Statistics Levels of Measurement Quiz
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Questions and Answers

What is the focus of the lecture?

Statistical analysis of quantitative data.

At the nominal level of measurement, how are numbers used?

  • To specify distances between items
  • To rank attributes
  • To categorize attributes (correct)
  • To measure continuous variables

    • What level of measurement includes a true 0?

  • Nominal
  • Interval
  • Ordinal
  • Ratio (correct)

    • What do descriptive statistics do?

    <p>Describe the data.</p> Signup and view all the answers

    The mean is also referred to as the ______.

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

    What does the standard deviation indicate?

    <p>Variability index.</p> Signup and view all the answers

    What is the significance level commonly set at?

    <p>Both .01 and .05</p> Signup and view all the answers

    What do Chi-Squared tests compare?

    <p>Categorical independent and dependent variables.</p> Signup and view all the answers

    What does a type one error signify?

    <p>Rejecting the null hypothesis when correct</p> Signup and view all the answers

    What does the R value represent in multiple regression?

    <p>Strength of correlation</p> Signup and view all the answers

    What is the statistic used to test the correlation of answers in a repeated survey?

    <p>Pearson r or the interclass correlation coefficient</p> Signup and view all the answers

    What does interrater reliability test?

    <p>The extent to which independent raters or observers score the same things</p> Signup and view all the answers

    What is the statistic used for interrater reliability?

    <p>Cohen's kappa or interclass correlation coefficient</p> Signup and view all the answers

    What does internal consistency reliability assess?

    <p>How well the components of a measure consistently measure the same attribute</p> Signup and view all the answers

    What statistic is used to test internal consistency?

    <p>Cronbach alpha</p> Signup and view all the answers

    What does content validity measure?

    <p>Whether the content adequately reflects the construct of interest</p> Signup and view all the answers

    What is the statistic used for content validity?

    <p>Content validity index</p> Signup and view all the answers

    What does criterion validity assess?

    <p>The extent to which scores on a measure are consistent with a gold standard</p> Signup and view all the answers

    What statistics can be used to assess criterion validity?

    <p>Pearson r correlations, sensitivity and specificity assessments, or ROC curve</p> Signup and view all the answers

    What does construct validity measure?

    <p>The extent to which a measure is measuring the target construct</p> Signup and view all the answers

    What should you look for in a research article regarding t-tests?

    <p>The symbol 't' along with degrees of freedom and the p-value</p> Signup and view all the answers

    What indicates statistical significance if the p-value is set at 0.05?

    <p>A result with a p-value lower than 0.05 is considered statistically significant</p> Signup and view all the answers

    What symbol represents the chi-squared test in research articles?

    <p>Chi-squared symbol</p> Signup and view all the answers

    What provides insight into participants' opinions on their proficiency with words and numbers?

    <p>Frequencies of responses to questions about being better with words or numbers</p> Signup and view all the answers

    What percentage of the class is currently working as a nurse?

    <p>75 percent</p> Signup and view all the answers

    What is the mean age of participants in the class?

    <p>32</p> Signup and view all the answers

    What was the mean grade point average reported in the class?

    <p>3.59</p> Signup and view all the answers

    What was the mean positivity score of the class?

    <p>6.33</p> Signup and view all the answers

    What is used to test the correlation of answers from a survey given to the same group one week apart?

    <p>Pearson r or the interclass correlation coefficient</p> Signup and view all the answers

    What statistic is used to test inter-rater reliability?

    <p>Cohen's kappa or the interclass correlation coefficient</p> Signup and view all the answers

    What statistic is used to test internal consistency reliability?

    <p>Cronbach alpha</p> Signup and view all the answers

    What does content validity measure?

    <p>Whether the content adequately reflects the construct of interest</p> Signup and view all the answers

    What statistic is used to determine content validity?

    <p>Content validity index</p> Signup and view all the answers

    What is criterion validity?

    <p>The extent to which scores on a measure are consistent with a gold standard</p> Signup and view all the answers

    What statistics can be used for assessing criterion validity?

    <p>Pearson r correlations, sensitivity and specificity assessments, or the ROC curve</p> Signup and view all the answers

    What does construct validity assess?

    <p>The extent to which a measure is measuring the target construct</p> Signup and view all the answers

    What percent of the class is currently working as a nurse?

    <p>75%</p> Signup and view all the answers

    Which statistic indicates the mean age of the participants?

    <p>32</p> Signup and view all the answers

    What is the focus of the lecture on statistical analysis?

    <p>Understanding why statistical tests are used and how to interpret statistical information.</p> Signup and view all the answers

    Which level of measurement uses numbers simply to categorize attributes?

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

    What distinguishes interval level measurement from ratio level measurement?

    <p>Interval does not have a true zero.</p> Signup and view all the answers

    What are the three measures of central tendency?

    <p>Mean, median, and mode.</p> Signup and view all the answers

    What is the purpose of descriptive statistics?

    <p>To describe the data.</p> Signup and view all the answers

    What does the standard deviation indicate?

    <p>How close scores are to the mean.</p> Signup and view all the answers

    The null hypothesis states that there is a relationship between variables.

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

    Which statistical test is used to test for differences in means when dealing with three or more groups?

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

    What is meant by the term 'alpha level' in statistical testing?

    <p>The probability of making a type one error.</p> Signup and view all the answers

    What is the significance of a p-value of 0.05?

    <p>It indicates a 5% chance of a Type I error.</p> Signup and view all the answers

    In hypothesis testing, if the null hypothesis is true but is rejected, this error is called a ______.

    <p>Type I error</p> Signup and view all the answers

    The measure that denotes the number that occurs most often is called the ______.

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

    Study Notes

    Levels of Measurement

    • Nominal: Numbers are used to categorize attributes.
      • Example: Females = 1, Males = 2
    • Ordinal: Attributes are ranked incrementally.
      • Example: Survey question using a 1 to 5 scale, where 1 = strongly agree and 5 = strongly disagree
    • Interval: Attributes are ranked, and the distance between each item is specified.
      • Example: Time - the difference between 1 minute and 2 minutes is numerically known.
      • Difference from Ratio: Interval measurement does not have a true zero.
    • Ratio: Attributes are ranked, the specified distance between each level is defined, and it has a true zero.
      • Example: The number of siblings - a person can have 0 siblings.

    Descriptive Statistics

    • Used to describe the sample.
      • Example: Age, gender, race of participants
    • Frequency Distributions: Counts and percentages of how often a value occurs.

    Central Tendency

    • Refers to the typical result.
    • Three measures:
      • Mean (Average): Sum of all values divided by the number of participants.
      • Median: The point dividing scores in half.
      • Mode: The number that occurs most often.

    Standard Deviation

    • Variability index.
    • Shows how much scores deviate from the mean on average.

    Range

    • The highest score minus the lowest score.

    Bivariate Statistics

    • Involves two variables.
    • Crosstabs: Evaluating intersections of two variables.
    • Correlation: A correlation matrix displays multiple variables – usually displayed as a table.
      • Pearson's r statistic: Used to measure linear correlation.

    Hypothesis Testing

    • Provides objective criteria to decide whether to accept or reject a hypothesis.
      • Null hypothesis: States that there is no relationship between variables.
      • Research hypothesis: Indicates a relationship between variables.

    Errors in Hypothesis Testing

    • Type 1 Error: The researcher concludes there is a relationship between variables when there is not.
    • Type 2 Error: The researcher concludes there is no relationship between variables when there is.

    Bivariate Tests for Hypothesis Testing

    • T-Test:
      • Used with a dichotomous (two levels) independent variable and a continuous dependent variable.
    • ANOVA (Analysis of Variance):
      • Used when there are three or more groups.
      • Independent variable is in categories and dependent variable is continuous.

    Chi-Squared Test

    • Similar to a crosstab, but both the independent and dependent variables are categorical (broken into groups, not continuous).

    Multivariate Statistics

    • Examines the impact of several independent variables on a dependent variable.
    • Multiple Regression: The most used multivariate statistic.

    Significance Levels

    • Indicates that the test results are not likely due to chance.
    • The level of significance is the probability of making a Type I error.
    • Alpha level: The significance level, most commonly set at .05.
      • .01 is a stricter alpha level.

    Reliability

    • Refers to the consistency of a measurement.
    • Test-retest reliability: Two separate measurements using the same people.
      • Statistics used: Pearson r and the Interclass correlation coefficient.
    • Inter-rater reliability: Different raters/observers scoring the same thing.
      • Statistic used: Cohen's kappa and the Interclass correlation coefficient.
    • Internal consistency reliability: Examines how consistent a measure is within it.
      • Statistic used: Cronbach alpha.

    Validity

    • Refers to the accuracy of a measurement.
    • Content validity: Measures whether the content of a measurement reflects the construct being measured.
      • Statistic used: Content validity index.

    Validity

    • Criterion Validity: Measures how well a test aligns with a "gold standard" measure for the same concept.
    • Construct Validity: Assesses if a measure accurately captures the intended construct.

    Statistical Tests and Data Analysis

    • t-Test: Used to compare means of two groups. Reports t-value, degrees of freedom, and p-value.
    • Chi-Squared Test: Evaluates relationships between categorical variables. Displays chi-squared value, degrees of freedom, and p-value.
    • Pearson's r: Measures the strength and direction of a linear association between two continuous variables. Shows correlation coefficient (r) and p-value.
    • ANOVA: Analyzes differences between means of three or more groups. Reports F statistic.

    Class Data Analysis Example

    • Descriptive Statisics: Used to summarize data, like mean, standard deviation, minimum, and maximum.
    • Frequencies: Used to examine the distribution of categorical variables, like how many students chose each option for a survey question.
    • Example Data: The class data includes quantitative data like age, GPA, and survey responses, and qualitative data like student reflections.
    • Example Data Findings: The average age is 32, with the youngest student being 20 and the oldest being 53. The average GPA is 3.59. 75% of the class is currently working as a nurse.

    Levels of Measurement

    • Nominal: Numbers categorize attributes. Example: Female = 1; Male = 2
    • Ordinal: Provides an incremental ranking of attributes. Example: Survey rating scale of 1-5 (1: Strongly Agree; 5: Strongly Disagree)
    • Interval: Ranks attributes and specifies the distance between each item. Example: Time - the difference between 1 minute and 2 minutes is 1 minute. No true zero point.
    • Ratio: Ranks attributes, has a specified distance between each level, and has a true zero point. Example: Number of siblings - someone can have 0 siblings.

    Data Output and Outliers

    • Qualitative data is in words, quantitative data is in numbers.
    • Outliers must be corrected prior to calculating.

    Descriptive Statistics

    • Used to describe the data or sample.
    • Frequency Distribution: Gives the count and percentage of times a data point occurs.
    • Central Tendency: Tells the typical result.
      • Mean: Average of all values.
      • Median: Middle value when all scores are arranged in order.
      • Mode: Most frequent value.
    • Standard Deviation: Average difference of scores from the mean.
    • Range: Difference between highest and lowest scores.

    Bivariate Statistics: Analyzing 2 Variables

    • Crosstabs: Used to evaluate two variables at a time.
    • Correlation Matrix: This is used when multiple variables are presented in a correlation table.
    • Pearson R Statistic: A measure of the strength and direction of a linear relationship between two continuous variables.
    • Significance (p-value): This is the probability of obtaining the observed results if there is no association between the variables.
    • N: Number of samples included in the calculation.

    Community Health Statistics

    • Absolute Risk: The probability of an event occurring in a population.
    • Absolute Risk Reduction: The difference in risk between two groups.
    • Odds Ratio: The ratio of the odds of an event occurring in one group compared to another group.
    • Number Needed to Treat: The number of people who need to be treated with a particular intervention to prevent one event.

    Statistical Hypothesis Testing

    • Null Hypothesis: States there is no relationship between variables.
    • Research Hypothesis: States the relationship between variables.
    • Type I Error: Rejecting the null hypothesis when it is actually true (false positive).
    • Type II Error: Failing to reject the null hypothesis when it is actually false (false negative).

    Bivariate Tests for Hypothesis Testing

    • T-Test: Used when there are two groups (dichotomous independent variable) and a continuous dependent variable.
    • ANOVA (Analysis of Variance): Used to test for differences in means when there are three or more groups.
    • Chi-Squared Test: Similar to a cross-tab. Used when both the independent and dependent variables are categorical.

    Multivariate Statistics: Analyzing Multiple Variables

    • Multiple Regression: Used to examine the relationship between multiple independent variables and a single dependent variable.
    • R Value: A measure of the overall strength of the relationship between the independent variables and the dependent variable.

    Significance Levels and How They Relate to Alpha Levels

    • Statistical Significance: The results are not likely due to chance.
    • Level of Significance (Alpha Level): The probability of making a Type I error. Typically set at .05 or .01 (stricter).
    • p-value: The probability of obtaining the observed results if there is no association between the variables.

    Evaluating Reliability

    • Test-Retest Reliability: The consistency of results over time.
    • Inter-Rater Reliability: The consistency of results between different raters.
    • Internal Consistency Reliability: The consistency of results within a measure.

    Evaluating Validity

    • Content Validity: The extent to which the content of a measure adequately reflects the construct of interest.

    Validity

    • Criterion validity: Determines how well a measure aligns with a "gold standard" (reliable and recognized method for measuring the same thing)
    • Example: If there's a reliable way to measure happiness, how well do questions in a survey match that standard?
    • Common techniques for assessing criterion validity: Pearson r correlations, sensitivity and specificity evaluations, and ROC curves.
    • Construct validity: Assesses if a measure truly captures the specific concept or construct it aims to measure.
    • Examples of construct validity: Using hypothesis testing (t-tests, chi-squared tests, ANOVA) to compare groups or analyze relationships, supporting the intended construct measurement.

    Statistical Symbols in Research Articles:

    • t-test: Represented by "t," degrees of freedom, and p-value.
    • Chi-squared test: Represented by "χ²," degrees of freedom, and p-value.
    • Pearson's r test: Displayed as "r" and p-value.
    • ANOVA: Features the "F" statistic.

    Example Class Data:

    • descriptive statistics: age, GPA, levels of positivity
    • frequencies: e.g., whether students consider themselves better with words or numbers, working as a nurse.

    Class data examples

    • Age: 20 (youngest), 53 (oldest), average 32.
    • GPA: Average 3.59
    • Positivity: More optimistic than previous class, with a mean of 6.33.
    • Nursing: 75% of the class are currently working as registered nurses.

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    Description

    Test your understanding of the levels of measurement in statistics, including nominal, ordinal, interval, and ratio scales. This quiz will also cover descriptive statistics and measures of central tendency, enhancing your knowledge of statistical concepts and their applications.

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