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Questions and Answers
A raw score is a processed score obtained from a test or assessment.
A raw score is a processed score obtained from a test or assessment.
False (B)
Raw scores are often transformed into standardized scores for meaningful comparisons.
Raw scores are often transformed into standardized scores for meaningful comparisons.
True (A)
A standard deviation in IQ testing is typically 10 points.
A standard deviation in IQ testing is typically 10 points.
False (B)
Approximately 68% of the population scores between 70 and 130 on IQ tests.
Approximately 68% of the population scores between 70 and 130 on IQ tests.
A z-score indicates whether a score is above or below the mean.
A z-score indicates whether a score is above or below the mean.
Only about 2% of the population scores above 130 in IQ testing.
Only about 2% of the population scores above 130 in IQ testing.
The peak of the bell curve for IQ scores is set at 115.
The peak of the bell curve for IQ scores is set at 115.
Transforming X values into z-scores does not affect their original meaning.
Transforming X values into z-scores does not affect their original meaning.
Probability relies on random samples to be accurately defined.
Probability relies on random samples to be accurately defined.
Sampling without replacement is a requirement for random sampling.
Sampling without replacement is a requirement for random sampling.
The null hypothesis states that the treatment has an effect on the individuals.
The null hypothesis states that the treatment has an effect on the individuals.
Percentile ranks indicate the proportion of individuals scoring above a particular X value.
Percentile ranks indicate the proportion of individuals scoring above a particular X value.
Hypothesis testing always begins with an assumption about a population parameter.
Hypothesis testing always begins with an assumption about a population parameter.
Statistics focuses on predicting future events based on past data.
Statistics focuses on predicting future events based on past data.
The sample mean is compared to the prediction made from a hypothesis during hypothesis testing.
The sample mean is compared to the prediction made from a hypothesis during hypothesis testing.
A percentile indicates how many individuals scored below a specific value in a distribution.
A percentile indicates how many individuals scored below a specific value in a distribution.
The distribution of z-scores will always have a mean of one.
The distribution of z-scores will always have a mean of one.
Transforming raw scores into z-scores changes the position of individuals within the distribution.
Transforming raw scores into z-scores changes the position of individuals within the distribution.
If the original distribution is normal, the resulting z-score distribution will also be normal.
If the original distribution is normal, the resulting z-score distribution will also be normal.
The deviation score is obtained by subtracting the mean from a raw score and dividing the result by the standard deviation.
The deviation score is obtained by subtracting the mean from a raw score and dividing the result by the standard deviation.
Classical probability is based on observed data rather than theoretical assumptions.
Classical probability is based on observed data rather than theoretical assumptions.
Empirical probability is calculated by conducting experiments and recording outcomes.
Empirical probability is calculated by conducting experiments and recording outcomes.
Subjective probability is derived from calculated outcomes and exact measurements.
Subjective probability is derived from calculated outcomes and exact measurements.
Probability is used in statistics to make inferences about populations based on sample data.
Probability is used in statistics to make inferences about populations based on sample data.
The null hypothesis states that there is a change, a difference, or a relationship in the general population.
The null hypothesis states that there is a change, a difference, or a relationship in the general population.
A sample mean that is very different from 15.8 is not consistent with the null hypothesis.
A sample mean that is very different from 15.8 is not consistent with the null hypothesis.
The alpha level represents the probability of making a Type II error.
The alpha level represents the probability of making a Type II error.
An alpha level of 0.05 corresponds to a confidence interval of approximately 95%.
An alpha level of 0.05 corresponds to a confidence interval of approximately 95%.
The alternative hypothesis suggests that the independent variable does not have any effect on the dependent variable.
The alternative hypothesis suggests that the independent variable does not have any effect on the dependent variable.
A researcher can set the alpha level to values such as 0.01, 0.05, or 0.10 depending on the context.
A researcher can set the alpha level to values such as 0.01, 0.05, or 0.10 depending on the context.
If the null hypothesis is supported, it means the sample data is consistent with the predicted hypothesis.
If the null hypothesis is supported, it means the sample data is consistent with the predicted hypothesis.
A sample mean near 20 would be consistent with the null hypothesis stating the population mean is μ = 15.8.
A sample mean near 20 would be consistent with the null hypothesis stating the population mean is μ = 15.8.
The critical region is where one would accept the null hypothesis.
The critical region is where one would accept the null hypothesis.
Setting an alpha level of 0.05 means 5% of the distribution lies outside the critical region.
Setting an alpha level of 0.05 means 5% of the distribution lies outside the critical region.
A Type I error occurs when a null hypothesis that is true is not rejected.
A Type I error occurs when a null hypothesis that is true is not rejected.
A Type II error means failing to detect a real effect in the treatment.
A Type II error means failing to detect a real effect in the treatment.
Directional tests, or one-tailed tests, focus on both tails of the distribution.
Directional tests, or one-tailed tests, focus on both tails of the distribution.
In a left-tailed test, the parameter being tested is expected to be greater than a specified value.
In a left-tailed test, the parameter being tested is expected to be greater than a specified value.
A directional hypothesis clearly indicates the expected outcome of a relationship between variables.
A directional hypothesis clearly indicates the expected outcome of a relationship between variables.
In hypothesis testing, the critical region is located in both directions for one-tailed tests.
In hypothesis testing, the critical region is located in both directions for one-tailed tests.
A one-tailed test contains two critical regions that each receive half of the alpha level.
A one-tailed test contains two critical regions that each receive half of the alpha level.
A two-tailed test is more suitable for exploratory research where any change is of interest.
A two-tailed test is more suitable for exploratory research where any change is of interest.
Effect size indicates the statistical significance of a research finding.
Effect size indicates the statistical significance of a research finding.
Cohen's d is used to measure the standardized difference between two means.
Cohen's d is used to measure the standardized difference between two means.
A large effect size suggests that a research finding has limited practical significance.
A large effect size suggests that a research finding has limited practical significance.
A right-tailed test is appropriate when there is no prior evidence suggesting a directional effect.
A right-tailed test is appropriate when there is no prior evidence suggesting a directional effect.
The critical values in a two-tailed test are split evenly between both tails for the alpha level.
The critical values in a two-tailed test are split evenly between both tails for the alpha level.
The classification of Cohen's d values includes 0.2 as a large effect.
The classification of Cohen's d values includes 0.2 as a large effect.
Flashcards
Raw Score
Raw Score
The original score on a test or assessment, representing an individual's performance without any modifications. It acts as the starting point for further statistical analysis.
Z-score
Z-score
A transformed score that indicates how many standard deviations a raw score is above or below the mean of a distribution.
Mean Score
Mean Score
The average of all the scores in a distribution. It represents the central tendency of the data.
Standard Deviation
Standard Deviation
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Standardization
Standardization
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Sign of a Z-score
Sign of a Z-score
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Value of a Z-score
Value of a Z-score
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Standardized Distribution
Standardized Distribution
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Shape of Z-score Distribution
Shape of Z-score Distribution
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Mean of Z-score Distribution
Mean of Z-score Distribution
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Standard Deviation of Z-score Distribution
Standard Deviation of Z-score Distribution
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Z-score Formula
Z-score Formula
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Probability
Probability
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Classical Probability
Classical Probability
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Empirical Probability
Empirical Probability
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Hypothesis testing
Hypothesis testing
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Null Hypothesis (H0)
Null Hypothesis (H0)
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Random Sampling
Random Sampling
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Statistics
Statistics
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Percentile value
Percentile value
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Percentile Rank
Percentile Rank
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Inferential Statistics
Inferential Statistics
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Alternative Hypothesis (H1)
Alternative Hypothesis (H1)
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Alpha Level (α)
Alpha Level (α)
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Type I Error
Type I Error
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Type II Error
Type II Error
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Confidence Interval
Confidence Interval
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Consistent with the Null Hypothesis
Consistent with the Null Hypothesis
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Critical Region
Critical Region
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Directional Hypothesis
Directional Hypothesis
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Directional Test (One-Tailed Test)
Directional Test (One-Tailed Test)
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Left-Tailed Test
Left-Tailed Test
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Right-Tailed Test
Right-Tailed Test
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Two-Tailed Test
Two-Tailed Test
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One-Tailed Test: Critical Region
One-Tailed Test: Critical Region
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Two-Tailed Test: Critical Region
Two-Tailed Test: Critical Region
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Effect Size
Effect Size
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Cohen's d
Cohen's d
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Interpretation of Effect Size
Interpretation of Effect Size
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Study Notes
Raw Score
- 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 analysis.
- Raw scores lack context; scores of 75 on different tests may not be comparable if tests differ in difficulty or scoring.
- Raw scores are often transformed (like z-scores) for meaningful comparisons.
Z-score
- A z-score describes a score's position within a distribution.
- It provides information about how far a score is from the mean, in standard deviation units.
- Raw scores are transformed into z-scores to locate their exact position in a distribution.
- Z-scores create a standardized distribution; it's directly comparable to other z-score distributions.
- Z-scores have a mean of zero.
- The sign (+ or −) of a z-score shows whether the score is above or below the mean.
- The numerical value of the z-score represents the distance from the mean in terms of standard deviations.
Mean Score and Standard Deviation
- The average IQ score is set to 100.
- Standard deviation (SD) in IQ testing is typically 15 points.
- Approximately 68% of scores fall within one SD of the mean (85-115).
- About 95% fall within two SDs of the mean (70-130).
- Only about 2% of scores fall below 70 or above 130.
Z-score Formula
- The z-score formula (z = (X - μ) / σ) calculates the z-score.
- X is the individual score.
- μ is the population mean.
- σ is the population standard deviation.
- The formula measures the distance of a score from the mean in standard deviation units.
Probability
- Probability assesses the likelihood of different outcomes in a situation with multiple possibilities.
- Probability is expressed as a fraction or proportion of all possible outcomes.
- Different types of probability include classical, empirical, and subjective.
- Probability is used to make predictions about populations based on sample data.
Hypothesis Testing
- Hypothesis testing is a statistical method to evaluate hypotheses about populations using sample data.
- First, state a hypothesis about the population, focusing on the value of a population parameter.
- Obtain a sample and compare the sample's data to the prediction made.
- If sample data matches the prediction, the hypothesis is reasonable.
- If the data differs significantly from the prediction, the hypothesis is deemed incorrect.
Alpha Level
- The alpha level (significance level) represents the probability of incorrectly rejecting a true null hypothesis.
- Common alpha levels are 0.05 (5%), 0.01 (1%), or 0.10 (10%).
- A higher alpha level means a higher risk of committing a Type I error (rejecting a true null hypothesis).
Critical Region
- The critical region contains values of a test statistic that would lead to rejecting the null hypothesis.
- If the calculated test statistic falls within this region, the observed data strongly contradicts the null hypothesis.
- The alpha level determines whether a calculated test statistic lies within the critical region.
Type I and Type II Errors
- A Type I error occurs when a true null hypothesis is rejected.
- A Type II error occurs when a false null hypothesis is not rejected.
Directional Tests
- Directional tests (one-tailed tests) specify the expected direction of the effect or relationship.
- They focus on one tail of the distribution where the critical region is located.
- These tests are appropriate when the expected outcome is already known.
Effect Size
- Effect size is a numerical value representing the strength of a relationship between variables or a difference between groups.
- Large effect sizes indicate practical significance, small effect sizes indicate limited practical applications.
- Cohen's d measures the standardized difference between two means.
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Description
Test your knowledge on raw scores, standard deviations, and IQ scoring in this statistics quiz. You'll explore concepts like z-scores, null hypothesis, and percentile ranks, focusing on their applications in assessment and research. Perfect for students looking to deepen their understanding of statistical methods.
