Statistics: Raw Scores and Z-scores
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Questions and Answers

What does a raw score represent in psychological statistics?

  • A standardized score for easy comparison
  • An original, unprocessed score from a test (correct)
  • A calculated average from multiple tries
  • A score adjusted for difficulty

Why are raw scores often transformed into z-scores?

  • To increase the difficulty of tests
  • To ensure all scores are standardized to 100
  • To simplify score calculations
  • To facilitate meaningful comparisons (correct)

What does a z-score indicate about the original score's position?

  • It reflects the score's total impact on performance
  • It indicates the percentage of scores below it
  • It shows the raw score's exact value
  • It tells whether the score is above or below the mean (correct)

What percentage of the population scores between 85 and 115 in IQ tests?

<p>About 68% (C)</p> Signup and view all the answers

What is the mean IQ score typically set at?

<p>100 (D)</p> Signup and view all the answers

What is the standard deviation commonly used in IQ testing?

<p>15 points (C)</p> Signup and view all the answers

What proportion of the population score below 70 or above 130 in IQ tests?

<p>Only about 2% (D)</p> Signup and view all the answers

What purpose do z-scores serve in a distribution?

<p>To describe the exact location of a score (D)</p> Signup and view all the answers

What does the alternative hypothesis (H1) predict?

<p>There is a change, difference, or relationship in the general population. (D)</p> Signup and view all the answers

How is the alpha level related to Type I errors?

<p>It denotes the risk of rejecting the null hypothesis when it is true. (A)</p> Signup and view all the answers

What does a sample mean consistent with the null hypothesis indicate?

<p>The sample mean should be around the population mean of 15.8. (C)</p> Signup and view all the answers

What is a common value for the alpha level in research contexts?

<p>0.05 (C)</p> Signup and view all the answers

What does a significance level of 0.05 imply?

<p>There is a 5% chance of incorrectly rejecting the null hypothesis. (C)</p> Signup and view all the answers

What is the relationship between the alpha level and confidence intervals?

<p>An alpha level of 0.01 corresponds to a 99% confidence interval. (D)</p> Signup and view all the answers

What does a large discrepancy between the data and the null hypothesis suggest?

<p>The null hypothesis should be rejected. (B)</p> Signup and view all the answers

What is typically considered an acceptable alpha level in research?

<p>0.05 (A)</p> Signup and view all the answers

What does the critical region signify in hypothesis testing?

<p>Values that indicate statistical significance (C)</p> Signup and view all the answers

What is a Type I error in hypothesis testing?

<p>Incorrectly rejecting a true null hypothesis (B)</p> Signup and view all the answers

In a one-tailed test, where is the critical region located?

<p>Entirely in one tail of the distribution (C)</p> Signup and view all the answers

If an alpha level of 0.05 is set, what proportion of the distribution is expected to fall in the critical region?

<p>0.05 (A)</p> Signup and view all the answers

What type of hypothesis test predicts a specific direction of effect?

<p>Directional test (A)</p> Signup and view all the answers

What is the result of a Type II error in hypothesis testing?

<p>Failing to reject a false null hypothesis (C)</p> Signup and view all the answers

In the example of cognitive training, what does the hypothesis suggest?

<p>Cognitive training improves performance on memory tasks (C)</p> Signup and view all the answers

What characterizes a left-tailed test?

<p>It tests if a parameter is less than a specified value (C)</p> Signup and view all the answers

What is the primary focus of probability in relation to statistical data?

<p>Predicting the likelihood of future events (B)</p> Signup and view all the answers

Which requirement is NOT necessary for a sample to be considered random?

<p>The sample must be large enough to represent the population (C)</p> Signup and view all the answers

What does a percentile rank represent in a distribution?

<p>The percentage of individuals scoring lower than a particular value (B)</p> Signup and view all the answers

What is the null hypothesis typically denoted by in statistical testing?

<p>H0 (A)</p> Signup and view all the answers

What does hypothesis testing aim to determine regarding a treatment applied to a population?

<p>Whether it has any measurable effect (C)</p> Signup and view all the answers

During hypothesis testing, what must be done after predicting characteristics from the hypothesis?

<p>Collect a random sample from the population (B)</p> Signup and view all the answers

What happens if there is a significant discrepancy between the sample data and the hypothesis prediction?

<p>The hypothesis is rejected (C)</p> Signup and view all the answers

Which of the following best describes the term 'confidence intervals'?

<p>A probability measure of a population parameter range (B)</p> Signup and view all the answers

What is the mean of a z-score distribution?

<p>Always equal to zero (B)</p> Signup and view all the answers

If the original distribution of scores is normal, what shape will the z-score distribution take?

<p>Normal distribution (B)</p> Signup and view all the answers

Which type of probability relies on personal judgment rather than statistical calculations?

<p>Subjective Probability (C)</p> Signup and view all the answers

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?

<p>2.00 (B)</p> Signup and view all the answers

What does the deviation score indicate when calculating z-scores?

<p>The distance in points between a score and the mean (A)</p> Signup and view all the answers

Which of the following best describes empirical probability?

<p>Calculated through experiments and observed data (C)</p> Signup and view all the answers

How does transforming raw scores into z-scores affect individual positions in the distribution?

<p>Positions remain unchanged (A)</p> Signup and view all the answers

If a distribution has a mean of μ = 60 and σ = 8, what X value corresponds to a z-score of z = -1.50?

<p>52 (B)</p> Signup and view all the answers

What does a right-tailed test aim to determine?

<p>If the parameter is greater than a specified value (A)</p> Signup and view all the answers

Which of the following is true about a two-tailed test?

<p>It assesses whether a parameter is significantly different in any direction. (B)</p> Signup and view all the answers

In a one-tailed test, how is the alpha level distributed?

<p>Concentrated entirely in one tail. (B)</p> Signup and view all the answers

When is a two-tailed test considered appropriate?

<p>When researchers want to detect any significant difference. (D)</p> Signup and view all the answers

What does effect size indicate?

<p>The strength of the relationship between two variables. (A)</p> Signup and view all the answers

Cohen's d is a measure used to represent what?

<p>The effect size calculated as the difference between two means. (B)</p> Signup and view all the answers

What characterizes a large effect size according to Cohen's d?

<p>0.8 (B)</p> Signup and view all the answers

How are critical regions defined in a two-tailed test?

<p>Both tails receive equal allocation of the alpha level. (D)</p> Signup and view all the answers

Flashcards

Raw Score

The original, unprocessed score obtained from a test or assessment. It reflects an individual's performance without any modifications.

Mean Score

The average score in a distribution. It represents the central point of the data.

Standard Deviation

A measure of how spread out data points are from the mean.

Z-score

A standardized score that indicates how many standard deviations an individual's score is away from the mean.

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Z-score Sign

The sign of a z-score tells you whether the score is above (+) or below (-) the mean.

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Z-score Magnitude

The magnitude of a z-score tells you how far the score is from the mean in terms of standard deviations.

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Z-score Transformation

Transforming raw scores into z-scores allows for meaningful comparison across different distributions.

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Z-score Probability

Z-scores can be used to determine the probability of a score occurring within a distribution.

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Mean of Z-Scores

The distribution of z-scores will always have a mean of zero.

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Standard Deviation of Z-Scores

The standard deviation of z-scores will always be one.

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Shape of Z-Scores

The distribution of z-scores will have the same shape as the original distribution.

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Deviation Score

The difference between a score and the mean. It tells us how far a score is from the mean in original units.

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Z-score Formula

The deviation score divided by the standard deviation. It indicates how many standard deviation units a score is from the mean.

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Classical Probability

Based on theoretical assumptions of equally likely outcomes. For example, flipping a fair coin has a 1/2 probability of landing heads.

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Empirical Probability

Based on observed data rather than theoretical assumptions. It's calculated by conducting experiments and recording outcomes.

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Hypothesis Testing

A statistical method that uses sample data to evaluate a hypothesis about a population. It involves setting up a hypothesis, collecting data, and comparing the data to the prediction made based on the hypothesis.

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Null Hypothesis

The hypothesis that states there is no effect of the treatment. It is the starting point for hypothesis testing, and the goal is to disprove it.

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Random Sample

A sample where every individual in the population has an equal chance of being selected. This is crucial for making valid inferences about the population.

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Percentile Rank

The percentage of individuals with scores at or below a particular value. It tells you how a score ranks relative to others.

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Percentile

A value that is identified by its rank. It represents the score at a specific percentile point.

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Probability

The likelihood of a future event occurring.

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Statistics

The process of analyzing data collected from past events to draw conclusions about those events. It helps make sense of the data and understand patterns.

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Probability Distributions

The study of probability distributions, which help assess the likelihood of various outcomes.

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Null Hypothesis (H0)

A statement that there is no difference or relationship between variables in the population. It's a baseline assumption that researchers aim to disprove.

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Alternative Hypothesis (H1)

A statement that there is a difference or relationship between variables in the population. It's the alternative to the null hypothesis.

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Type I Error (α)

The probability of incorrectly rejecting the null hypothesis when it is actually true. It's represented by the Greek letter alpha (α).

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Type II Error (β)

The probability of accepting the null hypothesis when it is false. It's represented as Beta (β).

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Alpha Level (α)

The level of risk a researcher is willing to take of committing a Type I Error. It's typically set at 0.05 (5%).

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Confidence Interval

The range of values in which the true population parameter is likely to lie.

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Statistical Significance

The degree to which data supports the alternative hypothesis. It represents the strength of evidence against the null hypothesis.

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Critical Region

A set of values for a test statistic that would lead to rejecting the null hypothesis. If the calculated test statistic falls within this region, it indicates that the observed data is sufficiently extreme under the null hypothesis, prompting rejection of the null hypothesis.

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Type I Error

An error made when a researcher rejects a true null hypothesis. In a typical research situation, it means concluding that a treatment has an effect when it doesn't.

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Type II Error

An error made when a researcher fails to reject a false null hypothesis. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.

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Directional Test

A hypothesis test where you predict the direction of the effect or relationship between variables (e.g., variable A is greater than variable B).

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Left-Tailed Test

A directional test that looks for evidence that the parameter is less than a specified value.

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Right-Tailed Test

A directional test that looks for evidence that the parameter is greater than a specified value.

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Two-Tailed Test

A statistical test that checks if a parameter is significantly different from a specified value, without specifying whether it's greater or lesser.

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One-Tailed Test

A statistical test that allocates the entire significance level to one tail of the distribution, making it easier to detect an effect in that specific direction.

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Effect Size

A numerical value that expresses the strength of the relationship between two variables or the size of the difference between groups.

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Cohen's d

A measure of the standardized difference between two means, often used to express the size of the effect in a study.

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Large Effect Size

A significant effect size indicates practical significance, meaning the findings are meaningful in real-world applications.

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Small Effect Size

A small effect size indicates limited practical applications, meaning the difference might not be meaningful in the real world.

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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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Raw Score and Hypothesis Testing PDF

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.

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