Lecture 9: Introduction to Inferential Statistics Flashcards
Inferential Statistics
Procedures for drawing conclusions about a population based on data collected from a sample
The z test: What it is and what it does
Comparing sample statistics to population statistics when the population variance (and thus standard deviation) is known.
Parametric test:
Assumes the population distribution is normal
Sampling Distribution
A sampling distribution is a distribution of sample means. Population means are, typically, a sampling
distribution grand mean.
Have a look at the slides for some helpful diagrams
Central Limit Theorem
A description of the distribution that would be obtained if you selected every possible sample, calculated every sample mean, and constructed a distribution of sample means. The central limit theorem states that for any population with a mean µ
Standard Error
The standard error is the standard deviation of a
sampling distribution. Calculated by dividing the population by the square root of sample N
Look at the slides for more helpful diagrams
z-test
The z-test represents finding the difference between the sample mean (X) and the population mean (µ) and the dividing by the standard error of the mean.
One-tailed and two-tailed z-tests
One-tailed and two-tailed tests have the same calculation. The difference is the cut off point for significance.
Theres a whole lot of diagrams and examples on the slides that you’ll have to have a look at
: )
Region of rejection:
The area of the sampling
distribution that lies beyond the test statistic’s critical value.
Confidence Intervals Based on the z Distribution
Estimation of population means based on confidence intervals rather than statistical hypothesis tests. For example, if you want to estimate a population mean based on sample data. This differs from the statistical test, which determined if the sample mean differed significant from the population mean
Confidence interval
A confidence interval is an interval of a certain length
that we can be ‘confident’ will contain the population mean (µ). e.g., a 95% confidence interval (CI) of 82.67 – 89.33 means we are 95% confident a population mean will fall
between these two values.
Assumptions and Appropriate Use of the z-test
The z-test is a parametric inferential test
The z-test is also based on a normal distributio
The z-test is a parametric inferential test
Parametric tests involve the use of parameters, or population characteristics. If the population mean and standard deviation is not known, the z-test is not appropriate.
The z-test is also based on a normal distribution
Small sample sizes often fail to form a normal distribution. If the sample size is small (N<30), the z-test may not be appropriate
The t test: What it is and what it does
The t-test is used when the population variance is
not known. The t-test, although symmetrical and bell-shaped, does not fit the standard normal distribution. Unless the sample size is quite large, the areas that apply for the z-test do not apply to the t-test. Every t with a different sample size has its own distribution. As N increases, the t distribution approaches normality.
