Podcast
Questions and Answers
What is the primary objective of a scientific study?
What is the primary objective of a scientific study?
To answer the research question as best as possible.
Where in a research paper are research questions typically found?
Where in a research paper are research questions typically found?
At the end of the Introduction section.
What is the difference between a scientific hypothesis and a statistical hypothesis?
What is the difference between a scientific hypothesis and a statistical hypothesis?
A scientific hypothesis is a testable statement about a research question, and a statistical hypothesis is a statement about population parameters that can be tested using statistical methods.
In the context of the text, what is the role of statistical methods in answering research questions?
In the context of the text, what is the role of statistical methods in answering research questions?
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What kind of language are research questions presented in?
What kind of language are research questions presented in?
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What is the relationship between scientific hypotheses and research questions?
What is the relationship between scientific hypotheses and research questions?
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True or false: Deciding about statistical hypotheses directly answers your scientific research question?
True or false: Deciding about statistical hypotheses directly answers your scientific research question?
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What must always be understood when using statistical tests according to the text?
What must always be understood when using statistical tests according to the text?
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What does the null hypothesis ($H_0$) state within the NHST framework?
What does the null hypothesis ($H_0$) state within the NHST framework?
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What does the alternate hypothesis ($H_A$) propose?
What does the alternate hypothesis ($H_A$) propose?
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In statistical testing, what are we examining, despite noise in our data?
In statistical testing, what are we examining, despite noise in our data?
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What two factors make us more confident in rejecting the null hypothesis?
What two factors make us more confident in rejecting the null hypothesis?
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What is not enough, on its own, for a researcher to answer their primary research question?
What is not enough, on its own, for a researcher to answer their primary research question?
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Name the two statisticians who developed the methods that make up NHST.
Name the two statisticians who developed the methods that make up NHST.
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What is considered a 'weird mixture'?
What is considered a 'weird mixture'?
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What has been a topic of debate for nearly a century regarding the two main approaches within NHST?
What has been a topic of debate for nearly a century regarding the two main approaches within NHST?
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What is the primary focus of the statistical inference system developed by Fisher?
What is the primary focus of the statistical inference system developed by Fisher?
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What philosophical challenge did statisticians face regarding scientific hypotheses, which led to the development of the null hypothesis?
What philosophical challenge did statisticians face regarding scientific hypotheses, which led to the development of the null hypothesis?
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Instead of proving a hypothesis is true or false, what does Fisher's approach involve?
Instead of proving a hypothesis is true or false, what does Fisher's approach involve?
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Why does the text suggest that the 'normal' use of NHST isn't always scientifically rigorous?
Why does the text suggest that the 'normal' use of NHST isn't always scientifically rigorous?
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What do social science researchers often expect in their approach to science?
What do social science researchers often expect in their approach to science?
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What system of statistical inference focuses on choosing between a main and an alternate hypothesis?
What system of statistical inference focuses on choosing between a main and an alternate hypothesis?
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What is the root cause of the "replication crisis" in the social sciences, according to the text?
What is the root cause of the "replication crisis" in the social sciences, according to the text?
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What is an important challenge presented in combining the Fisher and Neyman-Pearson approaches into NHST?
What is an important challenge presented in combining the Fisher and Neyman-Pearson approaches into NHST?
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In Fisher's method, what is the initial assumption (null hypothesis) regarding the existence of a signal?
In Fisher's method, what is the initial assumption (null hypothesis) regarding the existence of a signal?
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What does the test statistic, t, represent?
What does the test statistic, t, represent?
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How is the p-value derived from the test statistic, t, and the distribution, T?
How is the p-value derived from the test statistic, t, and the distribution, T?
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According to Fisher's method, what probability are we seeking to calculate based on observed data and the null hypothesis?
According to Fisher's method, what probability are we seeking to calculate based on observed data and the null hypothesis?
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If the probability P(data|H0) is very close to 0, what does this suggest about the null hypothesis?
If the probability P(data|H0) is very close to 0, what does this suggest about the null hypothesis?
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What does a small p-value suggest about the null hypothesis?
What does a small p-value suggest about the null hypothesis?
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When we assume the null hypothesis (H0), what else are we assuming about the observations?
When we assume the null hypothesis (H0), what else are we assuming about the observations?
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In statistical research, what does the term 'significant' indicate relative to p-values?
In statistical research, what does the term 'significant' indicate relative to p-values?
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What is a common misconception that the text warns against when interpreting p-values?
What is a common misconception that the text warns against when interpreting p-values?
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In the example comparing anxiety scores of undergrads and PhD students, what would be considered the signal?
In the example comparing anxiety scores of undergrads and PhD students, what would be considered the signal?
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If the null hypothesis is true in the anxiety study, what would we expect the value of the signal to be close to?
If the null hypothesis is true in the anxiety study, what would we expect the value of the signal to be close to?
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What is the main assumption when interpreting a p-value in research?
What is the main assumption when interpreting a p-value in research?
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What probability distribution does the example use to describe how our observed variable will behave?
What probability distribution does the example use to describe how our observed variable will behave?
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Why does the text urge caution in considering a single experiment as 'sufficient' proof?
Why does the text urge caution in considering a single experiment as 'sufficient' proof?
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What do we use, in addition to the signal, to calculate a test statistic?
What do we use, in addition to the signal, to calculate a test statistic?
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What does a p-value measure and what is its practical interpretation?
What does a p-value measure and what is its practical interpretation?
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In the context of hypothesis testing about the weight of babies in a small town, what does the null hypothesis state?
In the context of hypothesis testing about the weight of babies in a small town, what does the null hypothesis state?
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The null hypothesis can be represented mathematically as $H_0: μ_{ST} - μ = 0$. Why is this representation useful?
The null hypothesis can be represented mathematically as $H_0: μ_{ST} - μ = 0$. Why is this representation useful?
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If $H_0$ is true, what is the expected distribution of $x̄ - μ$, where $x̄$ is the sample mean and $μ$ is the population mean?
If $H_0$ is true, what is the expected distribution of $x̄ - μ$, where $x̄$ is the sample mean and $μ$ is the population mean?
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If the null hypothesis is true, is it more probable to see values of $x̄ - μ$ closer to zero or farther from zero?
If the null hypothesis is true, is it more probable to see values of $x̄ - μ$ closer to zero or farther from zero?
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What does it indicate if observed values of $x̄ - μ$ are far from 0, assuming the null hypothesis is true?
What does it indicate if observed values of $x̄ - μ$ are far from 0, assuming the null hypothesis is true?
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The text stated that $x̄ - μ$ follows a normal distribution if $H_0$ is true. What other property of this distribution is identified in the text?
The text stated that $x̄ - μ$ follows a normal distribution if $H_0$ is true. What other property of this distribution is identified in the text?
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What is the purpose of transforming $x̄ - μ$ into a $z$-score?
What is the purpose of transforming $x̄ - μ$ into a $z$-score?
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In the formula $z = \frac{x̄ - μ}{\frac{σ}{\sqrt{n}}}$, what does $z$ represent, and what is this value called in the context of hypothesis testing?
In the formula $z = \frac{x̄ - μ}{\frac{σ}{\sqrt{n}}}$, what does $z$ represent, and what is this value called in the context of hypothesis testing?
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Flashcards
Significance in Research
Significance in Research
Refers to the importance and implications of research findings.
Scientific Research Questions
Scientific Research Questions
Questions formulated to guide a scientific study and seek answers.
Scientific Hypotheses
Scientific Hypotheses
Proposed explanations or predictions based on scientific research questions.
Statistical Hypotheses
Statistical Hypotheses
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Null Hypothesis (H0)
Null Hypothesis (H0)
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Alternative Hypothesis (H1)
Alternative Hypothesis (H1)
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Quantitative Study
Quantitative Study
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Statistical Methods
Statistical Methods
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Alternate Hypothesis (HA)
Alternate Hypothesis (HA)
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Statistical Tests
Statistical Tests
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Signal vs. Noise
Signal vs. Noise
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NHST Framework
NHST Framework
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Statistical Significance
Statistical Significance
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Ronald Fisher
Ronald Fisher
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Neyman-Pearson Framework
Neyman-Pearson Framework
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NHST
NHST
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Falsification of the Null Hypothesis
Falsification of the Null Hypothesis
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P-Value
P-Value
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Fisher's Approach
Fisher's Approach
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Replication Crisis
Replication Crisis
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Assumption in NHST
Assumption in NHST
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Critical Evaluation of NHST
Critical Evaluation of NHST
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Null Hypothesis (𝐻0)
Null Hypothesis (𝐻0)
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Observed Data Probability
Observed Data Probability
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Low Probability Indicator
Low Probability Indicator
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Theoretical Probability Distributions
Theoretical Probability Distributions
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Mean Anxiety Scores
Mean Anxiety Scores
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Signal Definition
Signal Definition
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Noise Definition
Noise Definition
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Test Statistic Calculation
Test Statistic Calculation
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Test Statistic (t)
Test Statistic (t)
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Significant P-value
Significant P-value
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Assuming H0 is true
Assuming H0 is true
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Threshold (α)
Threshold (α)
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Standard Normal Distribution (T)
Standard Normal Distribution (T)
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Interpreting P-values
Interpreting P-values
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Normal Distribution
Normal Distribution
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Standard Deviation (𝜎)
Standard Deviation (𝜎)
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Signal
Signal
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Sample Mean (𝑥¯)
Sample Mean (𝑥¯)
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Random Noise
Random Noise
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Standardizing
Standardizing
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Study Notes
Introduction to Inferential Statistics
- Statistics is an art of making probabilistic guesses about phenomena observed.
- Inferential statistics makes an assumption that a signal does not exist and then examines how probable this assumption is given sample data.
- Null hypothesis significance testing (NHST) is a dominant framework for inferential statistics.
Null Hypothesis Significance Testing (NHST) Framework
- NHST is not the sole method for inferential statistics, but understanding it is crucial.
- NHST involves assuming a signal does not exist (null hypothesis) and evaluating the likelihood of this assumption given sample data.
- The quality and validity of research should not solely rely on p-values.
Historical Development of NHST
- NHST is an amalgamation of Ronald Fisher and Jerzy Neyman/Egon Pearson's work.
- Fisher's approach focused on falsifying the null hypothesis (showing that the assumption of no signal is unlikely).
- Neyman-Pearson's work emphasized choosing between a null and alternative hypothesis based on probabilities.
Significance
- The word "significance" suggests importance, but a result being significant does not automatically imply meaningfulness or usefulness.
- A result that is not significant doesn't mean the result is not meaningful or valuable.
Statistical vs. Scientific Hypotheses
- A scientific research question often leads to a hypothesis, but the hypotheses used in statistical methods have a different form.
- An inferential statistical method has one null hypothesis and another alternate hypothesis (either specified or implicit)
Null and Alternate Hypotheses (NHST)
- H0 (Null Hypothesis): Asserts that any observed signal within a sample is due to random chance (no signal at the population level)
- HA (Alternate Hypothesis): Asserts that any observed signal is not due to random chance but exists at the population level.
P-Values
- P-values represent the probability of observing a signal of a given strength or greater.
- A small p-value suggests that the assumption of no signal (null hypothesis) is unlikely, implying a signal may indeed exist.
- Misinterpretation of p-values is common, and p-value should not be mistaken as the probability that the null hypothesis is true.
P-Value - not...
- A measure of signal strength/magnitude
- Evidence for an alternate hypothesis
- The probability that the null hypothesis is true
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Description
This quiz tests your understanding of scientific research methods, including the roles of hypotheses, statistical tests, and research questions. Answer questions about the differences between scientific and statistical hypotheses as well as the importance of language in formulating research questions. Perfect for students in research methodology courses!