Podcast
Questions and Answers
A researcher aims to test an intervention designed to reduce chronic pain. What is the primary purpose of using statistical methods in this context?
A researcher aims to test an intervention designed to reduce chronic pain. What is the primary purpose of using statistical methods in this context?
- To describe the individual experiences of participants in the sample.
- To ensure the sample perfectly represents the population.
- To avoid the need for a control group in the study.
- To confidently generalize the findings from the sample to the larger population of individuals with chronic pain. (correct)
A research team is investigating a new therapy's effectiveness on a group of patients experiencing chronic pain. Considering the principles of hypothesis testing, what initial assumption should the researchers make?
A research team is investigating a new therapy's effectiveness on a group of patients experiencing chronic pain. Considering the principles of hypothesis testing, what initial assumption should the researchers make?
- The new therapy will have mixed results, with some patients improving and others not.
- The new therapy will definitely reduce pain in all patients.
- The new therapy will worsen the pain in all patients.
- There is no effect/association of the new therapy on pain. (correct)
In the context of null hypothesis significance testing, a researcher obtains a p-value of 0.03. Assuming the typical alpha level of 0.05, how should the researcher interpret this result?
In the context of null hypothesis significance testing, a researcher obtains a p-value of 0.03. Assuming the typical alpha level of 0.05, how should the researcher interpret this result?
- Retain the null hypothesis, as the p-value is below the alpha level, indicating no conclusive result.
- Reject the null hypothesis, concluding there is a significant effect. (correct)
- Fail to reject the null hypothesis, concluding there is no significant effect.
- Increase the alpha level to 0.10 to ensure significance.
Suppose researchers are investigating whether a new educational program improves test scores. What does it mean if they fail to reject the null hypothesis?
Suppose researchers are investigating whether a new educational program improves test scores. What does it mean if they fail to reject the null hypothesis?
In a study examining the effectiveness of a new drug, the null hypothesis states that the drug has no effect. What does it mean to seek 'evidence against the null hypothesis'?
In a study examining the effectiveness of a new drug, the null hypothesis states that the drug has no effect. What does it mean to seek 'evidence against the null hypothesis'?
A researcher aims to disprove the null hypothesis: $H_0: \mu = 50$. Which of the following alternative hypotheses would allow for a one-tailed test?
A researcher aims to disprove the null hypothesis: $H_0: \mu = 50$. Which of the following alternative hypotheses would allow for a one-tailed test?
How does increasing the sample size typically affect the standard error of the mean, and why is this important in hypothesis testing?
How does increasing the sample size typically affect the standard error of the mean, and why is this important in hypothesis testing?
A research team collected data showing a sample mean significantly lower than the established population mean. Considering the decision-making process in hypothesis testing after running a statistical test, what is the immediate next step?
A research team collected data showing a sample mean significantly lower than the established population mean. Considering the decision-making process in hypothesis testing after running a statistical test, what is the immediate next step?
What does the Central Limit Theorem state about the sampling distribution of the mean, and why is this theorem important in statistical inference?
What does the Central Limit Theorem state about the sampling distribution of the mean, and why is this theorem important in statistical inference?
In a one-sample z-test, what crucial assumption must be met regarding the population variance for the test results to be valid?
In a one-sample z-test, what crucial assumption must be met regarding the population variance for the test results to be valid?
In statistical hypothesis testing, what is the relationship between the null hypothesis ($H_0$) and the alternative hypothesis ($H_A$)?
In statistical hypothesis testing, what is the relationship between the null hypothesis ($H_0$) and the alternative hypothesis ($H_A$)?
How does a one-tailed test differ from a two-tailed test, and under what conditions is it appropriate to use a one-tailed test?
How does a one-tailed test differ from a two-tailed test, and under what conditions is it appropriate to use a one-tailed test?
In the context of hypothesis testing, what is a ‘directional alternative hypothesis,’ and how does it influence the testing procedure?
In the context of hypothesis testing, what is a ‘directional alternative hypothesis,’ and how does it influence the testing procedure?
A study compares a sample mean to a known population mean using a z-test. If the calculated z-score is -2.58 and a two-tailed test is being used with $\alpha = 0.01$, what decision should be made regarding the null hypothesis?
A study compares a sample mean to a known population mean using a z-test. If the calculated z-score is -2.58 and a two-tailed test is being used with $\alpha = 0.01$, what decision should be made regarding the null hypothesis?
In the context of statistical testing, what is a p-value, and how is it used to decide whether to reject the null hypothesis?
In the context of statistical testing, what is a p-value, and how is it used to decide whether to reject the null hypothesis?
A researcher conducts a hypothesis test and obtains a p-value of 0.06. How would the statistical decision change if the researcher used a significance level ($\alpha$) of 0.10 instead of a significance level of 0.05?
A researcher conducts a hypothesis test and obtains a p-value of 0.06. How would the statistical decision change if the researcher used a significance level ($\alpha$) of 0.10 instead of a significance level of 0.05?
What is a Type I error in hypothesis testing, and what symbol is associated with the probability of it occuring?
What is a Type I error in hypothesis testing, and what symbol is associated with the probability of it occuring?
A statistical test results in a decision to 'reject the null hypothesis'. What specific conclusion can be drawn?
A statistical test results in a decision to 'reject the null hypothesis'. What specific conclusion can be drawn?
In hypothesis testing, what does the term 'statistical significance' generally indicate about the results of a study?
In hypothesis testing, what does the term 'statistical significance' generally indicate about the results of a study?
A researcher calculates a z-score to determine the location of a sample mean within the sampling distribution. What information does the z-score provide in this context?
A researcher calculates a z-score to determine the location of a sample mean within the sampling distribution. What information does the z-score provide in this context?
Researchers found that a new job training program resulted in a significant reduction in unemployment rates in a specific city (p < 0.05). What is the most appropriate interpretation of their analysis?
Researchers found that a new job training program resulted in a significant reduction in unemployment rates in a specific city (p < 0.05). What is the most appropriate interpretation of their analysis?
A researcher decides to increase the significance level ($\alpha$) from 0.05 to 0.10. What is the direct effect of this change on the likelihood of committing a Type I error?
A researcher decides to increase the significance level ($\alpha$) from 0.05 to 0.10. What is the direct effect of this change on the likelihood of committing a Type I error?
In conducting a z-test for a single mean, what distribution is assumed for the sampling distribution of the sample means, and why is this assumption important?
In conducting a z-test for a single mean, what distribution is assumed for the sampling distribution of the sample means, and why is this assumption important?
A researcher specifies a one-tailed hypothesis asserting that a new teaching method will definitively increase student performance, but finds there is no significant statistical benefit. If the researcher decides to switch to a two-tailed test, what could be the impact of the switch?
A researcher specifies a one-tailed hypothesis asserting that a new teaching method will definitively increase student performance, but finds there is no significant statistical benefit. If the researcher decides to switch to a two-tailed test, what could be the impact of the switch?
What is the practical implication of the standard error of the mean in hypothesis testing?
What is the practical implication of the standard error of the mean in hypothesis testing?
In a study about an insomnia treatment, which of the following would be the alternative hypothesis in symbols?
In a study about an insomnia treatment, which of the following would be the alternative hypothesis in symbols?
Why does increasing sample size help with data in hypothesis testing?
Why does increasing sample size help with data in hypothesis testing?
In hypothesis testing, what factors do we want to see happen regarding the z-score and p-value?
In hypothesis testing, what factors do we want to see happen regarding the z-score and p-value?
Which of the following is true in how a z-score is calculated?
Which of the following is true in how a z-score is calculated?
Following a new training, a company reviews performance on new methods, with the population mean as $H_0: \mu_x =10$. Which of these alternative hypotheses would require a two-tailed test?
Following a new training, a company reviews performance on new methods, with the population mean as $H_0: \mu_x =10$. Which of these alternative hypotheses would require a two-tailed test?
If a study increases the alpha with the same test and criteria, what is the likely outcome?
If a study increases the alpha with the same test and criteria, what is the likely outcome?
What is true of the alternative directional hypothesis and why should it only sometimes be used?
What is true of the alternative directional hypothesis and why should it only sometimes be used?
What does statistical significance indicate from the test results of a study?
What does statistical significance indicate from the test results of a study?
The z-score determines the location, what does this mean about sampling distribution?
The z-score determines the location, what does this mean about sampling distribution?
A study is completed about high school grade data. There is a statistically significant impact for one school with data that shows .0432 for results. What would be true of what should happen based only on data:
A study is completed about high school grade data. There is a statistically significant impact for one school with data that shows .0432 for results. What would be true of what should happen based only on data:
What data does the z score actually provide?
What data does the z score actually provide?
What is meant by "reject the null hypothesis?"
What is meant by "reject the null hypothesis?"
What is an example of something you want to change during the test phase, and why?
What is an example of something you want to change during the test phase, and why?
Flashcards
What is a population?
What is a population?
A group of cases with a specific characteristic.
What is a sample?
What is a sample?
A smaller part of the population.
What is inferential statistics?
What is inferential statistics?
Using sample data to draw conclusions about the broader population.
What is the null hypothesis?
What is the null hypothesis?
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What is hypothesis testing?
What is hypothesis testing?
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What is (H_0: \mu_x = 7 )?
What is (H_0: \mu_x = 7 )?
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What is the alternate hypothesis (H_A)?
What is the alternate hypothesis (H_A)?
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What is a p-value?
What is a p-value?
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What do you do if p < .05?
What do you do if p < .05?
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When do we retain the null hypothesis?
When do we retain the null hypothesis?
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What is a sampling distribution of the mean?
What is a sampling distribution of the mean?
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What does the mean of sampling distribution equal?
What does the mean of sampling distribution equal?
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What is variance of sampling distribution?
What is variance of sampling distribution?
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What is standard error?
What is standard error?
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What is the Central Limit Theorem?
What is the Central Limit Theorem?
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What are Z-scores?
What are Z-scores?
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What is needed to run z-test for a single mean?
What is needed to run z-test for a single mean?
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What is a directional alternative hypothesis?
What is a directional alternative hypothesis?
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What does lower tail mean?
What does lower tail mean?
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Study Notes
- Describes properties of samples and populations, explaining their differences in research contexts
- Explains principles underlying null hypothesis significance testing and its role in statistical inference
- Outlines methodological processes involved in testing a research hypothesis
- Describes concept of the sampling distribution of the mean and its importance in statistical analysis
- Identifies research contexts where the z-test for a single mean is most appropriate
The Pain Example
- Imagine being a health professional treating people with chronic pain
- Developing an intervention with a multidisciplinary team to help patients manage their pain.
- Hypothesis: A new pain intervention reduces pain
- Note: The generality of the hypothesis isn't specific to this sample of 10 people
Samples and Populations
- "Population" refers to all cases with the target characteristic, such as people with chronic pain (~1.5 billion people)
- "Sample" is a subset of population, randomly drawn, every member of target population chance of being selected
- Example of a sample: 10 people with chronic pain recruited from the clinic
- Hypothesis testing: Samples are representative of the population of interest
- Population mean as μx.
- Sample mean
- Primary purpose of statistical methods is to confidently generalize from a sample to the population
Why Statistics Required
- Enables systematic organization and analysis of data to describe properties of a data set by summarizing key characteristics
- Allows making inferences from sample data to broader contexts.
- Example- a researcher studies the effect of new pain treatment on a a small group can determine results apply to the larger population
- Clinical perspective: Important that patients improve
- Research: Requires evidence of wider effectiveness of new intervention with results generalizing to a larger population.
Hypothesis Testing
- How to test the hypothesis that a pain intervention will reduce pain: -Devise the intervention by operationalizing the independent variable. -Determine how to assess the dependent variable by operationalizing it. -Determine how to judge whether the intervention was effective by selecting a comparator. -Collect data from people who have completed the intervention. -Run a statistical test -Make a decision -Draw a conclusion - statistical inference involves concluding about population from the sample.
The Intervention
- Based on biopsychosocial model:
- Bio: chronic pain may not be easily cured with medication (which can have negative side effects), but physical activity strategies can help
- Psycho: cognitive-behavioural-therapy-based intervention
- Social: involvement of families or relevant others
- Devise 3 elements to the new pain intervention (Bio, Psycho, Social)
- Since this pain intervention has 3 elements of pain, the question in terms of devising the model is does it actually reduce "pain?"
- Determine how it actually reduces pain via BPI measurement
- BPI pain interference sub-scale
- During the past week, how much has pain interfered with the following (0=Does not interfere to 10=Completely interferes):
- Your general activity?
- Your mood?
- Your walking ability?
- Your normal work (both outside the home and housework)?
- Your relations with other people?
- Your sleep?
- Your enjoyment of life?
- Select and operationalise - the extent to which pain interferes with life is more amenable to change than pain intensity.
- Scored as the average of these items, so has a range 0-10,where higher scores indicate greater interference.
- Could a particular aspect perhaps intervene with the interference of pain on everyday.
life?
- E.g., Psycho: making people tolerate it better.
Comparison Value
- Single sample for pragmatic reasons
- Compare to some "known" value for people with chronic pain who have not received treatment (Normative data) EX: BPI
- The mean BPI interference score was 7 (SD 2.1).
- Data collection is complex
- Focus is on null hypothesis significance testing.
The Null Hypothesis
- Begins with assumption that there is no effect/association = null hypothesis (statement about population parameters)
- In pain example, null hypothesis is that the intervention has no effect on pain
- Looking for evidence against the null hypothesis.
- Population mean (ux) for those who've had no treatment is 7.
- If the intervention is ineffective, sample should come from a population with a mean of 7
- Hypothesis of Pain
- Sample & Population Mean
- Those with chronic pain had no interventions and an average score of 7.
- the novel intervention is hypothesised to lower the pain effects if there is no effect Ho theaveragepainratingsshouldequal thepopulation mean 7 i.e Ho: μx= 7
- Seek to statistically test for alternative hypothesis, denoted HA (there is an effect/association), where HA: μx<7
- Seeking evidence against the null hypothesis When the hypothesis is tested there is an assumption it's true and the results are unlikely
- If unlikely, there are 2 possible outcomes: null hypothesis is true and results are unusual or null hypothesis is false
- Probability used is the p-value
P-Value
- Defined as probability of obtaining observed results (or more extreme results) if null hypothesis is true [p(obslHo)]
- Convention of "small" means < .05 (5%) small or not small If < .05, reject null hypothesis.
- EXAMPLES:
- Researcher discovers scale measuring materialism, developed in 1940s Adult mean on this scale was 35 and normally distributed Researchers hypothesize present day adults are more materialistic than in 1940s Present day sample mean was 39
- Null hypothesis: Ho: μx= 35 Alternative hypothesis: HA: μχ> 35 = 39
- When a=.05 and p(obslHo) = .04 decision = Reject Ho
Obtaining the P-Value
- Obtained same way as proportions/probabilities/percentiles for individuals within samples
- Main difference that with individual-within-sample all observation in sample is known
- When comparing sample mean to other sample mean distribution, the other sample means are hypothetical
- Will now describe the distribution of (hypothetical) sample means in terms of: mean, variance, shape
Sample Mean
- Want to make inferences about the target population, which are usually large
- Thus, recruit samples and calculate sample statistics, then make inferences about the population
- Sample mean as estimator of population mean unbiased estimator of the population mean The sampling distribution of the mean is the distribution of the means from all possible samples we could have obtained.
Sampling Distribution of the Mean
- Sample mean is an unbiased estimator of population mean
- If all possible samples of size "N" from all populations are taken and the mean calculated
- There would be a complete sampling distribution of the mean from our sample which may not be equal each time it is taken
- Variance of sampling distribution of the mean will be smaller because sample better estimates mean single score.
- The shape of the sampling is to do with the "Central Limit Theorem"
Central Limit Theorem
- the shape of the original distribution (normal; skewed; rectangular), as N increases, the sampling distribution of the mean approximates a normal distribution.
- To revise
- Standard normal distribution - revision
- Total area under the standard normal curve is 1 (i.e., 100% of the observations.)
- Certain z-scores cut off certain ranges,which can be thought of as:
- The probability of randomly selecting a score within a specified range, The percentage of scores within a specified range
- The proportion of scores within a specified range, The percentile rank at a particular point
- Individuals vs Samples - Now examine relative standing of the sample or Z score to identify p value
Z - Test
- Tests where samples sit in the distribution of hypothetical samples under null hypothesis
- Sample of the population variance is known where tests are run when the test is single mean
The Pain Model Example
- The test of a Hypothesis regarding pain is demonstrated by running a Z test via various observations and tests being conducted
- There are calculations completed from the sample and deviation of sample mean from Ho population mean standard error of sample
Critical Z Approach
- Criterion of significance (a) = .05
- directional test is run where (HA states a lower tail of the distribution is expected).
- With software, the critical value of z can be determined with a p-value of .05 for -1.64
- When the Z score is more extreme it will reject H value - with z score than 1.6
- Using a P Approach - To calculate the z result and compare to the value from .05
- As A method to test. A third alternative could be used to obtain the critical
Two Tailed - Analysis
- Where 2 Z are used the analysis can still conclude Ho - With software, the critical value of z can be determined with a p-value of .05 for -1.64
- Mean can be statistically significantly lower due to conditions
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