Data Analysis Oral Exam questionswith 100% correct answers

1. Explain the relationship between Type I errors, Type II errors, confidence level and power. How do you calculate the probability of occurrence for each of these elements in an experiment? A type 1 error is a false positive and occurs when a researcher incorrectly rejects a true null hypothesis. A type II error is when one accepts a null hypothesis that is actually false. The probability that the value of a parameter falls within a specified range of values. Power is the probability of avoiding a Type II error 2. What is the purpose of a power analysis? Explain the ways in which power can be increased Power analysis will tell you the probability of avoiding a Type II error. Using a larger sample is often the most practical way to increase power, using a higher significance level increases the probability that you reject the null hypothesis. 3. What is a p-value? How do p-values differ from effect sizes? Do sample sizes affect p-values? What about effect sizes? The p value will directly correlate to the hypothesis. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis. A significant p-value tells us that an intervention works, whereas an effect size tells us how much it works. In other words, which hypothesis is supported and by how much. Larger the sample size, smaller is the p-values if the null hypothesis is false. If your effect size is small then you will need a large sample size in order to detect the difference otherwise the effect will be masked by the randomness in your samples. 4. What are the assumptions for a one-sample t-test? Why are these assumptions necessary? How would violations to these assumptions affect the interpretation of the results of a t-test? The dependent variable must be continuous (interval/ratio). The observations are independent of one another. The dependent variable should be approximately normally distributed. The dependent variable should not contain any outliers. Assumptions are necessary or else the test won't be effective. The t-test won't be valid if one of the assumptions is violated. 5. How would small sample sizes affect a t-test and its assumptions? What about outliers? A sample size that is too small reduces the power, outliers skew the results. 6. How are a one-sample t-test and a paired-sample t-test similar? The test statistic for the Paired Samples t Test follows the same formula as the one sample t test. 7. Explain how an outlier in a set of raw scores might affect the results of a non-parametric test. Outliers reduce the probability of Type I errors and increase the probability of Type II errors, so that power declines. 8. Explain the difference between parametric and non-parametric tests. When is it appropriate versus inappropriate to use each type of test, and why? Parametric tests make assumptions about the parameters of the population distribution from a sample. Nonparametric statistics are not based on assumptions. The data can be collected from a sample that does not follow a specific distribution. 9. Explain how overgeneralization can affect your predicted values in a regression. Overgeneralization can skew the results and make them less accurate. 10. Why do we need to test for linearity when conducting a correlation and regression analysis? Regression and correlation needs the relationship between the independent and dependent variables to be linear. Or else the test is not effective. 11. What are residuals in a regression analysis? A residual is the vertical distance between a data point and the regression line 12. What are the similarities and/or differences between Pearson's r and Cohen's d? Cohen's d is a measure of relationship strength (or effect size) for differences between two group or condition means. ... Pearson's r is a measure of relationship strength (or effect size) for relationships between quantitative variables. 13. How is effect size calculated for a correlation/regression? The effect size is usually measured in three ways: (1) standardized mean difference, (2) odd ratio, (3) correlation coefficient. The effect size of the population can be known by dividing the two population mean differences by their standard deviation. 14. What is the purpose of calculating r adjusted? It shows how well terms (data points) fit a curve or line and also adjusts for the number of terms in a model 15. How is effect size calculated for chi-squared tests (goodness of fit or test of independence)? V = χ 2 n · d f , where n is total number of observation, and df is degrees of freedom calculated by (r - 1) * (c - 1). Here, r and c are the numbers of rows and columns of the contingency table. 16. Why do the critical values for a chi-squared distribution get larger as the degrees of freedom get larger (as opposed to the t and F distributions, in which larger degrees of freedom yield smaller critical values)? The d.f. is the number of opportunities that the statistic had to be large. More opportunities come from adding variables or adding categories in a frequency (contingency) table. The more opportunities (d.f.) the higher the critical value you must achieve to have evidence above the noise level. 17. Why do you divide by the expected frequencies or probabilities in chi-squared tests? χ2 is used to determine how well a particular model fits some observed data. Hence, we will need to check how different the model is to the observed data. We can check how different individual data points are from the expected values 18. How do outliers affect the results of a t-test, a chi-squared test, or a correlation/regression analysis? Outliers tend to increase the estimate of sample variance, thus decreasing the calculated t statistic and lowering the chance of rejecting the null hypothesis The chi-square statistic may be large due to the presence of outliers. An outlier that greatly affects the slope of the regression line 19. Explain why F = 1 in an ANOVA when the null hypothesis is true. An F-test is used to test if the variances of two populations are equal. a value of F=1 implies that the two variances are equal. 20. What is the difference between an ANOVA and an independent samples t-test? The t-test is a method that determines whether two populations are statistically different from each other, whereas ANOVA determines whether three or more populations are statistically different from each other. 21. Why do we need to test for homogeneity of variances when conducting an ANOVA? When homogeneity of variance is violated there is a greater probability of falsely rejecting the null hypothesis. 22. Explain the similarities and/or differences between the chi-squared, t and F distributions. A chi-square (χ2) statistic is a test that measures how a model compares to actual observed data. T test is used to determine if there is a significant difference between the means of two samples. An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different. 23. Describe the two ways in which you estimate the population variance in an ANOVA. In what circumstances are these estimates biased versus unbiased? Construct a test statistic that is a ratio of two different and independent estimates of an assumed common variance among populations. The numerator estimate is based on sample means and variation among groups. The denominator estimate is based on variation within samples. 24. Explain the difference between a treatment estimate of variance and the error estimate of variance in an ANOVA. How are they calculated? Error variance refers to variations caused by differences within individual groups Treatment variance is the average of all the variances for each population and is an estimate of whether the null hypothesis, H0 is true or not.