Statistics and Correlation Analysis Quiz
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Questions and Answers

What does a coefficient of correlation (r) of 0.75 indicate?

  • A weak negative linear relationship
  • An inverse relationship with high variability
  • No relationship between the variables
  • A strong positive linear relationship (correct)

Which of the following best describes a negative correlation?

  • Both variables increase together
  • Both variables decrease together
  • Both variables maintain a constant value
  • One variable increases while the other decreases (correct)

What is the range of values that a coefficient of correlation (r) can take?

  • -1.0 to 1.0 (correct)
  • 0 to 1.0 only
  • 1.00 to 10.0
  • 0.00 to 100

What signifies a positive correlation in variables?

<p>High values of one variable correspond to high values of the other (C)</p> Signup and view all the answers

In correlation analysis, which variable is considered the independent variable?

<p>The variable that is manipulated or changed (B)</p> Signup and view all the answers

What happens to the p value as the sample size increases?

<p>The p value typically decreases with larger sample sizes. (C)</p> Signup and view all the answers

Why is it important to examine effect sizes in research?

<p>Effect sizes indicate the magnitude of change, which is critical for interpretation. (D)</p> Signup and view all the answers

Which of the following statements best reflects a constructive hypothesis formulation?

<p>Our aim was to measure the specific impact of the new supplement on performance. (B)</p> Signup and view all the answers

What is a misconception about p values in research studies?

<p>A p value below 0.05 always indicates a strong effect. (C)</p> Signup and view all the answers

Which statement about the relationship between p values and sample sizes is true?

<p>An increase in sample size can cause a small effect to become statistically significant. (A)</p> Signup and view all the answers

What is Thomas Bayes best known for?

<p>Formulating Bayes' theorem (A)</p> Signup and view all the answers

What does Bayesian statistics primarily utilize in its analysis?

<p>Previous research and available knowledge (C)</p> Signup and view all the answers

Who edited and published Thomas Bayes' notes after his death?

<p>Richard Price (D)</p> Signup and view all the answers

What is a key responsibility of someone using Bayesian statistics?

<p>Taking on all the risk and responsibility (D)</p> Signup and view all the answers

Why might non-practitioners struggle with understanding clinical significance?

<p>They are unfamiliar with statistical analysis methods (B)</p> Signup and view all the answers

What percentage of reliability is accepted for a 1-RM Leg Press according to the content?

<p>10-14% (B)</p> Signup and view all the answers

What common fear affects people's approach to Bayesian statistics?

<p>Fear of making mistakes (A)</p> Signup and view all the answers

What is the accepted reliability limit for VO2 Max?

<p>6.0% (A)</p> Signup and view all the answers

What does a correlation value (r) of less than 0.00 signify?

<p>There is a negative relationship between the variables. (C)</p> Signup and view all the answers

What does R² (Coefficient of Determination) represent in a regression analysis?

<p>The proportion of variation explained by the independent variable. (A)</p> Signup and view all the answers

What does a standard error (SE) indicate in predictive modeling?

<p>The expected error in predicting the true value. (B)</p> Signup and view all the answers

What is generally accepted about a p value of 0.06 in research?

<p>It holds similar importance to a p value of 0.05. (C)</p> Signup and view all the answers

Why might researchers consider the p < 0.05 threshold arbitrary?

<p>It does not account for effect size and context. (D)</p> Signup and view all the answers

Which of the following best describes the relationship portion of a p value in significance testing?

<p>It indicates the likelihood of obtaining the observed effect due to chance. (A)</p> Signup and view all the answers

What does a correlation value near 1.0 indicate?

<p>A perfect positive linear relationship. (C)</p> Signup and view all the answers

What is implied when it is stated, 'I DON’T CARE!' regarding applied statistics for kinesiology?

<p>A controversial stance on the importance of statistical analysis. (B)</p> Signup and view all the answers

What does a 90% confidence interval (CI) signify?

<p>The true sample mean falls within the error bar range with 90% certainty. (B)</p> Signup and view all the answers

What is indicated by an error bar that ranges from -6.0% to 8.0%?

<p>The true value of the sample mean might be anywhere from -6.0% to 8.0%. (A)</p> Signup and view all the answers

How does a 99% confidence interval differ from a 90% confidence interval?

<p>A 99% CI provides greater certainty about the true mean. (D)</p> Signup and view all the answers

What is meant by the term 'true value of the sample mean' in this context?

<p>The actual mean value that the sample data estimates, which may fall anywhere within the interval. (D)</p> Signup and view all the answers

Which confidence level would provide the widest error bar range?

<p>99% Confidence Interval (C)</p> Signup and view all the answers

What could a decrease in confidence level from 99% to 90% imply?

<p>Greater possibility that the true mean is outside the error bar range. (D)</p> Signup and view all the answers

In the context of confidence intervals, what does a range of -2.0% to -10.0% indicate?

<p>The true sample mean is likely to be negative. (A)</p> Signup and view all the answers

What is a potential misconception about confidence intervals?

<p>Higher confidence levels guarantee the accuracy of the true mean. (C)</p> Signup and view all the answers

Why might someone use a confidence interval in research?

<p>To estimate the reliability of an observed sample mean. (A)</p> Signup and view all the answers

What does the null hypothesis (H0) state in a statistical test?

<p>There are no differences between treatments. (B)</p> Signup and view all the answers

What does an alpha level of 0.05 imply in hypothesis testing?

<p>There is a 5% chance that we conclude findings are significant by error. (B)</p> Signup and view all the answers

How does increasing the alpha level to 0.01 affect the reliability of results?

<p>It decreases the chances of results being due to error. (D)</p> Signup and view all the answers

What is a research hypothesis based on?

<p>Empirical studies and logical reasoning. (D)</p> Signup and view all the answers

In the example provided, what was the expected outcome regarding the wearable devices?

<p>Significant differences were expected between devices. (A)</p> Signup and view all the answers

What does probability (p) indicate in the context of hypothesis testing?

<p>The odds of a certain event occurring. (D)</p> Signup and view all the answers

Which statement is true regarding the level of chance occurrence?

<p>It varies from low to high. (D)</p> Signup and view all the answers

What is the significance of having a statistically significant finding?

<p>It demonstrates that findings are not likely due to chance. (D)</p> Signup and view all the answers

Flashcards

Research Hypothesis

A prediction about the outcome of a study, based on logic and prior research.

Null Hypothesis

A statement that there is NO difference or relationship between variables in a study.

Alpha (α)

The probability of making a Type I error, set by the researcher before the study.

Probability (p)

The likelihood of a certain event occurring.

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Type I Error

Rejecting the null hypothesis when it's actually true (false positive).

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Level of Significance

The threshold for rejecting the null hypothesis, usually set at 0.05.

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Gold Standard

A highly accurate and reliable method used as a benchmark for comparison.

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Wearable Device

A technology worn on the body to track health data (e.g., step count, heart rate).

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Confidence Interval (CI)

A range of values within which the true value of a population parameter (like a mean) is likely to fall, with a certain degree of confidence.

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Confidence Level

The probability that the true value of a population parameter falls within the confidence interval. Expressed as a percentage.

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Error Bar

A visual representation of the confidence interval, extending on both sides of the sample mean.

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90% Confidence Interval

A confidence interval with a 90% chance that the true value of the sample mean is within the range.

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95% Confidence Interval

A confidence interval with a 95% chance that the true value of the sample mean is within the range.

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99% Confidence Interval

A confidence interval with a 99% chance that the true value of the sample mean is within the range.

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Sample Mean

The average value of a sample taken from a population.

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True Value of the Mean

The actual, unknown average value of the entire population.

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Delta PV%

The percentage change in value from one point to another. Often used to compare changes over time.

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Day

A unit of time used to track changes over time.

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Correlation

A statistical technique used to determine the relationship between two or more variables.

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Coefficient of Correlation (r)

A numerical measure of the linear relationship between two variables, ranging from 0.00 to 1.0, with positive values indicating a positive correlation and negative values indicating a negative correlation.

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Positive Correlation

A linear relationship where a small value for one variable is associated with a small value for another, and a large value for one is associated with a large value for the other.

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Negative Correlation

A linear relationship where a small value for one variable is associated with a large value for another, and a large value for one is associated with a small value for the other.

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Dependent Variable

The variable being measured in an experiment, which is expected to change in response to variations in the independent variable.

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Bayes' Theorem

A mathematical formula used to update the probability of an event based on new evidence. It helps determine the likelihood of a hypothesis given observed data.

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Bayesian Statistics

A statistical approach where prior knowledge and data are combined to estimate the probability of an event. It involves the use of Bayes' Theorem.

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Clinical Significance

The practical importance of a statistical finding in a real-world setting. It involves considering the magnitude of the effect and its implications for decision-making.

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Reliability of Test

The consistency of a test result when repeated multiple times. It reflects the test's accuracy and ability to provide similar measurements.

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Athletic Assessment

Evaluating an athlete's physical capabilities, including strength, power, endurance, and biomechanics.

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One-Rep Maximum (1-RM)

The maximum weight an individual can lift for one repetition.

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VO2 Max

The maximum rate at which your body can use oxygen during exercise. It reflects your cardiovascular fitness.

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Range of Motion (ROM)

The extent of movement at a joint. It measures how far a joint can move.

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Correlation Coefficient (r)

A statistical measure indicating the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

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Strong Negative Correlation (r < 0.00)

A strong inverse relationship between two variables, meaning as one variable increases, the other decreases significantly.

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Coefficient of Determination (R²)

A statistical measure that indicates the proportion of variation in the dependent variable that can be explained by the independent variable. It represents the goodness of fit of the regression model.

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Standard Error (SE)

A measure of the average distance between the predicted values and the actual observed values in a regression model. It represents the uncertainty or error in the prediction.

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p-value

The probability of obtaining a result as extreme as the observed result, assuming the null hypothesis is true. A low p-value (< 0.05) suggests evidence against the null hypothesis.

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Statistical Significance

A result is considered statistically significant if the p-value is less than the predetermined alpha level (usually 0.05). This suggests that the result is unlikely to have occurred by chance alone.

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Magnitude of Effect

The size or strength of the relationship between variables. It indicates the practical importance of the findings, regardless of statistical significance.

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Arbitrary p-value

The choice of a p-value of 0.05 is somewhat arbitrary and may lead to the overemphasis of statistically significant but practically insignificant results.

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P-value Dependence on Sample Size

The p-value, indicating statistical significance, is influenced by the number of participants (sample size) in a study. Larger sample sizes tend to yield lower p-values, even if the effect size remains the same.

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Significance vs. Magnitude

Statistical significance (p-value) only tells if a difference or relationship is likely NOT due to chance, but it doesn't indicate the size of the effect. The magnitude of the effect, or effect size, reveals how meaningful the result is.

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Effect Size Matters

Research should focus on the magnitude of change (effect size) rather than solely relying on statistical significance (p-value). This gives a better understanding of the practical importance of findings.

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Hypothesis Focus: Magnitude Over Significance

When framing research questions, instead of simply aiming for a 'positive' or 'beneficial' outcome, focus on quantifying the effect size of a variable. This leads to more meaningful and impactful conclusions.

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Quantifying Performance Benefit

Research aims should specifically quantify the performance benefits of interventions. For example, instead of assuming a benefit, quantify the specific performance improvement expected from a supplement.

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Study Notes

Statistical Concepts in Kinesiology Research

  • This presentation covers chapters 6-9 of kinesiology research.
  • The presentation's title is "The Numbers Will Love You Back in Return-I Promise" by Martin Buchheit.
  • Key learning objectives include the importance of statistics in kinesiology, statistical definitions, differences between groups, relationships between variables, and applied statistics.
  • Statistics is a method of interpreting data objectively.
  • Descriptive statistics describe data characteristics.
  • Inferential statistics analyze relationships or differences in datasets.
  • Statistics involves inferring from samples to populations.

Importance of Statistics in Kinesiology

  • Statistical tools determine if observed differences are chance occurrences or true differences in larger populations.
  • Data analysis helps businesses optimize performance, increase efficiency, maximize profits, and make better decisions.
  • Data analytics is analyzing raw data to draw conclusions.

Prevalence of Obesity

  • Graphs displayed US maps showing prevalence of overall obesity (BMI ≥30) and severe obesity (BMI ≥35) in 2010 and 2020, 2030 showing projected increases.

Statistical Definitions

  • Mean (µ): The average score of a group of scores.

  • Standard deviation (σ): An estimate of the variability of scores around the mean.

  • Confidence intervals (CI): Displays the probability that the true score falls between lower and upper values.

  • 90% CI: Represents 90% confidence.

  • 95% CI: Represents 95% confidence.

  • 99% CI: Represents 99% confidence.

  • Central tendency: A score representing all scores (mean, median, mode).

  • Median: The mid-point score in a dataset.

  • Mode: The most frequent score.

  • Normal Distribution: When the mean, median, and mode are the same, and 68%, 95%, and 99% of scores lie within one, two, and three standard deviations from the mean, respectively.

  • Skewness: Describes the direction of the hump of a data distribution curve and the nature of its tails (skewed left or right).

  • Kurtosis: Measures the vertical characteristic of the data distribution—whether the curve is more peaked (leptokurtic) or flatter (platykurtic) than a normal curve.

  • Parametric statistical test: A test based on data assumptions of normal distribution, equal variance, and independence of observations.

  • Nonparametric statistical test: Statistical techniques used when data doesn't meet assumptions for parametric tests.

Statistical Issues in Research Planning and Evaluation (Chapter 7)

  • Hypothesis Testing:
    • Research hypothesis: Deduced from theory, based on logic, predicting study outcome.
    • Null hypothesis (H0): Assumes no difference (or relationship) between treatments/variables.
  • Alpha: A probability level (significance level) set by the experimenter before the study. A common value is 0.05 (i.e., the probability of a false-positive result is 5%).
  • Probability (p): The likelihood of an event occurring. Significance levels should be understood in context.

Importance of Applied Statistics for Kinesiology

  • p-values: Highly dependent on sample size. Larger sample size tends to produce lower p-values.
  • Effect size: The magnitude of change is more important than p-value significance.
  • Effect significance: The meaningful practical implications of found effects or relationships. Quantitative assessment of effects is better than simple significance tests.
  • Defining research questions: Clarifying the measurement of effect size can lead to better research questions.

Applied Research

  • Choices on p-values are often arbitrary, magnitude or importance of actual effects are key factors.

Applied Statistics for Kinesiology

  • Bayes' theorem: Using prior research knowledge to inform statistical analysis, decision about clinical significance.
  • Reliability of tests: Includes 1-RM leg press (kg), VO2 max (mL kg-1 min-1), ROM (degrees of knee joint), different tests have different degrees of reliability so these should be considered when designing a study.

Bayesian Statistics

  • You are the expert in clinical significance, and understand the risks/stress and responsibility of data interpretation

  • Typical hypotheses need clearer foundations and may be quantitatively defined.

### Additional Points

  • This presentation contained various graphs and images illustrative of the concepts discussed.
  • Many examples were cited to show the application of various statistical approaches.

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Lecture 7: Statistics in Kinesiology Research PDF

Description

Test your knowledge on correlation analysis and Bayesian statistics with this quiz. Explore concepts such as the coefficient of correlation, effect sizes, and the importance of independent variables in statistical research. Challenge yourself with questions related to misconceptions in p values and contributions by Thomas Bayes.

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