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Questions and Answers
What does a raw score represent in psychological statistics?
What does a raw score represent in psychological statistics?
Why are raw scores often transformed into z-scores?
Why are raw scores often transformed into z-scores?
What does a z-score indicate about the original score's position?
What does a z-score indicate about the original score's position?
What percentage of the population scores between 85 and 115 in IQ tests?
What percentage of the population scores between 85 and 115 in IQ tests?
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What is the mean IQ score typically set at?
What is the mean IQ score typically set at?
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What is the standard deviation commonly used in IQ testing?
What is the standard deviation commonly used in IQ testing?
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What proportion of the population score below 70 or above 130 in IQ tests?
What proportion of the population score below 70 or above 130 in IQ tests?
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What purpose do z-scores serve in a distribution?
What purpose do z-scores serve in a distribution?
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What does the alternative hypothesis (H1) predict?
What does the alternative hypothesis (H1) predict?
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How is the alpha level related to Type I errors?
How is the alpha level related to Type I errors?
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What does a sample mean consistent with the null hypothesis indicate?
What does a sample mean consistent with the null hypothesis indicate?
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What is a common value for the alpha level in research contexts?
What is a common value for the alpha level in research contexts?
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What does a significance level of 0.05 imply?
What does a significance level of 0.05 imply?
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What is the relationship between the alpha level and confidence intervals?
What is the relationship between the alpha level and confidence intervals?
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What does a large discrepancy between the data and the null hypothesis suggest?
What does a large discrepancy between the data and the null hypothesis suggest?
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What is typically considered an acceptable alpha level in research?
What is typically considered an acceptable alpha level in research?
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What does the critical region signify in hypothesis testing?
What does the critical region signify in hypothesis testing?
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What is a Type I error in hypothesis testing?
What is a Type I error in hypothesis testing?
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In a one-tailed test, where is the critical region located?
In a one-tailed test, where is the critical region located?
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If an alpha level of 0.05 is set, what proportion of the distribution is expected to fall in the critical region?
If an alpha level of 0.05 is set, what proportion of the distribution is expected to fall in the critical region?
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What type of hypothesis test predicts a specific direction of effect?
What type of hypothesis test predicts a specific direction of effect?
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What is the result of a Type II error in hypothesis testing?
What is the result of a Type II error in hypothesis testing?
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In the example of cognitive training, what does the hypothesis suggest?
In the example of cognitive training, what does the hypothesis suggest?
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What characterizes a left-tailed test?
What characterizes a left-tailed test?
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What is the primary focus of probability in relation to statistical data?
What is the primary focus of probability in relation to statistical data?
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Which requirement is NOT necessary for a sample to be considered random?
Which requirement is NOT necessary for a sample to be considered random?
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What does a percentile rank represent in a distribution?
What does a percentile rank represent in a distribution?
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What is the null hypothesis typically denoted by in statistical testing?
What is the null hypothesis typically denoted by in statistical testing?
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What does hypothesis testing aim to determine regarding a treatment applied to a population?
What does hypothesis testing aim to determine regarding a treatment applied to a population?
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During hypothesis testing, what must be done after predicting characteristics from the hypothesis?
During hypothesis testing, what must be done after predicting characteristics from the hypothesis?
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What happens if there is a significant discrepancy between the sample data and the hypothesis prediction?
What happens if there is a significant discrepancy between the sample data and the hypothesis prediction?
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Which of the following best describes the term 'confidence intervals'?
Which of the following best describes the term 'confidence intervals'?
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What is the mean of a z-score distribution?
What is the mean of a z-score distribution?
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If the original distribution of scores is normal, what shape will the z-score distribution take?
If the original distribution of scores is normal, what shape will the z-score distribution take?
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Which type of probability relies on personal judgment rather than statistical calculations?
Which type of probability relies on personal judgment rather than statistical calculations?
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In a distribution with a mean of μ = 100 and standard deviation of σ = 10, what is the z-score for a score of X = 130?
In a distribution with a mean of μ = 100 and standard deviation of σ = 10, what is the z-score for a score of X = 130?
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What does the deviation score indicate when calculating z-scores?
What does the deviation score indicate when calculating z-scores?
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Which of the following best describes empirical probability?
Which of the following best describes empirical probability?
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How does transforming raw scores into z-scores affect individual positions in the distribution?
How does transforming raw scores into z-scores affect individual positions in the distribution?
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If a distribution has a mean of μ = 60 and σ = 8, what X value corresponds to a z-score of z = -1.50?
If a distribution has a mean of μ = 60 and σ = 8, what X value corresponds to a z-score of z = -1.50?
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What does a right-tailed test aim to determine?
What does a right-tailed test aim to determine?
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Which of the following is true about a two-tailed test?
Which of the following is true about a two-tailed test?
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In a one-tailed test, how is the alpha level distributed?
In a one-tailed test, how is the alpha level distributed?
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When is a two-tailed test considered appropriate?
When is a two-tailed test considered appropriate?
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What does effect size indicate?
What does effect size indicate?
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Cohen's d is a measure used to represent what?
Cohen's d is a measure used to represent what?
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What characterizes a large effect size according to Cohen's d?
What characterizes a large effect size according to Cohen's d?
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How are critical regions defined in a two-tailed test?
How are critical regions defined in a two-tailed test?
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Study Notes
Raw Score
- A raw score is the original, unprocessed score from a test or assessment
- It represents 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 75 on another unless the tests have the same difficulty and scoring methods
- Raw scores need to be transformed into standardized scores (like z-scores) to allow for meaningful comparisons
Z-score
- A z-score describes a score's position within a distribution
- Raw scores are often transformed into z-scores to provide more information about the score's location
- The z-score transformation has two purposes:
- Locating the original score within the distribution
- Allowing for comparisons to other distributions that were transformed into z-scores
Mean Score & Standard Deviation
- The average IQ score is 100 (peak of the bell curve)
- Standard deviation in IQ testing is typically 15 points
- Approximately 68% of the population scores between 85 and 115 (within one standard deviation of the mean)
- About 95% score between 70 and 130 (within two standard deviations of the mean)
- Only about 2% score below 70 or above 130
Z-score Formula
- The z-score formula (deviation score) = (X-μ)/σ
- Measures the distance between a score (x) and the mean (μ).
- Divides the deviation score by the standard deviation (σ)
Z-score Distribution
- Z-score distribution has the same shape as the original distribution
- Z-scores will always have a mean of zero
Hypothesis Testing
- A hypothesis test uses sample data to evaluate hypotheses about populations
- A hypothesis concerns a population's parameter value
- Samples are selected to test the predicted characteristic based on the hypothesis
- Comparing sample data predictions with the hypothesis
- The goal is to determine whether a treatment has an effect
Alpha Level
- Alpha level (significance level) is a crucial concept in hypothesis testing
- Represents the probability of making a Type I error (rejecting a true null hypothesis)
- Common values include 0.05 (5%), 0.01 (1%), or 0.10 (10%). It sets a threshold for acceptable risk of error
Critical Region
- The critical region (rejection region) describes the set of values in a test statistic that leads to rejection of the null hypothesis.
- If the calculated test statistic falls within this region, the observed data is statistically significant enough to reject the null hypothesis.
Type I and Type II Errors
- A Type I error occurs when rejecting a true null hypothesis
- A Type II error occurs when failing to reject a false null hypothesis
Directional Tests
- Directional tests (one-tailed tests) specify the expected direction of the effect or relationship.
- They allocate the alpha level to one tail of the distribution
- One-tailed tests are appropriate when prior evidence suggests a particular direction
Effect Size
- Effect size is a numerical value expressing the strength of the relationship or difference between groups.
- A large effect size indicates practical significance; a small effect size suggests limited practical applications
- Cohen's d measures the standardized difference between two means. (d= (X1 - X2) / s)
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Description
This quiz covers essential concepts in statistics, including raw scores, z-scores, mean scores, and standard deviations. Understand how these scores are used to analyze and compare performance across different assessments. Test your knowledge and enhance your understanding of statistical methods.
