Research Methods Quiz
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Questions and Answers

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?

At the end of the Introduction section.

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?

<p>Statistical methods are tools used to analyze data and help answer the scientific research question.</p> Signup and view all the answers

What kind of language are research questions presented in?

<p>Plain language.</p> Signup and view all the answers

What is the relationship between scientific hypotheses and research questions?

<p>A scientific hypothesis is a statement about a research question. It's a testable idea about the answer to this question.</p> Signup and view all the answers

True or false: Deciding about statistical hypotheses directly answers your scientific research question?

<p>False.</p> Signup and view all the answers

What must always be understood when using statistical tests according to the text?

<p>That their results are in service to answering the scientific research question.</p> Signup and view all the answers

What does the null hypothesis ($H_0$) state within the NHST framework?

<p>The null hypothesis states that any observed signal in a sample is due to random chance and does not exist at the population level.</p> Signup and view all the answers

What does the alternate hypothesis ($H_A$) propose?

<p>The alternate hypothesis proposes that the observed signal is not due to random chance and does exist at the population level.</p> Signup and view all the answers

In statistical testing, what are we examining, despite noise in our data?

<p>We are evaluating how confident we are of the signal we observe despite the noise in the data.</p> Signup and view all the answers

What two factors make us more confident in rejecting the null hypothesis?

<p>The larger the signal and the smaller the noise.</p> Signup and view all the answers

What is not enough, on its own, for a researcher to answer their primary research question?

<p>Statistical significance alone is not enough.</p> Signup and view all the answers

Name the two statisticians who developed the methods that make up NHST.

<p>Ronald Fisher and Jerzy Neyman (with Egon Pearson).</p> Signup and view all the answers

What is considered a 'weird mixture'?

<p>NHST is considered a 'weird mixture' of the methods for statistical inference.</p> Signup and view all the answers

What has been a topic of debate for nearly a century regarding the two main approaches within NHST?

<p>Which approach is better.</p> Signup and view all the answers

What is the primary focus of the statistical inference system developed by Fisher?

<p>Falsification of the null hypothesis.</p> Signup and view all the answers

What philosophical challenge did statisticians face regarding scientific hypotheses, which led to the development of the null hypothesis?

<p>The impossibility of proving something is true, especially about human behavior.</p> Signup and view all the answers

Instead of proving a hypothesis is true or false, what does Fisher's approach involve?

<p>Assuming something is true and observing the world through this assumption.</p> Signup and view all the answers

Why does the text suggest that the 'normal' use of NHST isn't always scientifically rigorous?

<p>NHST has been misapplied for decades.</p> Signup and view all the answers

What do social science researchers often expect in their approach to science?

<p>To approach science in the “normal” and “customary” ways.</p> Signup and view all the answers

What system of statistical inference focuses on choosing between a main and an alternate hypothesis?

<p>The system developed by Neyman-Pearson.</p> Signup and view all the answers

What is the root cause of the "replication crisis" in the social sciences, according to the text?

<p>The misapplication of NHST.</p> Signup and view all the answers

What is an important challenge presented in combining the Fisher and Neyman-Pearson approaches into NHST?

<p>It has resulted in a mishmash of ideas that are often misunderstood and misapplied.</p> Signup and view all the answers

In Fisher's method, what is the initial assumption (null hypothesis) regarding the existence of a signal?

<p>That a signal does not exist.</p> Signup and view all the answers

What does the test statistic, t, represent?

<p>It represents a value calculated from the signal and noise that corresponds to a standard probability distribution T.</p> Signup and view all the answers

How is the p-value derived from the test statistic, t, and the distribution, T?

<p>The p-value is the probability of observing a value of t, or a greater value, which is calculated from the area under the curve of T.</p> Signup and view all the answers

According to Fisher's method, what probability are we seeking to calculate based on observed data and the null hypothesis?

<p>The probability of observing the sample data given the null hypothesis is true, i.e. P(data|H0).</p> Signup and view all the answers

If the probability P(data|H0) is very close to 0, what does this suggest about the null hypothesis?

<p>That the null hypothesis is likely to be wrong.</p> Signup and view all the answers

What does a small p-value suggest about the null hypothesis?

<p>A small p-value suggests that the assumption of the null hypothesis being true is likely wrong, and that a signal likely exists.</p> Signup and view all the answers

When we assume the null hypothesis (H0), what else are we assuming about the observations?

<p>That the observed variable will follow specific patterns according to theoretical probability distributions.</p> Signup and view all the answers

In statistical research, what does the term 'significant' indicate relative to p-values?

<p>The term 'significant' is applied to p-values that are less than a pre-established threshold, denoted as alpha.</p> Signup and view all the answers

What is a common misconception that the text warns against when interpreting p-values?

<p>It is easy to misinterpret a p-value and misunderstand what it actually means.</p> Signup and view all the answers

In the example comparing anxiety scores of undergrads and PhD students, what would be considered the signal?

<p>The difference between the mean anxiety scores of the two groups, i.e. $\bar{x}<em>{under} - \bar{x}</em>{PhD}$.</p> Signup and view all the answers

If the null hypothesis is true in the anxiety study, what would we expect the value of the signal to be close to?

<p>Close to 0.</p> Signup and view all the answers

What is the main assumption when interpreting a p-value in research?

<p>The main assumption is that the null hypothesis is true.</p> Signup and view all the answers

What probability distribution does the example use to describe how our observed variable will behave?

<p>A normal distribution.</p> Signup and view all the answers

Why does the text urge caution in considering a single experiment as 'sufficient' proof?

<p>Because no isolated experiment, however significant, can fully demonstrate a natural phenomenon.</p> Signup and view all the answers

What do we use, in addition to the signal, to calculate a test statistic?

<p>The noise, often represented by the standard deviation of observations.</p> Signup and view all the answers

What does a p-value measure and what is its practical interpretation?

<p>It measures the probability of observing your data assuming the null hypothesis is true and it indicates that the smaller the value, the less likely the data would have occurred, assuming the null.</p> Signup and view all the answers

In the context of hypothesis testing about the weight of babies in a small town, what does the null hypothesis state?

<p>The null hypothesis states that the average birth weight of babies in the small town is the same as the general average birth weight, or $𝜇_{ST} = 𝜇$.</p> Signup and view all the answers

The null hypothesis can be represented mathematically as $H_0: μ_{ST} - μ = 0$. Why is this representation useful?

<p>It's useful because $μ_{ST} - μ$ represents the signal or the difference we are trying to detect.</p> Signup and view all the answers

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?

<p>If the null hypothesis is true, $x̄ - μ$ is expected to be normally distributed around 0.</p> Signup and view all the answers

If the null hypothesis is true, is it more probable to see values of $x̄ - μ$ closer to zero or farther from zero?

<p>If $H_0$ is true, then values of $x̄ - μ$ closer to zero are more probable than values further from zero.</p> Signup and view all the answers

What does it indicate if observed values of $x̄ - μ$ are far from 0, assuming the null hypothesis is true?

<p>It indicates that it is less probable that the null hypothesis is true.</p> Signup and view all the answers

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?

<p>The text also states that if $H_0$ is true, values of $x̄$ have an equal chance of being less than or greater than $μ$.</p> Signup and view all the answers

What is the purpose of transforming $x̄ - μ$ into a $z$-score?

<p>The purpose is to standardize the difference so that it corresponds to the Z-distribution.</p> Signup and view all the answers

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?

<p>The value $z$ represents the test statistic.</p> Signup and view all the answers

Flashcards

Significance in Research

Refers to the importance and implications of research findings.

Scientific Research Questions

Questions formulated to guide a scientific study and seek answers.

Scientific Hypotheses

Proposed explanations or predictions based on scientific research questions.

Statistical Hypotheses

Formal statements that include the null and alternative hypotheses in statistics.

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Null Hypothesis (H0)

A statement that posits no effect or no difference in the research context.

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Alternative Hypothesis (H1)

The hypothesis that signifies the presence of an effect or a difference.

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Quantitative Study

A type of research focused on quantifying relationships or dependencies between variables.

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Statistical Methods

Techniques employed to analyze data and answer research questions using statistics.

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Alternate Hypothesis (HA)

Claims that the observed signal is real and not just random chance.

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Statistical Tests

Assess confidence in observed signals amidst data noise.

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Signal vs. Noise

The observed effect (signal) versus random variation (noise) in data.

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NHST Framework

A statistical method using null and alternate hypotheses for inference.

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Statistical Significance

Indicates the likelihood that the observed result is not due to chance alone.

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Ronald Fisher

One of the pioneers of methods for statistical inference.

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Neyman-Pearson Framework

An alternative approach for hypothesis testing developed by Neyman and Pearson.

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NHST

Null Hypothesis Significance Testing, a method to make inferences about a population based on sample data.

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Falsification of the Null Hypothesis

The process of assuming the null hypothesis is true and determining if observations support or contradict this assumption.

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P-Value

A statistic that measures the strength of the evidence against the null hypothesis.

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Fisher's Approach

A method of statistical inference focusing on falsifying the null hypothesis rather than proving hypotheses.

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Replication Crisis

A phenomenon where many scientific studies cannot be replicated or reproduced, often linked to NHST misuse.

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Assumption in NHST

In NHST, we assume the null hypothesis is true and investigate the likelihood of observations.

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Critical Evaluation of NHST

Encouragement to question and analyze the practices surrounding NHST due to potential misapplications.

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Null Hypothesis (𝐻0)

Assumes that no signal exists in the population.

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Observed Data Probability

The likelihood of observing data under the null hypothesis.

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Low Probability Indicator

A p-value approaching 0 indicates evidence against 𝐻0.

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Theoretical Probability Distributions

Patterns assumed for data under 𝐻0, e.g., normal distribution.

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Mean Anxiety Scores

Average anxiety levels calculated for two groups (undergrads, PhDs).

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Signal Definition

The calculated difference between group anxiety scores (𝑥¯𝑢𝑛𝑑𝑒𝑟 − 𝑥¯𝑃ℎ𝐷 ).

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Noise Definition

Variability in observations, often measured by standard deviation.

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Test Statistic Calculation

Combining signal and noise to evaluate the null hypothesis.

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Test Statistic (t)

A calculated value from signal and noise, corresponding to a standard probability distribution T.

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Significant P-value

A p-value is considered significant if it is less than a predetermined threshold, typically 0.05.

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Assuming H0 is true

When calculating p-values, we do so under the assumption that the null hypothesis is valid.

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Threshold (α)

A pre-established value (usually 0.05) that determines significance in statistical testing.

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Standard Normal Distribution (T)

A probability distribution with a mean of zero and a standard deviation of one, used in hypothesis testing.

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Interpreting P-values

Understanding p-values involves realizing they reflect data probability if H0 holds true, not proof of H0 being false.

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Normal Distribution

A probability distribution that is symmetric about the mean.

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Standard Deviation (𝜎)

A measure of the amount of variation in a set of values.

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Signal

The difference between sample mean and population mean.

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Sample Mean (𝑥¯)

The average weight calculated from the sample of babies.

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Random Noise

Unpredictable variations in data measurements.

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Standardizing

The process of transforming values to a standard normal distribution.

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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!

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