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Questions and Answers
What is a raw score in psychological statistics?
What is a raw score in psychological statistics?
In IQ testing, a standard deviation (SD) is typically ______ points.
In IQ testing, a standard deviation (SD) is typically ______ points.
15
A raw score can be directly compared across different tests regardless of their difficulty.
A raw score can be directly compared across different tests regardless of their difficulty.
False (B)
What is the mean IQ score typically set at?
What is the mean IQ score typically set at?
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What does a z-score indicate?
What does a z-score indicate?
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Approximately 95% of the population scores between 70 and 130 in IQ testing.
Approximately 95% of the population scores between 70 and 130 in IQ testing.
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Match the following percentages to their corresponding standard deviations regarding IQ scores:
Match the following percentages to their corresponding standard deviations regarding IQ scores:
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What is the mean of the z-score distribution after transforming raw scores?
What is the mean of the z-score distribution after transforming raw scores?
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What is one purpose of transforming raw scores into z-scores?
What is one purpose of transforming raw scores into z-scores?
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If the mean of a distribution is μ = 80 and the standard deviation is σ = 5, what is the z-score for a score of X = 85?
If the mean of a distribution is μ = 80 and the standard deviation is σ = 5, what is the z-score for a score of X = 85?
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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.
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In a distribution with a mean of μ = 60 and a standard deviation of σ = 8, a z-score of z = -1.50 corresponds to an X value of ______.
In a distribution with a mean of μ = 60 and a standard deviation of σ = 8, a z-score of z = -1.50 corresponds to an X value of ______.
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Match the types of probability with their definitions:
Match the types of probability with their definitions:
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What type of test is used when the hypothesis specifies that a parameter is greater than a specified value?
What type of test is used when the hypothesis specifies that a parameter is greater than a specified value?
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Which type of probability relies on experimental outcomes rather than theoretical assumptions?
Which type of probability relies on experimental outcomes rather than theoretical assumptions?
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The distribution of z-scores can have a different shape from the original distribution of scores.
The distribution of z-scores can have a different shape from the original distribution of scores.
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A Two-Tailed Test has only one critical region for assessing statistical significance.
A Two-Tailed Test has only one critical region for assessing statistical significance.
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What does Cohen's d measure?
What does Cohen's d measure?
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What is the deviation score in the context of z-scores?
What is the deviation score in the context of z-scores?
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A large effect size indicates __________ practical significance.
A large effect size indicates __________ practical significance.
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Which of the following situations is best suited for a One-Tailed Test?
Which of the following situations is best suited for a One-Tailed Test?
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Match the following hypothesis testing concepts with their correct descriptions:
Match the following hypothesis testing concepts with their correct descriptions:
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In a Two-Tailed Test, the alpha level is split between __________.
In a Two-Tailed Test, the alpha level is split between __________.
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A Type I error occurs when a researcher fails to reject a null hypothesis that is true.
A Type I error occurs when a researcher fails to reject a null hypothesis that is true.
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Which of the following best describes a Type II error?
Which of the following best describes a Type II error?
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What is the primary focus of a directional (one-tailed) test?
What is the primary focus of a directional (one-tailed) test?
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Which of the following is a requirement for a random sample?
Which of the following is a requirement for a random sample?
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In a one-tailed test, the critical region is located entirely in one ____.
In a one-tailed test, the critical region is located entirely in one ____.
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Match the effect sizes with their interpretations:
Match the effect sizes with their interpretations:
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What does the critical region refer to in hypothesis testing?
What does the critical region refer to in hypothesis testing?
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What is the alpha level in hypothesis testing?
What is the alpha level in hypothesis testing?
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Provide an example of a directional hypothesis.
Provide an example of a directional hypothesis.
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A Two-Tailed Test is more general than a One-Tailed Test as it checks for both increases and decreases.
A Two-Tailed Test is more general than a One-Tailed Test as it checks for both increases and decreases.
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Match the following alpha levels with their corresponding significance error risk.
Match the following alpha levels with their corresponding significance error risk.
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What is the purpose of hypothesis testing?
What is the purpose of hypothesis testing?
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What does H1 represent in hypothesis testing?
What does H1 represent in hypothesis testing?
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An alpha level of 0.01 indicates a 1% risk of making a Type II error.
An alpha level of 0.01 indicates a 1% risk of making a Type II error.
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What primarily distinguishes statistics from probability?
What primarily distinguishes statistics from probability?
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Sampling with replacement ensures that probabilities stay constant when selecting individuals.
Sampling with replacement ensures that probabilities stay constant when selecting individuals.
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The null hypothesis states that the treatment has an effect on the individuals in the population.
The null hypothesis states that the treatment has an effect on the individuals in the population.
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What does the null hypothesis (H0) indicate in research?
What does the null hypothesis (H0) indicate in research?
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Match the following terms with their definitions:
Match the following terms with their definitions:
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The percentile rank is the percentage of individuals with scores at or below a particular ________.
The percentile rank is the percentage of individuals with scores at or below a particular ________.
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The probability of incorrectly rejecting the null hypothesis is referred to as a Type ______ error.
The probability of incorrectly rejecting the null hypothesis is referred to as a Type ______ error.
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Which sample mean would be consistent with a null hypothesis stating that the population mean is μ = 15.8?
Which sample mean would be consistent with a null hypothesis stating that the population mean is μ = 15.8?
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What step must be taken after stating the hypothesis in hypothesis testing?
What step must be taken after stating the hypothesis in hypothesis testing?
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A significant alpha level means there is a high certainty that the null hypothesis is true.
A significant alpha level means there is a high certainty that the null hypothesis is true.
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In hypothesis testing, the sample mean should be _____ if the null hypothesis is true.
In hypothesis testing, the sample mean should be _____ if the null hypothesis is true.
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Study Notes
Raw Score
- A raw score is the unprocessed, original score from a test or assessment.
- It represents an individual's performance without any changes.
- Raw scores are the starting point for statistical analysis.
- Raw scores from different tests or assessments are not directly comparable if the tests have differing difficulty or scoring methods.
Z-score
- A z-score describes a score's position within a distribution.
- It doesn't provide information about position without context of distribution.
- Raw scores are transformed to z-scores to allow for meaningful comparisons across different distributions.
Transforming X Values to Z-scores
- Transforming raw scores (X values) to z-scores has two key purposes:
- It determines the precise location of each raw score within a distribution.
- It creates a standardized distribution that can be compared directly with other standardized distributions.
- Z-scores themselves form a standardized distribution, meaning they have a mean of zero.
Mean and Standard Deviation
- The mean IQ score is 100, serving as the center of the bell curve.
- Standard deviation (SD) is often 15 points in IQ testing.
- Approximately 68% of scores fall within one SD of the mean (85-115).
- Approximately 95% of scores fall within two SDs of the mean (70-130).
Z-score Formula
- A z-score is calculated by subtracting the mean (µ) from the raw score (X) and dividing the result by the standard deviation (σ).
- The formula is: z = (X - µ) / σ
- The z-score indicates the distance of a score from the mean in terms of standard deviations.
Z-score Distribution Properties
- The distribution of z-scores has the same shape as the original distribution.
- It will be normally distributed if the original data is normally distributed.
- Transforming scores into z-scores does not change their relative positions in the distribution.
Sample Calculation
- If a score of X = 130 corresponds to a distribution with a mean of µ = 100 and standard deviation of σ = 10, then it has a z-score of 3.00.
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Description
This quiz covers the concepts of raw scores and z-scores, important elements in statistical analysis. Understand the differences between unprocessed scores and their standardized equivalents, and learn how to transform raw scores into z-scores for better comparability. Test your knowledge on these foundational statistics concepts.
