Quantitative Methods Flashcards
Describe a nonparametric test and when its use may be appropriate.
Nonparametric tests either do not consider a particular population parameter or have few assumptions about the population that is sampled. They are used when there is concern about quantities other than the parameters of a distribution or when the assumptions of parametric tests can’t be supported. Also when the data are not suitable for parametric tests.
Describe a Parametric test.
Parametric tests rely on assumptions regarding the distribution of the population and are specific to population parameters.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the variances of two normally distributed populations based on two independent random samples.
The F-Test is calculated = (Variance of the sample of n observations drawn from population 1)/(variance of the sample of n2 observations drawn from population 2.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the variance of a normally distributed population.
The chi squared test (X^2). The chi-square distribution is asymmetrical and approaches the normal distribution as the degrees of freedom increase. The chi-square values correspond to the probabilities in the right-tail of the distribution (all positive).
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations.
T-statistics are involved and depend on the degrees of freedom. Note that when the samples are independent, you can use the difference in means test, and when they are dependent, the statistic is the average difference in (paired) observations divided by the standard error of the differences between observations.
Identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the population means of two at least approximately normally distributed populations, based on independent random samples with 1) equal or 2) unequal assumed variances.
The t-test is appropriate for both, though calculated differently. The variance of the pooled sample is used in the numerator when the sample variances are assumed to be equal. The sample variance for both populations are used when the population variance are unknown and assumed to be unequal. Interpreted as whether or not the sample means are very close together or not.
What are the 3 commonly used critical Z-values?
90% Confidence Interval = 1.65S 95% Confidence Interval = 1.96S 99% Confidence Interval = 2.58S
When is the Z-test appropriate?
It is appropriate when the population is normally distributed with a known population variance.
When is the t-test appropriate?
T-test is appropriate when the population variance is not known and either 1) the sample size is large (n>30) or 2) the sample size is small (n<30), but the distribution of the population is normal or approximately normal.
Chebyshev’s Inequality
1 - (1/k^2) K = number of std deviations This equation gives you the approximate percent of observations within a given number of standard deviations from the mean.
Calculate the odds of an event occurring.
P / (1 - P) P = the probability of an event occurring.
Explain and interpret the p-value as it relates to hypothesis testing.
It is the probability of obtaining a test statistic that would lead to a rejection of the null hypothesis, assuming the null hypothesis is true. It is the smallest level of significance for which the null hypothesis can be rejected.
Distinguish between a statistical result and an economically meaningful result.
There are factors outside of a statistical model that may make a statistically good strategy an economically unsound strategy. Some of these factors may include: - Transaction costs - Taxes - Closing out of short positions earlier than expected.
Explain the relation between confidence intervals and hypothesis testing.
Confidence Interval = [Sample Statistic - (Critical Value)(Std Error)] < Population Parameter < [Sample Statistic + (Critical Value)(Std Error)] - The Critical Value. i.e. a 95% confidence interval uses a critical value associated with a given distribution at the 5% level of significance, similar to a hypothesis test @ 5% level of significance.
Explain the power of a test.
- The probability of correctly rejecting the null when it is false. Calculated: 1 - P(Type 2 Error) - Used to determine which test statistic to use when multiple are available.
Excess Kurtosis
Sample Skewness
Portfolio Variance
