Statistical Inference

Statistical Inference

Definition

• The process of making conclusions or decisions about a population based on a sample of data
• Involves using statistical methods to make inferences about a population parameter

Types of Statistical Inference

• Estimation: making an educated guess about a population parameter based on a sample statistic
• Hypothesis Testing: testing a hypothesis about a population parameter based on a sample statistic

Estimation

• Point Estimation: estimating a population parameter with a single value
• Interval Estimation: estimating a population parameter with a range of values (confidence interval)

Hypothesis Testing

• Null Hypothesis (H0): a statement of no effect or no difference
• Alternative Hypothesis (H1): a statement of an effect or difference
• Test Statistic: a statistic used to decide between H0 and H1
• P-Value: the probability of observing a test statistic at least as extreme as the one observed, assuming H0 is true
• Significance Level (α): the maximum probability of rejecting H0 when it is true

Errors in Hypothesis Testing

• Type I Error: rejecting H0 when it is true
• Type II Error: failing to reject H0 when it is false

Confidence Intervals

• Margin of Error: the maximum amount by which the sample statistic may differ from the population parameter
• Confidence Level: the probability that the confidence interval contains the population parameter
• Width of the Interval: the range of values within which the population parameter is likely to lie

Statistical Inference

Definition and Purpose

• Statistical inference is the process of making conclusions or decisions about a population based on a sample of data
• It involves using statistical methods to make inferences about a population parameter

Types of Statistical Inference

Estimation

• Estimation involves making an educated guess about a population parameter based on a sample statistic
• There are two types of estimation:

Point Estimation

• Estimating a population parameter with a single value

Interval Estimation

• Estimating a population parameter with a range of values (confidence interval)

Hypothesis Testing

• Hypothesis testing involves testing a hypothesis about a population parameter based on a sample statistic
• There are two types of hypotheses:

Null Hypothesis (H0)

• A statement of no effect or no difference

Alternative Hypothesis (H1)

• A statement of an effect or difference
• The test statistic is used to decide between H0 and H1
• The p-value is the probability of observing a test statistic at least as extreme as the one observed, assuming H0 is true
• The significance level (α) is the maximum probability of rejecting H0 when it is true

Errors in Hypothesis Testing

• Type I Error:
  • Rejecting H0 when it is true
  • The probability of a Type I Error is α
• Type II Error:
  • Failing to reject H0 when it is false
  • The probability of a Type II Error is β

Confidence Intervals

• A confidence interval provides a range of values within which the population parameter is likely to lie
• The margin of error is the maximum amount by which the sample statistic may differ from the population parameter
• The confidence level is the probability that the confidence interval contains the population parameter
• The width of the interval is the range of values within which the population parameter is likely to lie

Learn about the process of making conclusions about a population based on a sample of data, including estimation and hypothesis testing.