Statistics in Psychology PSYC 241 Week 5
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Questions and Answers

What does skewness in a distribution indicate?

  • The mean value of the dataset
  • The overall variability of the dataset
  • The extent to which the frequency curve is lopsided (correct)
  • The average deviation from the mean

In a positively skewed distribution, which of the following statements is true?

  • The mean is greater than both the median and mode (correct)
  • The mode is less than the median
  • The mean and median are equal to the mode
  • The distribution has more scores to the left of the mode

What does a critical value of +/- 3 indicate in terms of kurtosis?

  • The distribution exhibits high peakedness
  • The distribution is platykurtic
  • The distribution is perfectly normal
  • The distribution has excessive outliers (correct)

How does increasing the sample size affect the distribution?

<p>It decreases the variability of the sample mean (B)</p> Signup and view all the answers

What is the standard deviation representation for approximately 68% of data in a normal distribution?

<p>1SD (B)</p> Signup and view all the answers

Which measure of central tendency is most influenced by extreme values in a dataset?

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

Which visual representation is least likely to reveal the distribution shape of a dataset?

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

When calculating the mean IQ from several samples, what is the expected shape of the distribution of those means?

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

What is the primary result of collecting multiple samples from the same population?

<p>You obtain a sampling distribution of the means. (B)</p> Signup and view all the answers

How does the number of samples collected affect the mean of those sample means?

<p>The mean approaches the population mean as sample size increases. (C)</p> Signup and view all the answers

What does a greater standard error indicate about a sample statistic?

<p>Less precision in representing the population. (C)</p> Signup and view all the answers

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?

<p>67 (A)</p> Signup and view all the answers

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?

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

In the context of sampling distributions, what is the standard error of the mean?

<p>The average deviation of sample means from the mean of those sample means. (D)</p> Signup and view all the answers

What happens to the precision of a sample statistic as the standard error increases?

<p>Precision decreases. (A)</p> Signup and view all the answers

When plotting the means of several samples, what is the resulting distribution called?

<p>Sampling distribution of the means. (B)</p> Signup and view all the answers

What score is the cutoff for receiving an F?

<p>59 (D)</p> Signup and view all the answers

How many standard deviations is a score of 84 away from the mean if the average is 75 and the standard deviation is 8?

<p>1.125 (A)</p> Signup and view all the answers

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?

<p>-1.5 (C)</p> Signup and view all the answers

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?

<p>2.73 (D)</p> Signup and view all the answers

What percentage of people earn more than Ahmet's family given his z-score of 2.73?

<p>2.5% (C)</p> Signup and view all the answers

What is the z-score for a score of 100 in a distribution with a mean of 85 and a standard deviation of 5?

<p>3.0 (B)</p> Signup and view all the answers

Which of the following is true about the normal distribution?

<p>It is symmetric around the mean. (B)</p> Signup and view all the answers

What percentage of cases falls within 1 standard deviation from the mean in a normal distribution?

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

Flashcards

Skewness

The measure of asymmetry in a probability distribution.

Positive Skew

More scores are to the right of the mode than to the left.

Negative Skew

More scores are to the left of the mode than to the right.

Kurtosis

The measure of the steepness of the bell-shaped curve of a probability distribution.

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Normal Distribution

A symmetrical bell-shaped distribution with a mean, median, and mode at the same point.

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Sampling Distributions

Distribution of a sample statistic obtained from multiple samples of a population

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Critical Values (Skewness)

Values used to evaluate if a distribution is symmetrical, and not significantly skewed.

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Critical Values (Kurtosis)

Values used to evaluate if a distribution is mesokurtic (normal), leptokurtic (peaked), or platykurtic (flattened).

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Sampling Distribution of Means

The distribution of sample means obtained from multiple samples of the same population.

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Standard Error of the Mean

The average deviation of sample means from the population mean.

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Population Mean

The average value of a variable across the entire population.

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Sample Mean

The average value of a variable within a sample from a population.

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Precision of Sample Statistic

How accurately a sample represents the population, related to the standard error of the mean.

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More Samples, Closer to Population

The more samples taken, the closer the mean of sample means is to the population mean.

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Exam Score to Letter Grade

Determining a grade based on a standard score value above or below the mean.

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Cut-off Score for F Grade

Determined by 2 standard deviations below the mean.

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Z-score

A measure of how many standard deviations a data point is away from the mean.

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Standard Deviation

A measure of the spread or variability of data around the mean.

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Normal Distribution

A symmetrical distribution where data cluster around the mean.

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Mean

The average of a set of data.

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Cut-off score

A score used to distinguish between different groups or outcomes based on a normal distribution.

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2 SD above/below mean

Scores that lie 2 standard deviations above or below the mean, often used in grading or identifying extreme cases.

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Percentage of high earners

Proportion of individuals earning more or less than a given amount. Calculated using Z-score.

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Z-score table

A table that shows the area under the standard normal distribution curve between the mean and z-score. Used to calculate the probability related to a z-score.

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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 - XÌ„) / s where:
    • X = a particular person's score
    • XÌ„ = 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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PSYC 241 Week 5 Fall 2024 PDF

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.

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