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    Statistics 1-1

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    • Introduction to Statistics
      • 1.1Importance and Applications of statistics
      • 1.2Types of Data
      • 1.3Classification of Statistics
    • Descriptive Statistics
      • 2.1Measures of Central Tendency
      • 2.2Measures of Dispersion
    • Probability
      • 3.1Basic Probability Concepts
      • 3.2Conditional Probability
      • 3.3Theories of Probability
    • Probability Distribution
      • 4.1Probability Mass Function & Probability Density Function
      • 4.2Special Distributions: Binomial, Poisson & Normal Distributions
      • 4.3Central Limit Theorem
    • Sampling and Sampling Methods
      • 5.1Concept of Sampling
      • 5.2Different Sampling Techniques
    • Estimation and Hypothesis Testing
      • 6.1Point and Interval Estimation
      • 6.2Fundamentals of Hypothesis Testing
      • 6.3Type I and II Errors
    • Comparison of Two Populations
      • 7.1Independent Samples
      • 7.2Paired Samples
    • Analysis of Variance (ANOVA)
      • 8.1One-way ANOVA
      • 8.2Two-way ANOVA
    • Regression Analysis
      • 9.1Simple Regression
      • 9.2Multiple Regression
    • Correlation
      • 10.1Concept of Correlation
      • 10.2Types of Correlation
    • Nonparametric Statistics
      • 11.1Chi-Square Test
      • 11.2Mann-Whitney U Test
      • 11.3The Kruskal-Wallis Test
    • Statistical Applications in Quality and Productivity
      • 12.1Use of Statistics in Quality Control
      • 12.2Use of Statistics in Productivity
    • Software Application in Statistics
      • 13.1Introduction to Statistical Software
      • 13.2Statistical Analysis using Software

    Nonparametric Statistics

    Understanding the Mann-Whitney U Test

    The Mann-Whitney U test, also known as the Wilcoxon rank-sum test, is a nonparametric test of the null hypothesis that two samples come from the same population against an alternative hypothesis, especially that a particular population tends to have larger values than the other.

    Introduction to Mann-Whitney U Test

    The Mann-Whitney U test is used when your data do not meet the assumptions required for a t-test. It is a nonparametric test that allows you to determine if there are differences between two groups on a ranked dependent variable. It's often used in fields such as psychology, education, and other social and health sciences.

    Assumptions of the Mann-Whitney U Test

    The Mann-Whitney U test has several assumptions. It assumes that the dependent variable is at least ordinal, which means that it is rank-ordered. It also assumes that the independent variable is categorical with two categories or groups. Lastly, it assumes independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.

    Applications of Mann-Whitney U Test

    The Mann-Whitney U test is used in a variety of research contexts. For example, it could be used to test whether there is a difference in test scores between male and female students, or whether a new drug has different effects than a standard drug.

    Steps to Perform Mann-Whitney U Test

    1. Rank the data: Combine all data from the two groups into one data set and rank the data from lowest to highest. Assign ranks to each data point.

    2. Calculate U: Calculate U for each group. U is the sum of the ranks in each group minus the smallest possible rank that each group could have.

    3. Find the critical value of U: The critical value of U is found in a table of critical values and is based on the sample sizes of the two groups.

    4. Decision: If the calculated U is less than or equal to the critical value of U, reject the null hypothesis.

    Interpretation of Mann-Whitney U Test Results

    If the U value calculated is less than the critical U value from the table, then the null hypothesis is rejected and it is concluded that there is a significant difference between the two groups. If the calculated U value is greater than the critical U value, then the null hypothesis is not rejected and it is concluded that there is not a significant difference between the two groups.

    In conclusion, the Mann-Whitney U test is a powerful statistical tool that allows researchers to test hypotheses about ranked data. It is particularly useful when the assumptions of a t-test cannot be met.

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    Next up: The Kruskal-Wallis Test