Ecology & Data Analyze Exam #1

Individual

Basic unit of analysis within a group being studied (ex. Frida)

Population

The larger group you want to know about. (what your research is about) (ex. Elephants in Kenya)

Sample

The group you actually study (ex. 1,000 followed elephants)

Quantitative variables (#s)

• Continuous (Anywhere along a continum)

• Discrete (whole #)

Categorical variables (categories/groups)

• Nominal (named variables without order)

• Ordinal (Low, medium, high with order)

Bar chart - categorical data

• Has bar gaps

• x axis has the labels

• y axis is numerical value or %

Pie charts

• Categorical data

Histogram - quantitative data (either type)

• x axis is numerical

• Bars touch, no gaps

• y axis is frequency/count of data

Distinguishing parts of a histogram

1. shape

   1. symmetrical, left skew (short on left), right skew (short on right)

2. Center

   1. Modality (unimodal, bimodal) and numerical value

   2. unimodal - 1 peak

   3. bimodal - 2 peaks

3. Spread

   1. Numerical range the data ranges from (1-60)

   2. *Do where the data starts not just the beginning number

Measures of center

• Mean (adding of data points and divide by # of data points)

• Median - middle value in ordered dataset (for even amt of data points take mean of two middle points)

Measures of spread

• Range of a sample = max - min

• Variance of a sample (s²) = tells you how spread out around the mean your data is

• Standard deviation = s (square variance) tells you how spread out around the mean your data is

  • larger = more scattered less predictable data

  • smaller = more tightly packed, predictable data

First quartile (25%)

Middle value between minimum and median.

Third quartile (75%)

Middle value between median and maximum.

Interquartile range (IQR)

3rd quartile - 1st quartile

5 number summary

min Q1 median Q3 max * this is represented by a box plot

Predicting shape on a histogram

• mean higher than median means right skew

• mean lower than median means left skew

Box plots * don’t usually overlap

Visual representation of 5 # summary, often grouped by a 2nd categorical variable.

• outliers as dots

Bar plots

• Shows 2 variables - 1 categorical, 1 quantitative

• Visual representation of mean (bar) and a measure of spread (whisker)

the mean is represented by the main bars while the whisker shows standard deviation (check the caption for what the whiskers represent if nothing says they are for standard deviation)

Violin plots

Shows multimodal distributions

Growing in popularity

Scatter plots

• can also use these to compare categorical variables (ungrazed, grazed)

2 variables

• 1 indep. (x axis)

• 1depen. (y axis)

• Direction (positive, negative, no direction)

• Form (linear or not)

• Strength (any outliers, how close are the points together or hugging the line?)

Pearson correlation coefficient ( r ) *not useful for nonlinear relationships

• unitless

• must fall between -1 and 1

• if r<0, negative and line goes down

• if r>0, positive and line goes up

• if your r value is close to -1 or 1 you have a strong correlation

• if your r value is closer to 0, weak correlation

Least squares regression line formula

^yi = a + b xi

y= response variable

i = single data point

^ = estimate

a = intercept

b = slope

xi = explanatory variable data point

Intercept (a)

y when x = 0

has units same as y

Slope (b)

Change in y for 1 unit change in x (y/x)

R² variance

• How much spread does the estimated linear equation account for?

• proportion of variance in y explained by x

• always positive when squaring

• when squaring your r value, it gives you the % of your axis

equation -

adds up leftover variance (variance residuals) / total variation (variance data points)

Residual deviation

Difference between an observed ecological data point and the value predicted.

Problems with r

1. r always assumes linearity * b also does

2. correlation does not equal causation

3. r is influenced by outliers * b is to

   1. these outliers can even change the entire directoin of data

Extrapolation

Trying to use that outside data. Huge problem with linear relationships hard to predict for data you don’t have.

Data

Values for individuals in your sample

Statistics

Numerical summaries of a sample (r, b, and r²)

Parameters

numerical summaries of a population