
When should a line graph be used?
When should a line graph be used?
A researcher wants to illustrate how the mean and variability of a continuous variable change over time. Which type of graph would be most suitable?
A researcher wants to illustrate how the mean and variability of a continuous variable change over time. Which type of graph would be most suitable?
For what purpose is a box plot most effectively used?
For what purpose is a box plot most effectively used?
A researcher suspects that their continuous dataset contains subgroups. Which type of graph is most suitable for visually identifying such subgroups?
A researcher suspects that their continuous dataset contains subgroups. Which type of graph is most suitable for visually identifying such subgroups?
A company wants to present its quarterly profits over the last 5 years. The goal is to highlight both the average profit for each quarter and the range of profit values observed. Which graph would be most effective?
A company wants to present its quarterly profits over the last 5 years. The goal is to highlight both the average profit for each quarter and the range of profit values observed. Which graph would be most effective?
A researcher is studying the average height of students at a university. They collect multiple random samples and calculate the mean height for each sample. What does the distribution of these sample means represent?
A researcher is studying the average height of students at a university. They collect multiple random samples and calculate the mean height for each sample. What does the distribution of these sample means represent?
In what way does increasing the sample size affect the properties of the sampling distribution of means?
In what way does increasing the sample size affect the properties of the sampling distribution of means?
A researcher wants to estimate a population parameter with a high level of confidence. How does the choice of confidence level affect the width of the confidence interval derived from the sampling distribution?
A researcher wants to estimate a population parameter with a high level of confidence. How does the choice of confidence level affect the width of the confidence interval derived from the sampling distribution?
Why is it important to examine the shape of a sample distribution when making inferences about a population?
Why is it important to examine the shape of a sample distribution when making inferences about a population?
What is the central limit theorem's (CLT) significance when analyzing sample distributions?
What is the central limit theorem's (CLT) significance when analyzing sample distributions?
Why is visual inspection (histograms, density plots, Q-Q plots) considered important when assessing the normality of a sample?
Why is visual inspection (histograms, density plots, Q-Q plots) considered important when assessing the normality of a sample?
Even though perfectly normal samples are rare in real-life data, why is assessing normality still a crucial step in statistical analysis?
Even though perfectly normal samples are rare in real-life data, why is assessing normality still a crucial step in statistical analysis?
In the context of Q-Q plots, what does it indicate when the data points deviate noticeably from the straight line?
In the context of Q-Q plots, what does it indicate when the data points deviate noticeably from the straight line?
How should a researcher address a non-normal sample?
How should a researcher address a non-normal sample?
What characteristic of a distribution does kurtosis primarily describe?
What characteristic of a distribution does kurtosis primarily describe?
In an asymmetrical distribution, which of the following statements is generally true regarding the mean, median, and mode?
In an asymmetrical distribution, which of the following statements is generally true regarding the mean, median, and mode?
When can sample statistics from an asymmetrical and kurtotic distribution be considered reliable estimators of population parameters?
When can sample statistics from an asymmetrical and kurtotic distribution be considered reliable estimators of population parameters?
Why are theoretical distributions useful in inferential statistics?
Why are theoretical distributions useful in inferential statistics?
Which characteristic is NOT a property of a normal distribution?
Which characteristic is NOT a property of a normal distribution?
What does the area under a curve in probability distribution directly represent?
What does the area under a curve in probability distribution directly represent?
In a normal distribution, if two distributions, A & C, have little area of curve overlap, what is implied about drawing a value from both distributions?
In a normal distribution, if two distributions, A & C, have little area of curve overlap, what is implied about drawing a value from both distributions?
What is the primary purpose of calculating Z-scores?
What is the primary purpose of calculating Z-scores?
In statistical terms, what do location and dispersion statistics primarily define about a normal distribution?
In statistical terms, what do location and dispersion statistics primarily define about a normal distribution?
In R programming, what is the primary distinction between an atomic vector and a matrix?
In R programming, what is the primary distinction between an atomic vector and a matrix?
You are writing an R script and want to add explanatory notes within the code. What is the MOST effective way to incorporate these annotations?
You are writing an R script and want to add explanatory notes within the code. What is the MOST effective way to incorporate these annotations?
Which of the following statements accurately describes the relationship between R and RStudio?
Which of the following statements accurately describes the relationship between R and RStudio?
Consider the following R code: > seq(from = 1, to = 10, by = 1). What does the > symbol typically indicate in this context?
Consider the following R code: > seq(from = 1, to = 10, by = 1). What does the > symbol typically indicate in this context?
In R, you need to store a dataset containing customer information, including names (character), ages (numeric), and whether they are subscribed to a service (logical). Which data structure is most appropriate?
In R, you need to store a dataset containing customer information, including names (character), ages (numeric), and whether they are subscribed to a service (logical). Which data structure is most appropriate?
Which scenario exemplifies the use of descriptive statistics?
Which scenario exemplifies the use of descriptive statistics?
What is the primary purpose of inferential statistics?
What is the primary purpose of inferential statistics?
A researcher aims to study the political opinions of all adults in Canada. Due to the impracticality of surveying every adult, they collect data from a smaller group. What is this smaller group called in statistical terms?
A researcher aims to study the political opinions of all adults in Canada. Due to the impracticality of surveying every adult, they collect data from a smaller group. What is this smaller group called in statistical terms?
In statistical analysis, what term refers to the entire group of individuals, objects, or events that are of interest in a study?
In statistical analysis, what term refers to the entire group of individuals, objects, or events that are of interest in a study?
A researcher is studying the average height of trees in a forest. They only measure trees along easily accessible paths, assuming these are representative of the entire forest. What type of issue is most likely to arise?
A researcher is studying the average height of trees in a forest. They only measure trees along easily accessible paths, assuming these are representative of the entire forest. What type of issue is most likely to arise?
If every member of a population does NOT have an equal chance of being selected for a study, what is the likely result?
If every member of a population does NOT have an equal chance of being selected for a study, what is the likely result?
Which scenario best illustrates the potential misuse of statistics?
Which scenario best illustrates the potential misuse of statistics?
What is a crucial limitation to keep in mind when using statistical tools for data analysis?
What is a crucial limitation to keep in mind when using statistical tools for data analysis?
A researcher is studying the effect of exercise on heart rate. They measure participants' heart rates before and after a workout. Which of the following BEST describes 'heart rate' in this study?
A researcher is studying the effect of exercise on heart rate. They measure participants' heart rates before and after a workout. Which of the following BEST describes 'heart rate' in this study?
Which of the following scenarios BEST exemplifies the use of ordinal data?
Which of the following scenarios BEST exemplifies the use of ordinal data?
A scientist is collecting data on the mass of different rock samples. Which scale of measurement is MOST appropriate for recording this data?
A scientist is collecting data on the mass of different rock samples. Which scale of measurement is MOST appropriate for recording this data?
A researcher is investigating the effectiveness of a new fertilizer on plant growth. They carefully control the experimental conditions, use precise measurement tools, and define clear criteria for assessing plant health. What aspect of data quality is the researcher primarily addressing through these actions?
A researcher is investigating the effectiveness of a new fertilizer on plant growth. They carefully control the experimental conditions, use precise measurement tools, and define clear criteria for assessing plant health. What aspect of data quality is the researcher primarily addressing through these actions?
Which of the following data types would permit the broadest range of mathematical analyses, including calculations of ratios and meaningful comparisons of absolute differences?
Which of the following data types would permit the broadest range of mathematical analyses, including calculations of ratios and meaningful comparisons of absolute differences?
Flashcards
Probability
Probability
The likelihood of an event occurring in a random experiment.
Probability Value (P)
Probability Value (P)
A value between 0 and 1 indicating the likelihood of an event.
Law of Large Numbers
Law of Large Numbers
As you repeat an experiment, the observed probability gets closer to the true probability.
Finite Probability Space
Finite Probability Space
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Independent and Mutually Exclusive Events
Independent and Mutually Exclusive Events
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Probability of Mutually Exclusive Events
Probability of Mutually Exclusive Events
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Probability of 'NOT' an Event
Probability of 'NOT' an Event
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How to calculate the probability of NOT rolling a 1?
How to calculate the probability of NOT rolling a 1?
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P(Not)
P(Not)
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Probability of A and B
Probability of A and B
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Independent Events
Independent Events
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Gambler's Fallacy
Gambler's Fallacy
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Recency Bias
Recency Bias
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Empirically Estimated Probability
Empirically Estimated Probability
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Context-Dependent Probabilities
Context-Dependent Probabilities
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Goal of a Good Graph
Goal of a Good Graph
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Should Data Be Visualized?
Should Data Be Visualized?
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How Many Graphs is Too Many?
How Many Graphs is Too Many?
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Effective Figure Captions
Effective Figure Captions
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Effective Use of Colors and Symbols
Effective Use of Colors and Symbols
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Box Plot
Box Plot
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Scatter Plot
Scatter Plot
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Line Graph
Line Graph
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Histogram
Histogram
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Bar Graph Axis Scaling
Bar Graph Axis Scaling
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Good Figure Captioning
Good Figure Captioning
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Pie Chart Weakness
Pie Chart Weakness
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Line Graph Axis
Line Graph Axis
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Absolute Risk
Absolute Risk
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Relative Risk
Relative Risk
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Relative Risk Use
Relative Risk Use
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Absolute Risk Calculation
Absolute Risk Calculation
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Relative Risk Calculation
Relative Risk Calculation
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Relative Risk ~1
Relative Risk ~1
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Relative Risk > 1
Relative Risk > 1
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Relative Risk < 1
Relative Risk < 1
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Null-Hypothesis Significance Testing
Null-Hypothesis Significance Testing
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Goal of NHST
Goal of NHST
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Thresholds of Acceptance in NHST
Thresholds of Acceptance in NHST
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P-Value
P-Value
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Interesting Patterns or Random Chance?
Interesting Patterns or Random Chance?
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Examining Samples
Examining Samples
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Sample Statistics
Sample Statistics
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Frequency Distribution
Frequency Distribution
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Central Tendency
Central Tendency
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N
N
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Asymmetrical Distribution
Asymmetrical Distribution
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Mode (Mo)
Mode (Mo)
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Range
Range
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Interquartile Range
Interquartile Range
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Quartile
Quartile
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Variance (s²)
Variance (s²)
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Standard Deviation (s, SD)
Standard Deviation (s, SD)
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Coefficient of Variation (CV)
Coefficient of Variation (CV)
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Sample Variance
Sample Variance
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Mode for Discrete Data
Mode for Discrete Data
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Statistical Significance
Statistical Significance
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Significance in Statistics
Significance in Statistics
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Statistical Significance Testing
Statistical Significance Testing
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Goal of Statistical Significance Testing
Goal of Statistical Significance Testing
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Graphs (Plots, Charts)
Graphs (Plots, Charts)
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Why use graphs before analysis?
Why use graphs before analysis?
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Spotting Outliers
Spotting Outliers
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Bar Graph
Bar Graph
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Categorical Data Comparison
Categorical Data Comparison
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Means Plot
Means Plot
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Distribution Shape - Why?
Distribution Shape - Why?
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Asymmetrical & Kurtotic Distributions
Asymmetrical & Kurtotic Distributions
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Theoretical Distribution
Theoretical Distribution
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Inferential Statistics
Inferential Statistics
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Normal Distribution Properties
Normal Distribution Properties
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Normal Distribution Name
Normal Distribution Name
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Area Under the Curve
Area Under the Curve
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Z-Score
Z-Score
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Standardized Sample
Standardized Sample
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Q-Q Plot
Q-Q Plot
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Skewed Distributions
Skewed Distributions
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Fat-tailed Distribution
Fat-tailed Distribution
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Parametric Tests
Parametric Tests
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What is R?
What is R?
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What is RStudio?
What is RStudio?
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What is a Function in R?
What is a Function in R?
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What are Arguments in R?
What are Arguments in R?
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What is an Object in R?
What is an Object in R?
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Statistics
Statistics
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Descriptive Statistics
Descriptive Statistics
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Statistical Population
Statistical Population
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Sample
Sample
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Bias
Bias
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Descriptive Role
Descriptive Role
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Inferential Role
Inferential Role
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Data
Data
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Datum/Data Point
Datum/Data Point
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Variable
Variable
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Discrete Data
Discrete Data
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Ordinal Data
Ordinal Data
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Study Notes
- 5% of the time, we will incorrectly conclude populations differ (or variables are associated), when they actually do not
- Reduce A, reduce likelihood of Type I error.
- Type II error: Is defined as failing reject HO when it is actually fals
- thus fail to detect a true difference
- in this case, a true difference between data populations fails to be measured, as a relationship has failed to be displayed by the samples
- Note: in type II data, not much can inferred, we can only infer from available data to hand
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Description
Explore probability's role in statistics, indicating the likelihood of sample patterns reflecting population reality. Learn about outcome probability, statistical notation, and the Law of Large Numbers. Understand how researchers determine event likelihood and manage uncertainty.
