# Chapter Summaries

• Analyzing qualitative data is an inductive process, involving the reduction of information that has been collected by organizing it into important themes and patterns.
• The three-step process for inductive analysis includes organization, description, and interpretation.
• The organizational step of inductive analysis involves the reduction of the potentially massive amounts of narrative data.
• Reduction of qualitative data is typically accomplished through the development of a coding scheme, which is used to group data that provide similar types of information.
• The process of coding narrative data often necessitates rereading your data numerous times.
• During the description step of inductive analysis, connections are made between the data and the original or emerging research questions.
• It is important to look for information in your data that contradicts or conflicts with the patterns or trends that have emerged.
• During the interpretation step, the practitioner-researcher examines events, behaviors, or others’ observations--as represented in the coded categories--for relationships, similarities, contradictions, and so on
• Reflection throughout the process of inductive analysis is an essential component to remaining objective and open-minded while gaining a better understanding of your data.
• Numerous computer software programs can aid the researcher with the organization and categorization of narrative data. The use of this software is only advantageous when you have a great deal of qualitative data.
• Analysis of quantitative data is a deductive process, using descriptive or inferential statistics or a combination of the two.
• Descriptive statistics are relatively simple mathematical procedures used to simplify, summarize, and organize large amounts of numerical data.
• Three categories of descriptive statistics include measures of central tendency, dispersion, and relationship.
• Measures of central tendency describe what is typical about a group. There are three measures of central tendency: the mean, the median, and the mode.
• The mean is the arithmetic average of scores.
• The median is the specific score in the set of data that separates the entire distribution in equal halves.
• The mode is the most frequently occurring score in the overall set of scores.
• Measures of dispersion indicate how much spread or diversity exists within a group of scores. Two primary measures of dispersion are the range and the standard deviation.
• The range is calculated by simply subtracting the lowest score in a set of data from the highest score.
• The standard deviation is the average distance of scores away from the mean.
• Measures of the direction and degree of relationship between two variables are called correlation coefficients, and there are many different types.
• Data can also be “described” visually through the use of frequency distribution tables and such graphs as histograms, bar charts, and pie charts.
• Inferential statistics are used to determine how likely a given statistical result is for an entire population, based on data collected from a smaller sample from that population.
• Inferential statistical procedures are typically used as the means of analysis for research designs that focus on group comparisons.
• The most common types of inferential statistical tests are the independent-measures t test, the repeated-measures t test, analysis of variance, and the χ2 test.

• An independent-measures t test is appropriate for designs where two groups are compared on a common dependent variable.
• A repeated-measures t test is appropriate for designs involving two measures (such as a pretest and a posttest) on the same group.
• Analysis of variance (or ANOVA) is appropriate for designs where more than two groups are being compared on a common dependent variable.
• χ2 analysis is used when data exist as frequency counts within categories.
• Inferential statistics help the researcher determine statistical significance, which indicates a true difference between groups being compared, as opposed to differences due only to chance.
• Statistical significance is determined by comparing the obtained p value to the preestablished α level, usually 0.05 in educational research studies.
• When the p value is less than the α level, the results are said to be statistically significant.
• There are numerous computer software programs available to assist in the analysis of numerical data.
• A low-cost and accessible software program called StatCrunch is available for K–12 educators.
• Analysis of mixed-methods data simply requires the individual to combine both qualitative and quantitative approaches to data analysis and to follow the sequence of data collection as specified by the particular mixed-methods design.
• When writing up the results section for qualitative data, your goal is to describe the most meaningful trends or patterns that you saw emerge from your analyses, not to report on every bit of data collected.
• Five guidelines for writing up qualitative results include: (1) make every effort to be impartial in your write-up; (2) include references to yourself where they are warranted; (3) take your readers along on all aspects of your study; (4) include representative samples when they enhance your presentation; (5) include interesting but nonessential information in appendices, if appropriate.
• When writing up results for quantitative data, results can be presented in narrative form or in graphical, visual form.
• In addition to the guidelines above, additional guidelines should be followed when presenting quantitative data results regarding best practices for describing numerical data.