Biostats Test 2

When should a Bar Plot be used?

- The data is normally distributed

- Comparing means

When should a Means Plot be used?

- Data is ranked or quantitative

- Comparing means

When Should a Box Plot be used?

- Data is skewed or has outliers

- Comparing medians

When should a Scatter Plot be used?

- Relationship between quantitative variables

- Checking assumptions for linear models

Frequency Distribution

A list of values in a dataset and how often they occur

- Grouped into bins for a histogram

- Smooth density curve

Density Curve

- The area under the curve represents probability and may be called a probability density function.

- Enables us to calculate the probability of a certain range of data values.

Normal distribution

Can be described by mu (population mean) and sigma (standard deviation)

Central Limit Theorem (CLT)

The averages calculated from independent, random samples will approach a normal distribution as sample size increases, regardless of the population distribution from which the samples are taken

Standard error of the means

Measures the precision of a sample mean as an estimate of the true population mean, representing the standard deviation of the sampling distribution of the mean

Kurtosis

Quantifies tailedness of a distribution

Standard normal Distribution

Symmetric, bell-shaped probibility distribution with a mean of 0. Also called a z-distribution.

Characteristics of a standard normal distribution

x = 0, SD = 1, skew = 0, kurtosis = 3, and area = 1

What percentage is within 1 SD

68%

What percentage is within 2 SD

95%

What percentage is within 3SD

99.7%

Advantages of standard normal distribution

1) Easier to calculate probabilities

2) Can directly compare different distributions

What is a z-score?

Measures a value relationship to the mean of a group in terms of standard deviation

Confidence Interval

Calculates margin or error around a statistic

Standard deviation

Communicates distribution of a symmetrical dataset; not influenced by sample size and good for illustrating data structure

Standard error

Communicate probability that the population mean falls within a given range; bars indicate range with 68%; Gets smaller as n increases

Confidence Interval

Communicates probability the population mean falls within a given range; bars indicate 90%, 95%, or 99% chance

Margin of error

Degree of uncertainty

Null Hypothesis

The hypothesis tested when performing significance test

Alternate Hypothesis

One or two sided hypotheses that differ from the null hypothesis

Whis hypothesis uses =

Null

What hypothesis uses ≠

Two sided alternative hypothesis

What hypothesis uses < or >

One sided alternative hypothesis

Steps in a Z-test

1) State Ho & Ha

2) Calculate test statistic that shows how “compatible,” the collected data are with the Ho

3) Based on how “compatible” the data are with the null, we form a conclusion about the null hypothesis

4) Clearly state conclusion

p > alpha

Fail to reject Ho

p <= alpha

Reject Ho

What does a conclusion look like?

We have evidence to ________ the null hypothesis

Biological Hypothesis

Clearly state proposed description of how a system works that includes

1) Biological Mechanism

2) Testable statement of cause and effect

Biological Prediction

Follows logically from hypothesis

1) Explain what will happen under conditions set

2) Measureable dependent variable

Biological vs. Statistical hypothesis

Biological is the intellecual driver behind research while statistical is the tool to provide logical framework for data analysis

Statistical hypothesis

Testable claims under a population parameter that are evaluated using sample data that involves two mutually exclusive statements (Ho & Ha)

Types of error

Type 1: Rejecting Ho that is true

- Frequency set by alpha

Type 2: Failing to reject Ho that is false

- Frequency set by beta

Why do we use statistics?

To help us sort among hypotheses to find the best explanations of what we are observing

t vs z distribution

t is used when the population standard deviation is unknown

What is a one-sample t-test

1) Compares a sample mean to an expected mean

2) population standard deviation is unknown

Assumptions met during a one-sample t-test

1) Data is independent

2) Data is random

3) Data is normally distributed (Histogram & QQ plot)

t-test qualifications for sample size

n < 15; even distribution

15 <= n < 40; Slight skew

n >= 40; there are no outliers

Non-parametric testing

Shapiro-wilks test; the closer to 1 the more normal it is