Design and Data Analysis

1. Design and Data Analysis Analyzing Experimental Data

2. Importance of Statistical Analysis • One of the most important components of being scientifically literate is the ability to successfully summarize experimental data obtained during an experiment. • As scientists, it is our job to provide anyone who is evaluating our work with the final underlying conclusion that we drew from our experiment. • There are many ways that students can summarize the observations that they made during their experiment. They can answer a series of direct questions about their raw data; or mathematically analyze their data, graph their data, and summarize any trends that they observed. • The important thing to understand is that some parts of the experiment can be explained by qualitative data and some parts can be explained by quantitative data. Any credible work will contain a mixture of both.

3. Quantitative or Qualitative? • Quantitative data: are represented by a number and a unit of measurement that is based upon a standard scale with equal intervals, such as the Metric system. • Continuous quantitative data: are collected using standard measurement scales that are divisible into partial units. • Discrete quantitative data: are collected using standard scales in which only whole integers are used. • Ratio data: quantitative data collected using a scale with equal intervals and an absolute zero. • Interval data: measurements made using a scale with equal intervals, but no absolute zero. • Qualitative data: verbal descriptions or information gathered using scales without equal intervals or zero points. Such scales are non-standard scales. • Nominal data: data for a series of discrete categories for which there is not a basis for rank ordering, for example gender or hair color. • Ordinal data: data collected for categories that can be rank ordered, such as a hardness scale for minerals. • Students should practice classifying data as either quantitative or qualitative data as well as classifying it into the subdivisions.

4. Describing Data (Central Tendency) • When describing experimental data, the goal is to mathematically represent a large amount of quantitative or qualitative data with a very small amount of data. • Measure of Central Tendency: the value that is most typical of a set of data. • Central tendency can be measured by the median, mode, or mean average of a data set. • Mode: the value of the variable that occurs most often. It is used for data at the nominal, ordinal, interval, or ratio levels. • Median: The middle value, after all cases have been ranked ordered from highest to lowest. The median can be used with ordinal, interval, or ratio data but not with nominal data. • Mean: The arithmetic average or the sum of the individual values divided by the number of cases. The mean can only be calculated for interval or ratio data. • For ratio and interval data, the mean, median, and mode can be calculated. • Mean is the most powerful measure of central tendency.

5. Describing Data (Variation) • Once you have represented the data set by the most typically occurring data point, the spread of the data point or how much the data changes needs to be expressed. • Variation: statistics that describe how spread out the values in a set of data are. • Simple measures of variation are the range for a set of quantitative data and the frequency distribution for a set of qualitative data. • Range: a measure of how a set of measurements or count data is spread out. It is calculated by subtracting the minimum value from the maximum value. • Frequency distribution: a summary or graph of the amount of variation (spread) within a set of qualitative data (observations); a frequency distribution states the number of items in each category.

6. Data Variation (continued) • Descriptive statistics mentioned before deal with the sample dealt with in the experiment. Inferential statistics expand the framework from a small group, the sample, to the entire group, the population. • Sample: the specific portion of the population that is selected for study. • Sampled Population: the population from which the sample was drawn. • Target Population: all units of the specific group whose characteristics are being studied. • The validity of an experiment depends on a precise definition of the population and careful sampling of the defined population. • Random samples in which every individual member of the population has an equal chance of being included are preferred and are an underlying assumption of many statistical tests.

7. Deciding Type of Graph • Utilize the table 8.6 on pg. 115 to determine which type of graph to represent your data.

8. Writing about Quantitative Data • Step 1: Write a topic sentence stating the independent and dependent variables, and a reference to tables and graphs. • Step 2: Write sentences comparing the measures of central tendency of the groups. • Step 3: Write sentences describing the variation within the groups. • Step 4: Write sentences stating how the data support the hypothesis.

9. Writing about Qualitative Data • Step 1: Write a topic sentence stating the independent and dependent variables, and a reference to tables and graphs. • Step 2: Write sentences comparing the measures of central tendency of the groups. • Step 3: Write sentences describing the variation (frequency distribution) within the groups. • Step 4: Write sentences stating how the data support the hypothesis.