Bbh 310 Exam 1 (Parts 7 And 8)

Front 1

Why use descriptives?

Back 1

- Quick way of summarizing a data set in a way that is comparable to other data sets
- Sometimes there are too many observations to read them all and understand it
- Provide the basis for inferential statistics (chi-sq., t-test, ANOVA, correlation)

Front 2

All descriptive statistics start with very simple number cruncing processes, such as:

Back 2

- Counting number of observations
- Sorting data into rank from high to low
- Adding up sum of observations
- Subtracting the difference between each observation and some other number
- Dividing by another number

Front 3

Categorical Distributions

Back 3

- Is it all in one category or evenly spread across the three categories?
- Bar chart, pie chart

Front 4

Quantitative Variables in Distribution

Back 4

- Which observations were most frequent?
- How does that change as one moves from low to high observations?

Front 5

Frequency Distributions are observed in...

Back 5

- A histogram

Front 6

Probability Distributions are expectations for...

Back 6

- Hypothesis testing
- Idealized curve, mathematical abstraction

Front 7

Types of quantitative probability distributions:

Back 7

1. Normal distribution
--> Bell-shaped curve
--> Concept: skew (ex.Long tail on right is skewed right)
--> Ex) Many biological traits

2. Uniform distribution
--> Similar frequency across all observations
--> Many regular activities
--> Makes a rectangle

3. Gamma distribution
- Long tail in only one direction
- Measuring frequency of events over time
- Ex) Phone data

Front 8

Central Tendency:
Mean, Median, and Mode

Back 8

1. Mean
- quantitative data only
- average
- very sensitive to extreme outliers
- bar charts compare group means

2. Median
- ordinal and quantitative data
- position of 50th percentile/2nd quartile
- not very sensitive to outliers

3. Mode
- nominal, ordinal, and quantitative data
- most frequent observation
- not sensitive to outliers at all

Front 9

Spread: (How much is the data spread out?)
Range, Interquartile range, variance, SD, error bars

Back 9

1. Range
--> = Max - Min

2. Interquartile Range
--> = 3rd quartile - 1st quartile

3. Variance
--> Take the difference of each observation from the mean and then square it, sum up all of these squared differences, and then divide by the sample size

4. Standard Deviation
--> Square root of the variance
- How dispersed every observation is from the mean

5. Error Bars
--> Errors on graphs

Front 10

Population Variance vs. Sample Variance

Back 10

Population Variance
--> Assumes whole pop. in data set and seeing all variance there is to see (SumSquaredDiffs/N)

Sample Variance
--> Assumes there's more variance out there in pop. that's unobserved in your sample, b/c the severe outliers are rare and unlikely to be caught in a small sample (SumSquaredDiffs/[N-1])
--> Gives bigger variance

Front 11

Why use statistical hypothesis tests?

Back 11

- To avoid interpreting random events as things that happen for another reasons
- There are ALWAYS differences b/t group means and associations between variables due to chance
- Need a logical way of seperating the random associations from the consistent associations (which are the basis for discovering causation)

Front 12

4 Rules for Causation:

Back 12

1. Cause is associated with effect
--> Association

2. Cause comes before effect
--> Precedence

3. Most simple and clear explanation that fits the available data; no other alternative cause makes more sense
--> Parsimony (no other questions laying around)

4. Plausible and validated mechanism of action
--> Believability

Front 13

Hypotheses about Association:
Which methods compare quantitative and categorical variables?

Back 13

1. Correlation --> Quantitative
2. T-Test, Anova --> Categ. vs. Quant.
3. Chi-Sq. --> Categ. vs. Categ.

Front 14

What is the difference between Parametric Statistics and Non-Parametric Statistics?

Back 14

- Parametric statistics use parameters like mean and variance to model an assumed distribution.
- Non-Parametric statistics don't make these assumptions about the distribution and can be used for ordinal/ranked and nominal data

Front 15

Null Hypothesis

Back 15

A mathematical model of what we think the random situation is like (when there isn't any causal agent affecting our outcome measure)

Front 16

Alternative Hypothesis

Back 16

What exactly is the difference from randomness that we expect?
Ex) Higher rates of this category, different means in this category, linear slope on a scatter plot

Front 17

Alpha (b/t 0 and 1) is intended to exactly model the probability of type 1 error. How?

Back 17

- Large alpha = high type 1 error
- Small alpha = small type 1 error
- Inverse relationship w/ type 2 error but not easily calculated

Front 18

When calculating the test, what exactly are you doing?

Back 18

- Summing up the difference from expectation and dividing by the uncertainty

Front 19

What is the p-value?

Back 19

- The probability of seeing at least this much deviation from expectation in the data, given the assumptions

Front 20

Criterion for rejecting the Null:

Back 20

- Comparing P Value to Alpha
- If p < alpha, reject the null (supports alt. hypothesis)