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Questions and Answers
The distribution of z-scores will have a different shape compared to the original distribution of scores.
The distribution of z-scores will have a different shape compared to the original distribution of scores.
False
Transforming raw scores into z-scores changes everyone's position in the distribution.
Transforming raw scores into z-scores changes everyone's position in the distribution.
False
The z-score distribution will always have a mean of five.
The z-score distribution will always have a mean of five.
False
A z-score is calculated by measuring the distance in points between X and the mean then dividing by the standard deviation.
A z-score is calculated by measuring the distance in points between X and the mean then dividing by the standard deviation.
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In classical probability, outcomes are assumed to be equally likely.
In classical probability, outcomes are assumed to be equally likely.
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Empirical probability relies solely on theoretical assumptions.
Empirical probability relies solely on theoretical assumptions.
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Subjective probability is based on personal judgment rather than precise calculations.
Subjective probability is based on personal judgment rather than precise calculations.
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Statistics uses probability solely for theoretical predictions without considering sample data.
Statistics uses probability solely for theoretical predictions without considering sample data.
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A raw score is the original, processed score obtained from an assessment.
A raw score is the original, processed score obtained from an assessment.
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Z-scores are used to transform raw scores into new values with more information.
Z-scores are used to transform raw scores into new values with more information.
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The average IQ score is set at 120.
The average IQ score is set at 120.
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Approximately 68% of the population scores between 70 and 130 on an IQ test.
Approximately 68% of the population scores between 70 and 130 on an IQ test.
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The null hypothesis is also known as the one-effect hypothesis.
The null hypothesis is also known as the one-effect hypothesis.
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A z-score tells whether a score is above or below the mean.
A z-score tells whether a score is above or below the mean.
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A sample mean significantly different from 15.8 supports the null hypothesis.
A sample mean significantly different from 15.8 supports the null hypothesis.
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Standard deviations in IQ testing typically measure 20 points.
Standard deviations in IQ testing typically measure 20 points.
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The alpha level indicates the probability of making a Type II error.
The alpha level indicates the probability of making a Type II error.
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Raw scores can be directly compared across different tests without any transformations.
Raw scores can be directly compared across different tests without any transformations.
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An alpha level set at 0.01 indicates a 1% risk of committing a Type I error.
An alpha level set at 0.01 indicates a 1% risk of committing a Type I error.
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About 2% of the population scores above 130 on an IQ test.
About 2% of the population scores above 130 on an IQ test.
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A confidence interval of approximately 95% corresponds to an alpha level of 0.10.
A confidence interval of approximately 95% corresponds to an alpha level of 0.10.
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The alternative hypothesis (H1) predicts that the independent variable has no effect on the dependent variable.
The alternative hypothesis (H1) predicts that the independent variable has no effect on the dependent variable.
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Setting an alpha level is crucial to balance sensitivity and specificity in hypothesis testing.
Setting an alpha level is crucial to balance sensitivity and specificity in hypothesis testing.
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The alternative hypothesis states that there is no difference for the general population.
The alternative hypothesis states that there is no difference for the general population.
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In hypothesis testing, the null hypothesis is indicated by the symbol H1.
In hypothesis testing, the null hypothesis is indicated by the symbol H1.
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Random sampling requires that every individual in the population has an equal chance of being selected.
Random sampling requires that every individual in the population has an equal chance of being selected.
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Probability is primarily concerned with analyzing data from past events.
Probability is primarily concerned with analyzing data from past events.
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The percentile rank indicates the percentage of individuals with scores at or above a particular X value.
The percentile rank indicates the percentage of individuals with scores at or above a particular X value.
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The goal of hypothesis testing is to determine if the treatment has any effect on individuals in the population.
The goal of hypothesis testing is to determine if the treatment has any effect on individuals in the population.
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Sampling with replacement ensures that the probabilities of selection remain constant when multiple individuals are chosen.
Sampling with replacement ensures that the probabilities of selection remain constant when multiple individuals are chosen.
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Percentiles measure the exact score a value corresponds to within a distribution.
Percentiles measure the exact score a value corresponds to within a distribution.
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The discrepancies between sample data and predictions in hypothesis testing lead to conclusions about the null hypothesis.
The discrepancies between sample data and predictions in hypothesis testing lead to conclusions about the null hypothesis.
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The critical region is also known as the acceptance region.
The critical region is also known as the acceptance region.
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A Type I error occurs when a true null hypothesis is rejected.
A Type I error occurs when a true null hypothesis is rejected.
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In a one-tailed test, the critical region for rejecting the null hypothesis is found in both tails of the distribution.
In a one-tailed test, the critical region for rejecting the null hypothesis is found in both tails of the distribution.
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The significance level, often denoted as alpha, represents the probability of making a Type II error.
The significance level, often denoted as alpha, represents the probability of making a Type II error.
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Directional tests are called one-tailed tests because they consider both tails of the distribution.
Directional tests are called one-tailed tests because they consider both tails of the distribution.
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A left-tailed test is designed to evaluate if a parameter is greater than a specified value.
A left-tailed test is designed to evaluate if a parameter is greater than a specified value.
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Type II errors occur when researchers correctly reject a false null hypothesis.
Type II errors occur when researchers correctly reject a false null hypothesis.
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In psychological research, if cognitive training leads to better memory performance, it would support a directional hypothesis.
In psychological research, if cognitive training leads to better memory performance, it would support a directional hypothesis.
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A one-tailed test has two critical regions for testing a hypothesis.
A one-tailed test has two critical regions for testing a hypothesis.
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A two-tailed test checks for both increases and decreases in a parameter.
A two-tailed test checks for both increases and decreases in a parameter.
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Cohen's d value of 0.5 is considered a large effect size.
Cohen's d value of 0.5 is considered a large effect size.
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Effect size expresses the strength of the relationship between two variables.
Effect size expresses the strength of the relationship between two variables.
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In a right-tailed test, the alpha level is split equally between both tails.
In a right-tailed test, the alpha level is split equally between both tails.
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Two-tailed tests are most appropriate when researchers have a strong hypothesis about the direction of the effect.
Two-tailed tests are most appropriate when researchers have a strong hypothesis about the direction of the effect.
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A large effect size indicates that a research finding has limited practical applications.
A large effect size indicates that a research finding has limited practical applications.
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A right-tailed test is appropriate when there is prior evidence suggesting that an effect will occur in one direction.
A right-tailed test is appropriate when there is prior evidence suggesting that an effect will occur in one direction.
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Study Notes
Raw Scores
- Raw score: The original, unprocessed score from a test or assessment, reflecting an individual's performance without modifications.
- Raw scores are the starting point for statistical analyses.
- Raw scores lack context; a score of 75 on one test isn't directly comparable to a 75 on another if the difficulty or scoring methods differ.
- Raw scores are often transformed into standardized scores (e.g., z-scores) for meaningful comparisons.
Z-Scores
- Z-score: A standardized score that indicates a score's position within a distribution.
- Raw scores, by themselves, don't directly show where a score lies within a distribution.
- Z-scores transform raw scores into new values that offer more information about a score's position relative to the mean of the data set.
- Z-scores transform X values into z-scores to show exactly where the original scores are located within a distribution.
- Z-scores standardize a distribution, enabling direct comparison with other standardized distributions.
- Mean score: Average IQ score is 100, peak of the bell curve, with most scores clustering around it.
- Standard Deviation: Typically 15 points in IQ testing. About 68% of scores fall within one standard deviation (SD) of the mean (85-115), 95% within two SDs (70-130).
Z-Score Formula
- The Z-score formula is a deviation score. It measures the distance between an X value and the mean (μ).
- This distance is then divided by the standard deviation (σ) to provide a standardized distance in terms of standard deviation units.
- The formula is Z = (X - μ) / σ
Probability
- Probability: The fraction or proportion of a specific outcome in a situation with multiple possible outcomes.
- Probability is used to calculate predictions, estimate population characteristics, and assess the likelihood of future outcomes.
- Types of probability include classical (equally likely outcomes), empirical (based on observed data), and subjective (based on personal judgments).
Hypothesis Testing
- Hypothesis Testing: A statistical method to evaluate hypotheses about a population using sample data.
- The process involves stating a hypothesis, using it to predict sample characteristics, collecting data from a sample, and comparing the sample data to the predictions.
- Null hypothesis (H0): The treatment has no effect; the default assumption to be tested.
- Alternative hypothesis (H1): The treatment has an effect; a statement that contradicts or differs from the null hypothesis.
Alpha Level (Significance Level)
- Alpha level (α): The probability of incorrectly rejecting the null hypothesis.
- Common α values are 0.05 (5%), 0.01 (1%), or 0.10 (10%), representing acceptable risks of error.
- A higher α level increases the chance of falsely rejecting the null hypothesis, while a lower α level decreases this risk but might also make it harder to detect real effects.
- The alpha level establishes the critical region, which contains a set of values indicating when to reject a null hypothesis.
Critical Region
- Critical region: A set of values that represents statistical significance in a hypothesis test.
- It's determined by the alpha level and the distribution of the test statistic.
- Data that falls within this region leads to rejection of the null hypothesis because it is sufficiently different compared with the predictions according to the null hypothesis.
Type I and Type II Errors
- Type I error: Incorrectly rejecting a true null hypothesis.
- Type II error: Failing to reject a false null hypothesis.
Directional Tests
- One-tailed test: Used when the hypothesis specifies a direction (e.g., greater than or less than), focusing on detecting effects in a particular direction.
- Two-tailed test: Used when the hypothesis does not specify a direction; it investigates differences regardless of whether the outcome is an increase or a decrease.
Effect Size
- Effect size: A numerical measure of the strength of a relationship or difference between groups.
- Large effect sizes have practical importance.
- Cohen's d: A common measure of effect size, calculated by standardizing the difference between two means.
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Description
This quiz covers fundamental concepts in statistics and probability, including z-scores, distributions, and different types of probability. Learn how to compute z-scores and understand their significance in interpreting data. Explore the differences between raw scores and z-scores, as well as various probability frameworks.
