Data+ Exam DAO-001 - Lesson 11: Understanding the Use of Different Statistical Methods

Confidence Intervals

  • Confidence intervals provide a range of values within which a population parameter is likely to fall.
  • The Excel CONFIDENCE function can be used to calculate confidence intervals.
  • The function requires the alpha (significance level), standard deviation, and sample size as inputs.
  • Formula: =CONFIDENCE(alpha, standard_dev, size)
  • Alpha: Significance level, a number greater than 0 and less than 1.
    • Example: 0.05
  • Standard_dev: Standard deviation of the population.
  • Size: Sample size.
  • The CONFIDENCE function returns the confidence interval for a population mean using a normal distribution.

T-Tests and P-Values

  • T-test: A statistical test used to determine if there is a significant difference between the means of two groups.
  • Dependent variable: The variable being measured.
  • Independent variable: The variable that is different between the groups.
  • T-tests are appropriate for data that is normally distributed.
  • P-value: The probability that the observed difference between the means of two groups occurred by chance.
  • Statistical significance requires a significant difference that is unlikely to have occurred by chance.

Review Questions (Importance of Statistical Tests)

  1. Question: The calculation of values that describes the certainty or uncertainty of an estimate made on the analysis is known as what?
    • Answer: Confidence Intervals
  2. Question: What is the percentage of a confidence interval that is most commonly strived for in analysis?
    • Answer: Commonly 95%
  3. Question: What are the two variables we use when conducting a t-test?
    • Answer: Dependent and Independent Variables
  4. Question: Which two conditions must be met for data to be considered statistically significant?
    • Answer: Significance and not happened by chance
  5. Question: What does the "p" in p-value stand for?
    • Answer: Probability

Hypothesis Testing

  • Null Hypothesis (H0): Assumes there is no relationship between two variables.
    • Example: There is no relationship between the students having extra study hours and student score.
  • Alternative Hypothesis (Ha): Assumes that a relationship between two variables does exist.
    • Example: There is a relationship between the extra study hours and student score.

Understanding the Results of Hypothesis Testing

  • Type I Error: A false positive.
  • Type II Error: A false negative.

Review Questions (Getting Started with Analysis)

  1. Question: Which type of hypothesis assumes that a relationship between two variables does exist?
    • Answer: Alternative Hypothesis
  2. Question: Which type of hypothesis assumes that a relationship between two variables does not exist?
    • Answer: Null Hypothesis
  3. Question: Which type of error creates a false negative?
    • Answer: Type II error
  4. Question: What are some of the impacts of type I and type II errors on hypothesis testing? Use an example.

Chi-Square

  • Pronounced as \'ki-'skwer\
  • A chi-square statistic compares the size of the difference between the expected result and the actual result.
  • Used to measure how the model compares to the actual data.
  • A chi-square test can be used to determine if a difference exists between groups.
  • A chi-square test is used to compare actual results to what we expected the results would be.
  • A chi-square test also allows us to rule out that the observations happened by chance.
  • Chi-square testing identifies how confident we are that the results are (or are not) different from what we expected and that there is a relationship between the variables.
  • Chi-square testing is useful when we are analyzing data from a random sample and working with a categorical variable, like education, race, or gender.

Chi-Square Tests

  • Test of independence: Tests against multiple variables.
  • Goodness of fit: Tests against a single variable.

Example Chi-Square Data Set

  • Student Preparedness
    • Fail
    • Pass
    • Total
      • Very prepared: 9, 17, 26
      • Somewhat prepared: 11, 40, 51
      • Not Prepared: 12, 11, 23
      • Total: 32, 68, 100

Simple Linear Regression

  • Regression analysis is a statistical method used to estimate relationships between a dependent variable and one or more independent variables.
  • Simple linear regression is used to study the relationship between one dependent variable and one predictor, or independent variable.
  • Linear refers to the straight-line relationship between the two quantitative values. The analysis tells us which predictor may have the largest impact.

Correlation

  • Correlation is the statistical association between two (or more) equal variables.
  • Attempts to determine what relationship might exist between two variables; A relationship in which one variable is proven to have an effect on another would be considered a causal relationship.
  • To investigate whether a causal relationship exists, a correlation coefficient must be calculated.
  • Correlation does not imply causation.

Pearson's Correlation Coefficient

  • Calculation used to measure a linear relationship between the data points, returning a value that is plus or minus 1 to determine the strength of the relationship.
  • The correlation coefficient value is expressed as an r value.
    • An r value that is close to 1 tells us that there is a strong correlation between the values, while an r value of or close to 0 means there is no correlation.
    • R values between 0.4 and 0.7 represent a moderate correlation.
  • Coefficient of determination: Expressed as R2 or the square of the correlation coefficient value.
  • This value is used to interpret the determination, and it is easier to understand if you multiply it by 100%.

Using Excel for Statistical Methods

  • Excel provides built-in functions and tools for statistical analysis.
  • Statistical functions can be accessed through the Formulas tab.
  • The Data Analysis ToolPak add-in provides advanced statistical analysis options.
  • In later versions of excel you can work with the selected values in columns A, B, and C and use the analyze Data option

Review Questions (Getting Started with Analysis)

  1. Question: What type of analysis will typically involve an x and y scatter plot with a line?
    • Answer: Simple linear regression
  2. Question: What are two commonly used types of chi-square tests?
    • Answer: Test of independence and goodness of fit
  3. Question: Correlation is used to measure what?
    • Answer: The statistical association between two or more equal variables.
  4. Question: A relationship in which one variable is proven to have an effect on another would be considered what?
    • Answer: Causal relationship
  5. Question: Regarding simple linear regression, how do we refer to the variables and the outcome?
    • Dependent and independent variables

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