What are the potential disadvantages of using non-parametric statistical methods?
- They always give inaccurate results
- They can be less powerful than parametric tests when assumptions for parametric tests are met
- They cannot be used for certain types of data
- They cannot handle large data sets
Non-parametric statistical methods can be less powerful than parametric tests when the assumptions for the parametric tests are met. This is because they use less information (e.g., they use ranks rather than actual values). Therefore, if the data does meet the assumptions of parametric tests, parametric tests might be preferred.
Hypothesis testing in statistics is a way to test the validity of a claim that is made about a _______.
- Dataset
- Population
- Sample
- Statistic
In statistics, hypothesis testing is typically used to test claims about a population parameter, not a sample statistic, dataset, or an individual statistic.
The _______ Information Criterion is a measure used in model selection that takes into account the goodness of fit and the simplicity of the model.
- Akaike
- Bayesian
- Pearson
- Spearman
The Akaike Information Criterion (AIC) balances goodness of fit with model simplicity by including a penalty for the number of parameters in the model. This discourages overfitting.
How would an outlier affect the confidence interval for a mean?
- It would make the interval narrower
- It would make the interval skewed
- It would make the interval wider
- It would not affect the interval
An outlier can significantly affect the mean and increase the variability in the data, which would lead to a larger standard error and thus a wider confidence interval.
What is the difference between descriptive and inferential statistics?
- Descriptive and inferential statistics are the same
- Descriptive statistics predict trends; inferential statistics summarize data
- Descriptive statistics summarize data; inferential statistics make predictions about the population
- Descriptive statistics summarize data; inferential statistics visualize data
Descriptive statistics provide simple summaries about the sample and the measures. It's about describing the collected data using the measures such as mean, median, mode, etc. On the other hand, inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. It is the process of using data analysis to deduce properties of an underlying distribution of probability.
Non-parametric tests are also known as ________ tests because they make fewer assumptions about the data.
- assumption-free
- distribution-free
- free-assumption
- free-distribution
Non-parametric tests are also known as distribution-free tests because they make fewer assumptions about the data, specifically, they do not require the data to follow a specific distribution.
How can you test the assumption of independence in a Chi-square test for goodness of fit?
- By calculating the standard deviation of the observations
- By conducting a separate Chi-square test of independence
- By conducting a t-test
- By examining the correlation between observations
To test the assumption of independence in a Chi-square test for goodness of fit, you can conduct a separate Chi-square test of independence. This test compares the observed frequencies in each category with what we would expect if the variables were independent.
How does skewness affect the relationship between the mean, median, and mode of a distribution?
- Changes the relationship
- Increases the standard deviation
- No effect
- Reduces the kurtosis
Skewness affects the relationship between the mean, median, and mode. In a positively skewed distribution, the mean is usually greater than the median, which is greater than the mode. In a negatively skewed distribution, the mode is usually greater than the median, which is greater than the mean.
Under what conditions does the Central Limit Theorem hold true?
- When the data is skewed
- When the population is normal
- When the sample size is sufficiently large
- When the standard deviation is zero
The Central Limit Theorem holds true when the sample size is sufficiently large (usually n > 30), regardless of the shape of the population distribution. This theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
How does effect size impact hypothesis testing?
- Effect size has no impact on hypothesis testing
- Larger effect sizes always lead to rejection of the null hypothesis
- Larger effect sizes always lead to smaller p-values
- Larger effect sizes increase the statistical power of the test
Effect size measures the magnitude of the difference or the strength of the relationship in the population. A larger effect size means a larger difference or stronger relationship, which in turn increases the statistical power of the test. Power is the probability that the test correctly rejects the null hypothesis when the alternative is true.