Podcast
Questions and Answers
Which of the following is NOT a primary source of uncertainty in biological measurements?
Which of the following is NOT a primary source of uncertainty in biological measurements?
- Systematic environmental differences
- Variations of instrumentation
- Reporting errors by the experimenter
- Consistent data entry practices (correct)
What is the primary goal of inferential statistics?
What is the primary goal of inferential statistics?
- Describing precisely what a collection of data shows
- Summarizing a large amount of information in simple form
- Reducing uncertainty and predicting future experimental results (correct)
- Planning current experiments based on existing data
Why is random sampling considered essential?
Why is random sampling considered essential?
- To allow for easier data collection
- To make the sample larger than the population
- To ensure the sample includes every member of the population
- To avoid bias in selecting our sample (correct)
The mean is best described as:
The mean is best described as:
Why is the squaring of deviations important when calculating variance?
Why is the squaring of deviations important when calculating variance?
What does the standard deviation represent?
What does the standard deviation represent?
In statistical terms, what does 'population' refer to?
In statistical terms, what does 'population' refer to?
When might the median be preferred over the mean?
When might the median be preferred over the mean?
Which of the following is the formula for variance?
Which of the following is the formula for variance?
What is the formula for standard error of the mean (SEM)?
What is the formula for standard error of the mean (SEM)?
What is the key characteristic of data that follows a normal distribution?
What is the key characteristic of data that follows a normal distribution?
If a dataset has a normal distribution, approximately what percentage of values fall within one standard deviation of the mean?
If a dataset has a normal distribution, approximately what percentage of values fall within one standard deviation of the mean?
What does the range of a dataset represent?
What does the range of a dataset represent?
What is the purpose of using a histogram?
What is the purpose of using a histogram?
In a relative frequency histogram, what does the area under all bars equal?
In a relative frequency histogram, what does the area under all bars equal?
If data points extend further away from the mean, what does this indicate about the standard deviation?
If data points extend further away from the mean, what does this indicate about the standard deviation?
What type of data is 'hair color' considered?
What type of data is 'hair color' considered?
What is the primary distinction between a sample and a population?
What is the primary distinction between a sample and a population?
What does the 'mode' represent in a dataset?
What does the 'mode' represent in a dataset?
If you have a skewed distribution, which measure of central tendency is generally more appropriate to use than the mean?
If you have a skewed distribution, which measure of central tendency is generally more appropriate to use than the mean?
What is a 'baseline value' in the context of measurements?
What is a 'baseline value' in the context of measurements?
Which of the following is an example of a systematic difference between subjects?
Which of the following is an example of a systematic difference between subjects?
What is the purpose of descriptive statistics?
What is the purpose of descriptive statistics?
What does a larger standard deviation imply regarding the variation in a population?
What does a larger standard deviation imply regarding the variation in a population?
A researcher aims to estimate the average height of all students in a university. Due to the large number of students, they take a random sample of 200 students and measure their heights. In this scenario, what does the 'average height of all students in the university' represent?
A researcher aims to estimate the average height of all students in a university. Due to the large number of students, they take a random sample of 200 students and measure their heights. In this scenario, what does the 'average height of all students in the university' represent?
A dataset concerning the weights of mice contains the following values (in grams): 18.4, 19.0, 19.7, 18.3, 22.7, 20.9, and 26.0. One value is missing. If the mean weight of the set is known to be 21.00g, what is the missing value?
A dataset concerning the weights of mice contains the following values (in grams): 18.4, 19.0, 19.7, 18.3, 22.7, 20.9, and 26.0. One value is missing. If the mean weight of the set is known to be 21.00g, what is the missing value?
Which of the following data types is 'cell diameter' (small, medium, large) an example of?
Which of the following data types is 'cell diameter' (small, medium, large) an example of?
What is the most common method of summarizing data graphically, especially for medium-large sample sizes?
What is the most common method of summarizing data graphically, especially for medium-large sample sizes?
Which of the following formulas is correct for calculating the sample standard deviation?
Which of the following formulas is correct for calculating the sample standard deviation?
Why are samples used instead of studying an entire population?
Why are samples used instead of studying an entire population?
If the range of a dataset is 19 mm, with the smallest value being 64 mm, what is the largest value in the dataset?
If the range of a dataset is 19 mm, with the smallest value being 64 mm, what is the largest value in the dataset?
What is the difference between the population mean ($\mu$) and the sample mean ($\bar{x}$)?
What is the difference between the population mean ($\mu$) and the sample mean ($\bar{x}$)?
In a normal distribution, what percentage of data falls within 2 standard deviations of the mean?
In a normal distribution, what percentage of data falls within 2 standard deviations of the mean?
Consider a sample of male mice weights at 6 weeks: 22.7, 18.4, 19.0, 19.7, 18.3, 22.7, 20.9, 26.0 (in grams). What is the variance of this sample? (Given $\sum(x-\bar{x})^2 = 50.525$ and $\bar{x} = 21.00g$)
Consider a sample of male mice weights at 6 weeks: 22.7, 18.4, 19.0, 19.7, 18.3, 22.7, 20.9, 26.0 (in grams). What is the variance of this sample? (Given $\sum(x-\bar{x})^2 = 50.525$ and $\bar{x} = 21.00g$)
Which of the following describes the characteristics of 'counts' data?
Which of the following describes the characteristics of 'counts' data?
Suppose a study finds that 32% of the population is affected by a certain condition. If the study includes 500 individuals, how many individuals are affected?
Suppose a study finds that 32% of the population is affected by a certain condition. If the study includes 500 individuals, how many individuals are affected?
In a population, 95% of individuals have heights between 150 cm and 190 cm. Assuming the height distribution is approximately normal, within what range would you expect approximately 68% of individuals to fall?
In a population, 95% of individuals have heights between 150 cm and 190 cm. Assuming the height distribution is approximately normal, within what range would you expect approximately 68% of individuals to fall?
Flashcards
Biological Measurement Uncertainty
Biological Measurement Uncertainty
Uncertainty arises from instrumentation, experimenter errors, biological variations (genetic,environmental).
Sources of Error in Experiments
Sources of Error in Experiments
Measurement error, random differences/changes, systematic differences (genetic/environmental, time)
Descriptive Statistics
Descriptive Statistics
Summarizing a large amount of information in simple form.
Inferential Statistics
Inferential Statistics
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Population (Statistics)
Population (Statistics)
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Sample (Statistics)
Sample (Statistics)
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Sampling (Statistics)
Sampling (Statistics)
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Mean
Mean
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Median
Median
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Mode
Mode
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Deviation
Deviation
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Variance (s²)
Variance (s²)
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Standard Deviation (SD or s)
Standard Deviation (SD or s)
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Histogram
Histogram
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Population Mean (μ)
Population Mean (μ)
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Population Variance (σ²)
Population Variance (σ²)
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Population Standard Deviation (σ)
Population Standard Deviation (σ)
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Range
Range
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Unordered Categories
Unordered Categories
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Ordered Categories
Ordered Categories
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Binary Categories
Binary Categories
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Counts Data
Counts Data
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Measurements Data
Measurements Data
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Proportion (Statistics)
Proportion (Statistics)
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Percentage
Percentage
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Random Differences
Random Differences
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Systematic Differences
Systematic Differences
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Study Notes
- All biological measurements have uncertainty due to variability in instrumentation, experimenters, and biological factors (genetic and environmental differences).
Main Sources of Error
- Measurement error can occur
- Random differences exist between subjects
- Random changes can occur between repeated measurements on the same subject
- Systematic differences can arise between subjects (genetic or environmental)
- Systematic differences can occur over time
Summarizing Experimental Results
- Description (Descriptive Statistics) summarizes data in a simple form
- Inference (Inferential Statistics) reduces uncertainty by explaining what data shows and predicts future experiment results
Statistical Concepts
- A population consists of all subjects of interest, and is often too large to study directly
- A sample involves observing a subset of the population
- Sampling involves measuring some individuals and inferring population values
- Samples should be representative and randomly selected to avoid bias when summarizing data
Averages
- Mean is calculated by the sum of values / number of observations and is the most common average
- It is also called the arithmetic mean
- Median is the middle value in an ordered dataset, used instead of mean in some cases
- Mode is the most frequent value in a dataset, and it can be the peak of the frequency distribution
Variance and Standard Deviation
- Deviation is the difference between each value and the average
- Variance (s²) is the average of the squared deviations, which ensures all values are positive
- Standard deviation (SD or s) is the square root of the variance
Sample Variance and SD Formula
- Refer to the image for the formula
- Answers should be calculated with more decimal places and rounded for presentation
Population Parameters
- Population mean is μ
- Population variance is σ²
- Population standard deviation is σ
- The goal is to estimate population parameters (μ and σ) using sample data (x and s)
Summarizing Data Graphically
- Bar Charts and Histograms are common for graphical summarization
- Histograms are useful for medium-large sample sizes (>30)
- Line graphs, XY plots, and dot plots are also options
Histograms
- Histograms are used to summarize datasets graphically
- It identifies where most values lie, visualizes data variation, and the shape of the distribution
Relative Frequency Histogram
- Relative Frequency Histograms are similar to frequency histograms but compares intervals to the total number of observations
- It is useful for comparing different samples
- Interval is the frequency / total number of observations
Frequency Histograms
- In a relative frequency histogram, the area under all bars equals 1
- The area under the distribution curve between two points is the proportion of data or probability
Normal Distribution
- Most populations exhibit a normal distribution
- Examples include height, blood pressure, sample means, errors in measurements
- Normal distributions are bell-shaped and symmetrical about the mean
Normal Distribution Facts
- 68% of values are within 1 standard deviation of the mean
- 95% of values are within 2 standard deviations of the mean
- 99.7% of values are within 3 standard deviations of the mean
Standard Deviation
- Larger standard deviations indicate greater variation in the population, resulting in data points further from the mean
Definitions
- Mean is the average toal of observed values divided by the number of values
- Median is the middle value when data is placed in order that us useful when the distribution is not normal
Sample and Population
- The sample is the group of subjects actually studied
- The population is the larger group that the sample represents
Standard Deviation
- Standard Deviation is a measure of the spread of observations
Data Types
-
Unordered Categories (Qualitative, Nominal): hair colour, smoking status
-
Ordered Categories (Qualitative, Ordinal): Cell diameter such as small, medium or large
-
Binary Categories (Yes/No): Coded as 0 and 1 such as smoking status
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Counts (Quantitative, Discrete): Number of bacteria on plate or number of students obtaining a First
-
Measurements (Quantitative, Continuous): Blood pressure, height, serum glucose level
Counts and Percentages Formulas
- Refer to the image for the formulas
Counts and Percentages formula
- It is used for categorical data (gender, ethnicity etc)
- It is very useful for test and diagnosis results
Variation Sources
- Potential mistakes in glucose level measurements
- Random differences/changes between students and over time
Systematic differences
- Systematic differences between students such as male / female
- Differences between students eating / not eating lunch
- Systematic differences over time like the effect of glucose levels over time
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