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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 Chi-Square Test

    statistical test

    Statistical test.

    Introduction to Chi-Square Test

    The Chi-Square test is a nonparametric statistical test that is used to determine if there is a significant association between two categorical variables in a sample. It is based on the difference between the observed frequencies in a categorical variable and the frequencies that we would expect to get by chance alone.

    Assumptions of the Chi-Square Test

    The Chi-Square test makes the following assumptions:

    1. The data in the cells should be frequencies, or counts of cases rather than percentages or some other transformation of the data.
    2. The groups or categories must be mutually exclusive.
    3. The data should be randomly sampled.

    Applications of Chi-Square Test

    The Chi-Square test is widely used in research. It is commonly used in biology to test the independence of two factors. In market research, it can be used to check the association between two categorical variables, like the association between brand preference and demographic variables.

    Steps to Perform Chi-Square Test

    1. State the hypotheses: The null hypothesis assumes that there is no association between the variables. The alternative hypothesis assumes that there is an association between the variables.
    2. Construct a contingency table: A contingency table (also known as a cross-tabulation, crosstab, or two-way table) is used in statistics to summarize the relationship between several categorical variables.
    3. Calculate the expected frequencies: The expected frequency counts are computed separately for each level of one categorical variable at each level of the other categorical variable.
    4. Compute the Chi-Square statistic: The Chi-Square statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.
    5. Interpret the result: If the Chi-Square statistic is large enough, you reject the null hypothesis and conclude that there is a significant association between the variables.

    Interpretation of Chi-Square Test Results

    The result of a Chi-Square test is a Chi-Square statistic and a p-value. If the p-value is less than the chosen significance level (typically 0.05), we reject the null hypothesis and conclude that there is evidence of an association between the variables.

    In conclusion, the Chi-Square test is a valuable tool in statistics. It allows us to determine the significance of the association between two categorical variables, providing valuable insights in various fields of study.

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    Next up: Mann-Whitney U Test