Hypothesis Testing: Confidence Intervals (Test 1)

1) to measure variability in the data in an effort to assess the role of chance

2) to estimate effects after correcting for biases such as confounding

What are the 2 primary roles of the analysis of epidemiological data?

descriptive statistics

are generally concerned with organizing, tabulating, summarizing, depicting, or describing data; essentially reducing a large quantity of data to a manageable (and useable) form

inferential statistics

collecting data from a sample and are interested in drawing valid conclusions about a population based on information contained in a sample from that population which is the realm of what?

estimation and hypothesis testing

What are the 2 general categories of statistical inference?

statistics

descriptive measures computed from the data of a sample

parameters

measures computed from the data of a population (usually, but not always, symbolized by lower-case Greek letters)

the probability pattern (distribution) of the variables

Estimation and hypothesis testing are based on assumptions about what?

probability distribution

All the possible values of a variable and their relative frequency of occurrence

empirical distribution

actual data that you observe

statistical distribution

is a type of distribution defined by a theoretical probability distribution

expected

Statistical distribution describes the way in which random variables are ____________ to behave.

normal distribution

-for variables measured at the continuous level

-"bell curve" that is symmetrical around the mean

mean and standard deviation

What is the shape of a normal probability distribution defined by?

normal distribution examples

-height

-birth weight

-reading ability

-job satisfaction

-SAT scores

z-distribution (standard normal distribution)

special type of normal distribution where data are transformed so that the mean is 0 and the standard deviation is 1

t-distribution (Student's t-distribution)

very similar in shape and properties to the standard normal distribution (t distribution has wider tails); it is used when the sample size is small or when the population variance is unknown and has to be estimated from a sample

central limit theorem (CLT)

-fundamental to interval estimation and hypothesis testing

1.The mean of all sample means will equal the population mean.

2.The standard deviation of the sampled means is equal to the standard error of the mean.

3.As the sample size increases, the distribution of the sample means will approach a normal distribution regardless of the underlying distribution of the variable

point estimation

the process of finding a single value that is the best guess of an unknown population parameter

NO

Does point estimation provide information about random error?

interval estimation

is the process of associating with the point estimate a measure of statistical variation or random error

confidence interval (interval estimate)

consists of two numerical values defining a range of values that, with a specified degree of confidence, we feel covers the parameter being estimated

precision of a point estimate

Confidence intervals indicate what?

more

The smaller the random error, the _________ precise the estimate.

lower; higher

A wider confidence interval indicates __________ precision and a narrower confidence interval indicates ____________ precision.

statistical theory

is used to determine the distribution of the estimator (called a sampling distribution) and this information can be used to determine both the reliability coefficient and the standard error

size of the sample

What is the key component in standard error?

smaller

The larger the sample size, the __________ the standard of error

-confidence level

-sample size

What affects the confidence interval?

larger

A higher confidence level results in a ____________ reliability coefficient.

smaller

Larger sample sizes result in a ___________ standard error

95%

What % is the most common value in confidence levels for scientific disciplines?

hypothesis

-declarative sentence

-describes a relationship between 2 or more variables

-must be testable

null hypothesis

no relationship or no difference between groups or some variables

alternative hypothesis (research hypothesis)

opposite of the null hypothesis (there is a relationship or a difference)

null hypothesis

Do we test the null hypothesis or alternative hypothesis?

tails

Hypotheses have ________!

Two-tailed (2-sided or non-directional hypothesis)

Tests of ______________ are more common in biomedical literature.

-2 tailed

-1 tailed

What are the 2 types of hypotheses?

Type 1 error

rejecting the null hypothesis when it's actually true

Type 2 error

rejecting the null hypothesis when its actually false

power

__________ of the test is defined as the probability of correctly rejecting the null hypothesis when false ( 1- beta)

condtitional

Alpha, beta, and power are _________ probabilities.

alpha

level of significance or the significance level

before

Concepts related to power are often used in calculating necessary sample sizes _________ a study is conducted.

decreases

Alpha increases as beta _____________.

increases

Alpha decreases as beta ________________.

increase the sample size

How can you decrease both alpha and beta?

p value

is a measure that is often used to guide decision making when performing hypothesis testing

reject the null hypothesis

If the p value is less than or equal to alpha what do we do?

fail to reject the null hypothesis

If the p value is greater than alpha what do we do?

rejecting the null hypothesis

The smaller the p value, the "stronger" the evidence for what?