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METHODS OF DATA PRESENTATION AND ANALYSIS

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Gerald W. Ouma

25 March 2010

Data Graphics

- Data graphics are a good way to communicate important data in your reports. The purpose of putting results of research into graphs, charts and tables is two-fold. First, it is a visual way to look at the data and see what happened and make interpretations.

- Second, it is usually the best way to show the data to others. Reading lots of numbers in the text puts people to sleep and does little to convey information.
- Tables are the most commonly used form of data graphics, but graphs, charts or diagrams that include symbols and pictures will get your results across to the reader faster and will liven up your presentation or report.

- Tables
- Line Graphs
- Bar Graphs
- Pie Charts
- Diagrams

When creating graphic displays, keep in mind the following questions:

- What am I trying to communicate?
- Who is my audience?
- What might prevent them from understanding this display?
- Does the display tell the entire story?

Tables display numbers or words arranged in a grid. They are good for situations where exact numbers need to be presented like:

- Describing the components of a program's implementation.
- Displaying attrition.
- Displaying pre- and post-test results.
- Presenting correlations or comparisons.

Example

- Line graphs show sets of data points plotted over a time period and connected by straight lines. Line graphs are useful for displaying:
- Any set of figures that needs to be shown over time.
- Results from two or more groups compared over time.
- Data trends over time.

Summary of State Funding of South African Higher Education, 1996-2005 (Rands Billions)

Source:DoE (2005)

- Bar graphs show quantities represented by horizontal or vertical bars and are useful for displaying:
- The activity of one thing through time.
- Several categories of results at once.
- Data sets with few observations.

Selecting a Type of Bar Graph

- One may choose from three types of bar graphs, depending on the type of data they have and what they want to stress:
- Simple bar graphs sort data into simple categories.
- Grouped bar charts divide data into groups within each category and show comparisons between individual groups as well as between categories. (It gives more useful information than a simple total of all the components.)

- Divided/stacked bar graphs show proportional relationships between data within each bar. In addition, divided bar graphs can show changes over time (They make clear both the sum of the parts and each group’s contribution to that total).

Total State Funds Per FTE Student, 1996 – 2004 (Rands ‘000)

Source: DoE (2005)

Pass rates of UWC Education students by gender, 2001 - 2007

- Pie charts show proportions in relation to a whole, with each wedge representing a percentage of the total. Pie charts are useful for displaying:
- The component parts of a whole in percentages.
- Budget, geographic or population analysis.
- Pie charts use pictures to compare the sizes, amounts, quantities, or proportions of various items or groupings of items.

Racial composition of learners at school X

- Collected data needs to be summarized and interpreted.
- Pages of field notes or interview transcripts must be critically examined and synthesized.
- Analysis is done during data collection as well as after all the data have been gathered.
- The goal of the analysis is to discover patterns, ideas, explanations and “understandings”
- A thorough analysis requires three steps: organization of the data, summarizing the data, and then interpreting the data

- Qualitative data is generally analyzed through content analysis. Content analysis focuses on the search for patterns and relationships within a text, be it field notes of a classroom observation or a student term paper.
- Three types of analyses are common in qualitative research: thematic content analysis, where themes are extracted from the text, indexing, where specific words are viewed in context, and quantitative descriptive analysis, or word counting.

- Thematic Content Analysis - In conducting a thematic analysis, themes are usually identified inductively, such that themes emerge naturally from the data (Patton, 1990; Denzin and Lincoln, 1998). Inductive analysis limits bias, as the researcher is not imposing external themes on the data; however, with practice, predetermined thematic analysis can be a quick method for analyzing data.

- Once dominant themes have been identified in the data through open coding, the researcher links and reorganizes themes in an attempt to develop a dominant structure. This structure will eventually evolve into a conceptual framework of the system under study. Quotes and anecdotes are useful as examples of the types of data that led to the extraction of themes and connections, and should be used to bolster arguments (Golden-Biddle and Locke, 1997).

- Indexing and Quantitative Descriptive Analysis - Indexing and quantitative descriptive analysis (QDA) are additional methods that can be used to quantify qualitative data (Trochim, 2001). Both techniques involve documenting word occurrences, although indexing is primarily concerned with the context in which words exist.
- Context is usually defined as the words that immediately precede and follow the targeted term. QDA, on the other hand, reports the frequency with which words are used throughout a text, independent of a specific context. Computer programs have been developed for conducting these types of analyses, although coding by hand is certainly possible.

Qualitative data can always be transformed into quantitative data, although it is not necessarily desirable to do so. Converting the qualitative to the quantitative strips the data of the context in which they occur, and any data transformations should be made cautiously.

- Descriptive statistics: used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. Descriptive statistics include: Mean; Median; Mode (measures of central tendency); Range; Inter-quartile range; Frequency distribution. The following questions would be answered by descriptive statistics.

- What is the average age of learners in the sample?
- What is the age range of teachers in the sample?
- What percentage of teachers in the sample took part in the recent strike by public service employees?

- Inferential statistics: Inferential statistics are used to draw inferences about a population from a sample. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think.

- Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what's going on in our data.
- There are two main methods used in inferential statistics: estimation and hypothesis testing. Inferential statistics include the t-test, Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA), regression analysis, etc.