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Questions and Answers
What does skewness in a distribution indicate?
What does skewness in a distribution indicate?
In a positively skewed distribution, which of the following statements is true?
In a positively skewed distribution, which of the following statements is true?
What does a critical value of +/- 3 indicate in terms of kurtosis?
What does a critical value of +/- 3 indicate in terms of kurtosis?
How does increasing the sample size affect the distribution?
How does increasing the sample size affect the distribution?
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What is the standard deviation representation for approximately 68% of data in a normal distribution?
What is the standard deviation representation for approximately 68% of data in a normal distribution?
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Which measure of central tendency is most influenced by extreme values in a dataset?
Which measure of central tendency is most influenced by extreme values in a dataset?
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Which visual representation is least likely to reveal the distribution shape of a dataset?
Which visual representation is least likely to reveal the distribution shape of a dataset?
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When calculating the mean IQ from several samples, what is the expected shape of the distribution of those means?
When calculating the mean IQ from several samples, what is the expected shape of the distribution of those means?
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What is the primary result of collecting multiple samples from the same population?
What is the primary result of collecting multiple samples from the same population?
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How does the number of samples collected affect the mean of those sample means?
How does the number of samples collected affect the mean of those sample means?
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What does a greater standard error indicate about a sample statistic?
What does a greater standard error indicate about a sample statistic?
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If the mean is 75 and the standard deviation is 8, what is the cutoff score for failing (F) which is 2 SD below the mean?
If the mean is 75 and the standard deviation is 8, what is the cutoff score for failing (F) which is 2 SD below the mean?
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What letter grade corresponds to a score of 93 if the mean is 75 and the cutoff for an A is 2 SD above the mean?
What letter grade corresponds to a score of 93 if the mean is 75 and the cutoff for an A is 2 SD above the mean?
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In the context of sampling distributions, what is the standard error of the mean?
In the context of sampling distributions, what is the standard error of the mean?
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What happens to the precision of a sample statistic as the standard error increases?
What happens to the precision of a sample statistic as the standard error increases?
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When plotting the means of several samples, what is the resulting distribution called?
When plotting the means of several samples, what is the resulting distribution called?
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What score is the cutoff for receiving an F?
What score is the cutoff for receiving an F?
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How many standard deviations is a score of 84 away from the mean if the average is 75 and the standard deviation is 8?
How many standard deviations is a score of 84 away from the mean if the average is 75 and the standard deviation is 8?
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In a normal distribution with a mean of 70 and a standard deviation of 12, what is the z-score for a value of 58?
In a normal distribution with a mean of 70 and a standard deviation of 12, what is the z-score for a value of 58?
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If Ahmet's family earns 5230 TL per month, what is the z-score given the average income of 2500 TL and a standard deviation of 1000 TL?
If Ahmet's family earns 5230 TL per month, what is the z-score given the average income of 2500 TL and a standard deviation of 1000 TL?
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What percentage of people earn more than Ahmet's family given his z-score of 2.73?
What percentage of people earn more than Ahmet's family given his z-score of 2.73?
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What is the z-score for a score of 100 in a distribution with a mean of 85 and a standard deviation of 5?
What is the z-score for a score of 100 in a distribution with a mean of 85 and a standard deviation of 5?
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Which of the following is true about the normal distribution?
Which of the following is true about the normal distribution?
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What percentage of cases falls within 1 standard deviation from the mean in a normal distribution?
What percentage of cases falls within 1 standard deviation from the mean in a normal distribution?
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Study Notes
Statistics in Psychology PSYC 241
- Course: Statistics in Psychology PSYC 241
- Week: 5
- Topic: Shapes of distribution & z-score
- Fall: 2024
- Instructor: Demet Kara, PhD
Visualizing Data
- Methods: Pie chart, bar chart, histogram
Measures of Central Tendency
- Data: Mean, median, mode
Variability of Dataset
- Data: Range, variance, standard deviation
Areas under a Normal Distribution
- Data: 1SD-68%, 2SD-95%, 3SD-99%
Standard Normal Distribution
- Data: Normal bell curve with percentages for each standard deviation
Ways of Analyzing Distribution Shape
- Skewness: Extent to which the frequency curve is lopsided rather than symmetrical.
- Kurtosis: Steepness of the bell-shaped curve.
- Critical values for skewness: +/-1
- Critical values for kurtosis: +/-3
Non-normality in Distributions
- Negative Skew: More scores are to the left of the mode than to the right, and the mean and median are smaller than the mode.
- Positive Skew: More scores are to the right of the mode than to the left, and the mean and median are bigger than the mode.
- Critical values for both negative and positive skew are +/- 1
From Samples to Population
- Increasing sample size affects the distribution of sample means. Larger samples of sample means become closer to population mean.
Sampling Distributions
- Sampling a number of people from a population.
- Obtaining sample statistics (e.g. sample mean for IQ).
- Collecting the mean from multiple different samples from the same population.
- Plotting the means, which results in a sampling distribution of the means.
- The more samples obtained, the closer the mean of the sample means will be to the population mean.
Standard Error of the Mean
- Average deviation of sample means from the mean of the sample means.
- The greater the standard error, the less precisely a sample statistic represents the population.
Calculating Letter Grades
- Assume an example research methods exam situation where grading is based on 2 standard deviations
- Given average = 75
- Given standard deviation = 8
- Given an exam score = 93, student's score is greater than 2SD for A, hence an A grade.
- Given an exam score = 59, student's score is less than 2SD for F, hence an F grade.
Normal Distribution & Standard Deviation
- Assume normal distribution with mean 70 and standard deviation 12.
- Example to find the limits that would include the middle 68% of cases.
Z-scores
- Indication of how many standard deviations a value in a sample is away from the mean.
- Formula: z = (x - μ) / σ
- μ = Mean
- σ = Standard Deviation
- Z score of 0 = mean
- Z score of 1 = 1 SD above the mean
- Z score of -1 = 1 SD below the mean.
- Z scores are equally applicable to many different types of variables.
- Z scores are an universal way to measure variables.
Calculation 5.2- Converting scores to z-scores
- Formula: z = (X - X̄) / s where:
- X = a particular person's score
- X̄ = mean score of all scores
- s = standard deviation of all scores
Exercise
- Ahmet's family earns 5,230 TL per month. The average income in Turkey is 2,500 TL with a standard deviation of 1000 TL. What percentage of people earn more than Ahmet's family?
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Description
This quiz covers essential concepts in statistics relevant to psychology, focusing on the shapes of distributions and z-scores. Key topics include data visualization methods, measures of central tendency, variability, and the analysis of normal and non-normal distributions. Test your understanding of skewness, kurtosis, and standard deviations.
