Mastering Statistical Analysis in R

What is the purpose of hypothesis testing in statistics?

• The purpose of hypothesis testing is to determine if there is enough evidence in a sample to infer that a certain condition holds for the entire population.

• To summarize data without making any inferences.

• To prove a hypothesis is true without any evidence.

• To collect data without any statistical analysis.

Explain the difference between Type I and Type II errors.

• Type I error: false negative; Type II error: false positive.

• Type I error: true negative; Type II error: true positive.

• Type I error: false positive; Type II error: false negative.

• Type I error: missed detection; Type II error: confirmed detection.

What is a p-value and how is it interpreted?

• A p-value is a measure of the probability that an observed result would occur by chance under the null hypothesis.

• A p-value measures the effect size of a statistical test.

• A p-value is the probability of the null hypothesis being true.

• A p-value indicates the strength of the alternative hypothesis.

Describe the Central Limit Theorem and its significance.

• The Central Limit Theorem applies only to small sample sizes.

• The Central Limit Theorem states that all populations are normally distributed.

• The Central Limit Theorem indicates that sample means will always equal the population mean.

• The Central Limit Theorem is a fundamental statistical principle that states that the means of sufficiently large samples from a population will be normally distributed, regardless of the population's distribution.

What is the difference between parametric and non-parametric tests?

• Parametric tests can only be used with small sample sizes, while non-parametric tests can be used with large samples.

• Non-parametric tests require a specific distribution; parametric tests do not.

• Parametric tests assume a specific distribution; non-parametric tests do not.

• Parametric tests are always more accurate than non-parametric tests.

How do you interpret a confidence interval?

• A confidence interval shows the exact value of the population parameter.

• A confidence interval is a measure of the sample size used in the study.

• A confidence interval indicates the probability of a sample mean being accurate.

• A confidence interval indicates the range of values that likely contains the true population parameter.

What is linear regression and when would you use it?

• Linear regression is used for predicting outcomes and understanding relationships between variables.

• Linear regression is only used for categorical data analysis.

• Linear regression is a method for clustering data points.

• Linear regression is primarily used for time series forecasting.

Explain the concept of correlation and how it differs from causation.

• Correlation indicates a relationship between variables, while causation indicates a direct cause-and-effect relationship.

• Correlation and causation are interchangeable terms.

• Causation is a statistical measure of how two variables relate.

• Correlation implies that one variable causes the other.

What is ANOVA and when is it used in data analysis?

• ANOVA is used to analyze single-variable data.

• ANOVA is a method for predicting future outcomes.

• ANOVA compares the median values of two groups.

• ANOVA is a statistical method used to compare means among three or more groups.

How can you check for normality in a dataset?

• Apply linear regression to determine normality.

• Check for normality by calculating the range of the dataset.

• Use visual methods (Q-Q plots, histograms) and statistical tests (Shapiro-Wilk, Kolmogorov-Smirnov) to check for normality.

• Use only mean and median to assess normality.