Intro to Statistics!Mythvestigations

What is Statistics?

And why do we need it?

Types of Data● Quantitative

○ A numerical description

■ Temperature, height, etc.

● Qualitative○ Describes a quality:

■ Color, type of product, etc.

vs Observational

● Does not assign treatment

groups

● Cannot keep factors constant

● Good for when assigning

treatments is implausible or

unethical/illegal

Experimental

● Applies treatments to a group

and measures the effects

● Has a control and treatment

● Strongly preferred over

observational studies,

especially for science fairs

For example...

An OBSERVATIONAL STUDY would be taking a group of people currently taking vitamins and a group of people not taking vitamins and comparing their health status. (these people were taking vitamins beforehand)

An EXPERIMENTAL STUDY would be randomly selecting a group of, say, 60 people, splitting them up randomly into two 30-person groups, and assigning one group to take vitamins and the other group to not.

VariablesCategorical

● Binary● Nominal● Ordinal

Quantitative

● Continuous● Ratio

Limitations of Data Collection

Quantitative

● Clear, specific, and can easily be shown graphically

● Complex statistical analysis

● Limited response options

Qualitative

● Patterns of behavior and further explanation

● May not represent population

● Time consuming and evaluator bias

General Tips for Data Collection

● The more data, the better!● Randomize

○ Random samples give accurate results○ If you’re experimenting on people, random selection is

almost impossible, but try to get a varied sample - not just friends and family

● Add dates/times to all your data recordings● Stratification/blocking depending on your data

Qualitative Graphs● Bar Graph

○ Shows number of data in

each category

● Pie Chart/Circle Graph

○ Shows data as

percentages/proportions/

parts of a whole

Quantitative Graphs● Scatter Plots

○ Show correlation

● Histogram

○ Interval for each bar

● Line Graph

○ Change over time

Descriptive Statistics

Measures of Central Tendency

● Mean○ Average value

● Median○ “Middle” value

● Mode○ Most frequently occurring value

Mean

● The “average”● Can easily be affected by outliers● Found by adding all values and dividing by the

number of data points

What are outliers?● Data points that are far beyond the spread of the rest of

the data

○ Be careful when using mean

● Can be excluded in analysis

○ You must EXPLICITLY state that you are excluding

data when drawing conclusions

Standard Deviation

● The average distance that a data point is from the mean

● Square root of another value called the variance

● Represented by σ (sigma)● You can use a TI-83/84, Excel, or

an online calculator to find this

Sample Standard Deviation

● When doing statistical testing, you may need to know the standard deviation

● Usually only a SAMPLE of data is taken from a group, which means you have to use the sample standard deviation, s

● Represents a generalized result to the ENTIRE POPULATION

Standard Error

● Measure of the statistical accuracy

Statistical Tests

Confidence Intervals

● 95% confidence intervals● Chance that results and correlations aren’t a coincidence● Mean ± 2 standard error

ANOVA

● Three or more independent groups● Null + Alternative hypothesis

Example of format

T-Test

● One sample vs Two sample● One-tailed vs two-tailed

○ One tailed for when you want to see if there is a difference in one direction (< or >)

○ Two tailed for when you want to see if there is a difference in either direction (≠)

● Paired T-Test○ Whether there is a difference between means where you

have two samples that are related/paired○ For example, before and after experiments have paired

values

Chi-Squared

● Used for the comparison of two categorical variables to see if there is significant association.

Chi-Squared Cont.

1. Chi-squared test statistic2. Degrees of freedom

a. Number of categories-1

Now, let’s see how much you know!