Statistics in Research and Data Distributions
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Statistics in Research and Data Distributions

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Questions and Answers

What is the definition of a population parameter in statistics?

  • A measure derived from a sample
  • An estimate of variability in a sample
  • A description of the sample mean
  • A numerical characteristic of a population (correct)

    • Which condition leads to the rejection of the null hypothesis?

  • When p < 0.05 (correct)
  • When p = 0.05
  • When p > 0.05
  • When p is equal to the sample mean

    • What does the mode represent in measures of central tendency?

  • The average of all scores
  • The height of the bell curve
  • The value that occurs most frequently (correct)
  • The middle value of a dataset

    • Which measure of variability is defined as the difference between the highest and lowest values?

    <p>Range</p> Signup and view all the answers

    In statistics, what does a z score represent?

    <p>A standardized score indicating how many standard deviations an element is from the mean</p> Signup and view all the answers

    Which of the following is true about frequency distributions?

    <p>They summarize data and show how often each value occurs.</p> Signup and view all the answers

    What does the standard deviation measure in a data set?

    <p>The dispersion or spread of values</p> Signup and view all the answers

    Which statistic helps to determine a score's position within a distribution?

    <p>Z score</p> Signup and view all the answers

    What effect does increasing the sample size have on the Standard Error of the Mean (SEM)?

    <p>SEM decreases because the sample gets closer to the population</p> Signup and view all the answers

    What do confidence intervals (CI) provide?

    <p>A range of scores within specific boundaries</p> Signup and view all the answers

    Which z score corresponds to a 90% confidence level?

    <p>1.645</p> Signup and view all the answers

    What is the primary purpose of hypothesis testing?

    <p>To determine if one treatment is more effective than another</p> Signup and view all the answers

    What is a Type I error in hypothesis testing?

    <p>Rejecting the null hypothesis when it is true</p> Signup and view all the answers

    When are parametric statistics typically used?

    <p>When samples assume a normal distribution</p> Signup and view all the answers

    Which of the following best describes a Type II error?

    <p>Failing to reject the null hypothesis when it is false</p> Signup and view all the answers

    What type of statistics would you use when normal distribution assumptions do not hold?

    <p>Non-parametric statistics</p> Signup and view all the answers

    Study Notes

    Statistics in Research

    • Statistics help analyze and interpret numbers in research, allowing for inferences and generalizations about populations.

    • Population measures are parameters, while sample measures are statistics.

    • Statistical tests produce a p-value to determine the significance of findings.

      • Reject the null hypothesis (Ho) if p < 0.05, indicating a statistically significant result.
      • Do not reject (or accept) Ho if p > 0.05, indicating no statistically significant difference.

    Data Distributions

    • A single dice roll results in a uniform distribution with equal probability for each outcome.

    • The sum of two dice rolls follows a normal distribution, represented by a bell curve shape.

    • Frequency distributions summarize data by showing the frequency of each value.

    Measures of Central Tendency

    • Mean: The average of all scores (sum of scores divided by the number of scores).
    • Median: The middle value in a ranked dataset, dividing the data into equal halves. More reliable than the mean for skewed data like income.
    • Mode: The most frequently occurring value in a dataset.

    Measures of Variability

    • Range: The difference between the highest and lowest values in a dataset.
    • Percentile: A score's relative position within a distribution, offering a comparative reference point.
    • Variance: Measures the variation within a complete set of scores.
    • Standard Deviation: Measures the spread or dispersion of values around the mean.
    • Coefficient of Variation: Ratio of standard deviation to the mean, useful for comparing variables with different units.

    Normal Distribution and Z-Scores

    • Many biological, psychological, and social phenomena exhibit a normal distribution.
    • Z-scores are standardized scores, allowing for percentile estimation based on a normal distribution.

    Standard Error of the Mean (SEM) and Confidence Intervals (CI)

    • SEM is the standard deviation of a theoretical sampling distribution of the mean.
    • SEM is estimated based on sample size and standard deviation.
    • As sample size increases, SEM decreases, signifying a closer approximation to the population mean.
    • SEM forms the basis for confidence intervals.
    • CI is a range of scores within specific boundaries, representing a degree of confidence (90%, 95%, 99%).
    • Z-scores associated with these confidence levels are used to calculate CI:
      • 90% = 1.645
      • 95% = 1.96
      • 99% = 2.58
    • CI offers a more accurate representation than mean +/- standard deviation.

    Statistical Inferences

    • Estimation of population characteristics from sample data is facilitated by statistical inferences.
    • These inferences rely on statistical concepts:
      • Probability: The likelihood of an event occurring given all possible outcomes.
      • Sampling Error: The tendency for sample values to differ from population values.

    Hypothesis Testing

    • Hypothesis testing involves comparing two or more groups to determine if observed differences are statistically significant.
    • The null hypothesis (Ho) states that there is no difference between group means, implying that they come from the same population.
    • The goal is to test Ho, but it is never actually "proven"; instead, the goal is to disprove it based on data evidence.
    • The alternative hypothesis (H1) suggests that observed differences are not due to chance and that the groups are different. It can be directional (greater than or less than) or non-directional (not equal to).

    Types of Errors in Hypothesis Testing

    • Type I Error (false positive): Rejecting Ho when it is true, denoted by alpha (α), with a typical significance level of 0.05.
    • Type II Error (false negative): Failing to reject Ho when it is false, denoted by beta (β), commonly with a 20% acceptance threshold.
    • Statistical power (1-β) refers to the sensitivity of a test to detect differences between groups, influenced by factors like alpha, variance, sample size, effect size, and the design of the test procedure.

    Parametric vs Non-Parametric Statistics

    • Parametric statistics assume that samples are randomly drawn from normally distributed populations with homogenous variances, allowing for population parameter estimation and arithmetic manipulation of scores.
    • Non-parametric statistics are used when parametric assumptions cannot be met, particularly with smaller samples, and utilize measures like the median. These methods do not assume a specific distribution.

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    Description

    This quiz covers essential concepts of statistics as applied to research, including population parameters and sample statistics. It also explores different data distributions, measures of central tendency, and the significance of statistical tests. Test your understanding of these fundamental statistical principles.

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