Quantitative Skills 1: Graphing

Categories of data: Qualitative data is not numerical and is usually subjective. Quantitative data is numerical and lends itself to statistical analysis. http://ibscrewed4maths.blogspot.com/2011/03/types-of-data.html 1.75 mL

Quantitative data can be either discrete or continuous. Discrete data has finite values, such as integers, or bucket categories such as “red” or “tall”. Continuous data has an infinite number of values and forms a continuum.

Which graph shows continuous data and which graph shows discrete data? Graph A Graph B

One of the first steps in data analysis is to create graphical displays of the data. Visual displays can make it easy to see patterns and can clarify how two variables affect each other. AP Biology Quantitative Skills Manual

Line Graphs Used when data on both scales of the graph (the x and y axes) are continuous. The dots indicate measurements that were actually made.

Basic Traits of A Good Graph 1. A Good Title A good title is one that tells exactly what information the author is trying to present with the graph. Relation Between Study Time and Score on a Biology Exam in 2011 -or- Study Time vs. Score on a Biology Exam in 2011 AP® Biology Investigative Labs: An Inquiry-Based Approach

Basic Traits of A Good Graph Axes should be consistently numbered. Axes should contain labels, including units. AP® Biology Investigative Labs: An Inquiry-Based Approach

Basic Traits of A Good Graph A frame should be put around the outside of the graph. AP® Biology Investigative Labs: An Inquiry-Based Approach

Basic Traits of A Good Graph Small marks, called index marks, can be drawn in. AP® Biology Investigative Labs: An Inquiry-Based Approach

Basic Traits of A Good Graph The independent variable is always shown on the x axis. The dependent variable is always shown on the y axis. Dependent Variable AP® Biology Investigative Labs: An Inquiry-Based Approach Independent Variable

Basic Traits of A Good Graph The line should not be extended to the origin if the data do not start there. AP® Biology Investigative Labs: An Inquiry-Based Approach

Extrapolation is a prediction of what the chart might look like beyond the measured set of data. A broken line is used, indicating this a prediction and not data actually collected.

The slope of a line indicates the rate at which the variables being graphed are changing. y y2 – y1 m = = x x2 – x1 Rise Slope = Run

Positive Slope Negative Slope Zero Slope Rate Increasing Rate Decreasing Constant Rate Indicates some values were skipped

Line charts can be plotted with multiple data sets, allowing for better comparison. Makes use of a legend

Effective graphs use statistics as an essential part of the display Effective graphs use statistics as an essential part of the display. Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. 

Population vs. Sample Often, researchers want to know things about a population (N), but it may not be feasible to obtain data for every member of an entire population. A sample (n) is a smaller group of members of a population selected to represent the population. The sample must be random.

Descriptive statistics and graphical displays allow us to estimate how well sample data represent the true population.

If a sample is not collected randomly, it may not closely reflect the original population. This is called sampling bias.

A normal distribution, also known as a “bell curve” or “normal curve”, can be formed with continuous data.

The type of data being collected during an investigation should be determined before performing the actual experiment. The type of data will determine the statistical analyses that can be used.

Three Types of Data: Parametric data: data that fit a normal curve Nonparametric data: data that do not fit a normal curve Frequency or count data: generated by counting

Normal or parametric data Measurement data that fit a normal curve or distribution. Data is continuous, generally in decimal form.

Nonparametric data Do not fit a normal distribution, may include large outliers, or may be count data that can be ordered. Can be qualitative data. http://www.e-cigarette-forum.com/forum/medical-research/254529-effect-electronic-nicotine-delivery-device-e-cigarette-smoking-reduction-cessation.html

Frequency or count data Generated by counting how many of an item fit into a category. Can be data that are collected as percentages. AP Biology Quantitative Skills Manual

Two Types of Descriptive Statistics: Comparative statistics: compare variables Association statistics: look for correlations between variables

Comparative statistics compare phenomena, events, or populations (Is A different from B?). Bar Graph or Pie Chart Bar Graph Box-and-Whisker Plot Parametric Data (normal data) Nonparametric Data Frequency Data (counts)

Association statistics look for associations between variables (How are A and B correlated?). Scatterplot AP Biology Quantitative Skills Manual Parametric Data and Nonparametric Data

Types of graphs commonly used with the three data types and suggested statistical tests: Source: Redrawn from “Statistics for AS Biology,” available as part of a download at: http://www.heckmondwikegrammar.net/index.php?highlight=introduction&p=10310

Bar Graphs Used to visually compare two samples of categorical or count data. Are also used to visually compare the calculated means with error bars of normal data . AP Biology Quantitative Skills Manual

Sample standard error bars (also known as the sample error of the sample mean) are the notations at the top of each shaded bar that shows the sample standard error (SE). AP Biology Quantitative Skills Manual

Scatterplots Used when comparing one measured variable against another. Used when looking for trends. AP Biology Quantitative Skills Manual

If the relationship is thought to be linear, a linear regression line or best fit line can be plotted to help define the pattern. AP Biology Quantitative Skills Manual

Box-and-Whisker Plots Allow graphical comparison of two samples of nonparametric data (data that do not fit a normal distribution).

In a box-and-whisker graph, the ticks at the tops and bottoms of the vertical lines show the highest and lowest values in the dataset, respectively. The top of each box shows the upper quartile, the bottom of each box shows the lower quartile, and the horizontal line represents the median. AP Biology Quantitative Skills Manual

Histograms (Frequency Diagrams) Used to display the distribution of data, providing a representation of the central tendencies and the spread of data. AP Biology Quantitative Skills Manual

Creating a histogram requires setting up bins — uniform range intervals that cover the entire range of the data. Then the number of measurements that fit in each bin are counted and graphed. AP Biology Quantitative Skills Manual

If the data on a histogram show an approximate normal distribution, then these are parametric data. If the data do not approximate a normal distribution then they are nonparametric data. AP Biology Quantitative Skills Manual

References: AP® Biology Investigative Labs: An Inquiry-Based Approach and AP® Biology Quantitative Skills: A Guide for Teachers