7.5.2.2.1 Choosing a Statistical Test

• What are key phrases associated with unpaired data?

  Independent samples, different groups or subjects
• What type of data is represented by the number of pets?

  Numerical data
• Why is it important to determine if data is paired or unpaired?

  It indicates if data points are related or independent
• What is unpaired data?

  • Data points are independent
  • Come from different groups or subjects
  • Examples:
  • Test scores between male and female students
  • Satisfaction ratings from two different cities
• What defines ordinal data?

  Order or rank without uniform intervals
• What are the key phrases associated with ratio data?

  Equal intervals, true zero
• What are the two main types of data in statistics?

  • Categorical data
  • Numerical data
• What is the summary of data types in statistics?

  | Data Type | Description | Key Characteristics | Examples |

  |-------------|-----------------------------------|----------------------------------------|-----------------------------------|

  | Categorical | Describes categories or groups | Discrete, qualitative, no order | Eye color, gender, favorite sports |

  | Numerical | Represents numbers that can be measured | Continuous or discrete, quantitative, can be ordered | Height, age, test scores, number of pets |
• What defines ratio data?

  Equal intervals with a true zero point
• What is the first step in selecting the right statistical test?

  Identify the type of data
• What is paired data?

  • Data points are related
  • Come from the same subject or matched pair
  • Examples:
  • Student's exam scores before and after revision
  • Twins' blood pressure levels
• What are the key characteristics of categorical data?

  Discrete categories, qualitative, no order
• Why is it important to know if data is paired or unpaired?

  It affects the choice of statistical test
• What are hypotheses in research?

  Statements proposing an explanation for a question
• Which statistical test would you use to compare test scores between two groups?

  Independent t-test
• What should you do if the normality assumption is not met?

  Use a non-parametric test like Mann-Whitney U
• What is a null hypothesis?

  No effect exists
• Why is it important to identify the type of data?

  To select the right statistical test
• When are paired tests used in statistical analysis?

  For related samples
• What are the key characteristics of numerical data?

  Continuous or discrete, quantitative, can be ordered
• Why is it important to determine the level of measurement?

  To choose the most appropriate statistical test
• What are the four levels of measurement?

  1. Nominal
  2. Ordinal
  3. Interval
  4. Ratio
• What is the summary of the levels of measurement?

  | Level | Description | Examples |

  |---------|--------------------------------------------------|-----------------------------------|

  | Nominal | Categories with no inherent order | Eye color, gender |

  | Ordinal | Categories or numbers with order but non-uniform intervals | Satisfaction levels, contest rankings |

  | Interval| Equal intervals with no true zero | Temperature in Celsius, years |

  | Ratio | Equal intervals with a true zero | Height, weight, age, income |
• What is the key phrase associated with nominal data?

  Categories, labels, no order
• What does it mean for data to be normally distributed?

  Data follows a bell-shaped curve
• What are the key phrases associated with interval data?

  Equal intervals, no true zero
• What is an alternative to the t-test if homogeneity of variance is violated?

  Welch's t-test
• What factors should be considered when selecting a statistical test?

  • Data type (categorical or numerical)
  • Paired or unpaired data
  • Level of measurement (nominal, ordinal, interval, ratio)
• What does independence of data points mean?

  Data points should not be related to each other
• Which statistical test would you use to compare the weights of identical twins raised in different environments?

  Independent t-test
• How do you calculate the test statistic for an independent t-test?

  $t =$$\frac{\text{average score of Method 1} - \text{average score of Method 2}}{\text{standard error}}$
• Why is it important to check for independence in unpaired tests?

  To ensure valid statistical results
• What are the key steps in applying a statistical test?

  1. Set up the hypotheses (null and alternative)
  2. Calculate the test statistic
  3. Determine the p-value
  4. Make a decision
• What is the purpose of determining the p-value?

  It represents the probability of observed results
• How does the decision-making process depend on the p-value?

  It determines whether to reject H₀ or not
• Which test is appropriate for unpaired numerical data at the interval or ratio level?

  Independent t-test
• What does categorical data describe?

  Categories or groups
• What are the common statistical tests based on data characteristics?

  • Chi-square Test: Categorical, Unpaired, Nominal
  • Paired t-test: Numerical, Paired, Interval or Ratio
  • Independent t-test: Numerical, Unpaired, Interval or Ratio
  • Mann-Whitney U Test: Numerical, Unpaired, Ordinal
• Why is it important to match your research question and hypotheses to the statistical test?

  • Ensures focused analysis
  • Increases reliability of results
  • Helps in accurately answering the research question
• What are key phrases associated with paired data?

  Related samples, same subject or matched pairs