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Unit 11(Evaluating Descriptive
Data)questions with answers
Purpose of DESCRIPTIVE STATISTICS - correct answer ✔✔The goal of descriptive statistics is to describe, summarize, or make sense of numerical data. Researchers use graphic representations such as bar graphs, line graphs, and scatter plots as well as measures of central tendency (i.e., mode, median, and mean) to display and analyze this data. Before this analysis can start, a researcher must have data set to interpret. The researcher can summarize the variables in a data set one at a time, as well as examine how the variables are interrelated (e.g., by examining correlations). The key question in descriptive statistics is how researchers should communicate the essential characteristics of the data. statistics - correct answer ✔✔a branch of mathematics that deals with the analysis of numerical data. It can be divided into two broad categories called descriptive statistics and inferential statistics. Inferential statistics was discussed previously in Unit 3, Module 3 in regards to Quantitative research. In descriptive statistics, however, the goal is to describe, summarize, or make sense of a particular set of data. The focus is more on interpretation than on calculation. inferential analysis - correct answer ✔✔Uses the laws of probability to make suggestions about populations based on sample data descriptive analysis - correct answer ✔✔Goal is to summarize and explain a set of data qualitative analysis - correct answer ✔✔Focused on the analysis of nonnumerical data, such as words and pictures Descriptive statistics starts with a data set - correct answer ✔✔the researcher attempts to convey the essential characteristics of the data by arranging it into a
more interpretable form (e.g., by forming frequency distributions and generating graphical displays) and by calculating numerical indexes, such as averages, percentile ranks, and measures of spread. The researcher can summarize the variables in a data set one at a time, as well as examine how the variables are interrelated (e.g., by examining correlations). The key question in descriptive statistics is how researchers can communicate the essential characteristics of the data. In organizing a data set - correct answer ✔✔Each participant gets a row, each variable gets a column Graphs - correct answer ✔✔pictorial representations of data in two-dimensional space. Many graphs display the data on two dimensions or axes. These two axes are the x- and y-axes, where the x-axis is the horizontal dimension and the y-axis is the vertical dimension. When graphing the data for a single variable, the values of this variable are represented on the x-axis, and the frequencies or percentages are represented on the y-axis. If two variables are being graphed, the values of the independent variable are put on the x-axis, and the values of the dependent variable are put on the y-axis. Graphs can also be constructed for more than two variables. Bar Graphs - correct answer ✔✔bar graph is a graph that uses vertical bars to represent the data Notice that the x-axis of the bar graph represents the variable called "College Major" and the y-axis represents "Frequency of occurrence." The bars provide graphical representations of the frequencies of the three different college majors. Histograms - correct answer ✔✔a graphic presentation of a frequency distribution Bar graphs are used when the variable is a categorical variable. However, if your variable is a quantitative variable, a histogram is preferred It is especially useful because it shows the shape of the distribution of values. Compare the table of starting salaries (on the right) with the associated histogram (on the left) using the same data set.
For example, if someone asked a teacher how well his or her students did on their last exam, using a measure of central tendency would provide an indication of what a typical score was Mode - correct answer ✔✔the most frequently occurring number in a set of data bimodal- two modes multimodal- multiple modes Median - correct answer ✔✔or 50th percentile, is the middle point in a set of numbers that has been arranged in order of magnitude (either ascending order or descending order). Mean - correct answer ✔✔the arithmetic average, or commonly called the average. The symbol X stands for the variable whose observed values are 1, 2, and 3 in our example. The symbol ∑ (the Greek letter sigma) means "sum what follows." Therefore, the numerator (the top part) in the formula says "sum the X values." The n in the formula stands for the number of numbers. The average is obtained by summing the observed values of the variable and dividing that sum by the number of numbers. normal distribution - correct answer ✔✔or normal curve, is a unimodal, symmetrical distribution that is the theoretical model used to describe many physical, psychological, and educational variables. It is said to be bell shaped, because the curve is highest at the center and tapers off as you move away from the center. The height of the curve shows the frequency or density of the data values. Now, the most important characteristic of the normal distribution is that the mean, the median, and the mode are the same number. skewed - correct answer ✔✔one tail is stretched out longer than the other tail, making the distribution asymmetrical. negatively skewed - correct answer ✔✔If one tail appears to be stretched or pulled toward the left, the distribution is said to be skewed to the left
In the negatively skewed distribution, the numerical value of the mean is less than the median and the numerical value of the median is less than the mode. A good example of a variable that is negatively skewed is self-esteem. Most people generally score high on self esteem with a few people scoring very low. Those few people with low scores pull down the mean. The modal score is at the high end of the distribution, as illustrated below. positively skewed - correct answer ✔✔If a tail appears to be stretched or pulled toward the right, the distribution is said to be skewed to the right, in the positively skewed distribution, the numerical value of the mean is greater than the median, which is greater than the mode. A good example of positive skew are housing prices. Most people live in modest houses so the mode is at the lower end of the distribution. The small number of million dollar mansions at the high end of the distribution pull the mean up, but the mode is where most of the scores appear at the low end of the distribution, as illustrated below. Skewed distributions - correct answer ✔✔Why does the mean change more than the other measures of central tendency in the presence of a skewed distribution? The answer is that the mean takes into account the magnitude of all of the scores. In contrast, the median takes into account only the number of scores and the values of the middle scores. As a general rule, the mean is the best measure because it is the most precise. The mean takes into account the magnitude of all scores. The median and the mode do not do this. The mean is also the most stable from sample to sample. The median takes into account only the number of scores and the values of the middle scores. The mode is usually the least desirable because it provides information only about what data value occurs the most often. Therefore, mode should be used only when it is important to express which single number or category occurs the most frequently. Otherwise, the mean or the median is usually the preferred measure of central tendency. On helpful rule to remember is: Mean is less than median? Skewed left Mean is greater than median? Skewed right
Variance - correct answer ✔✔a measure of the average deviation of all the numbers from the mean in squared units. Standard Deviation - correct answer ✔✔When you take the square root of the variance, you obtain the standard deviation. To calculate the variance and standard deviation, follow these five steps: - correct answer ✔✔1. Find the mean of a set of numbers. Add the numbers in column 1 and divide by the number of numbers. (Note that we use the symbol "X-bar" to stand for the mean.)
- Subtract the mean from each number. Subtract the mean from each number in column 1 and place the result in column 2.
- Square each of the numbers you obtained in the last step. Square each number in column 2 and place the result in column 3. (To square a number, multiply the number by itself. For example, 2 squared is 2 × 2, which is equal to 4.)
- Put the appropriate numbers into the variance formula. Insert the sum of the numbers in column 3 into the numerator (the top part) of the variance formula. The denominator (the bottom part) of the variance formula is the number of numbers in column 1. Now divide the numerator by the denominator, and you have the variance.
- You obtained the variance in the previous step. Now take the square root of the variance, and you have the standard deviation. (To get the square root, type the number into your calculator and press the square root [√] key.) The following will always be true if the data fully follow a normal distribution: - correct answer ✔✔68.26% of the cases fall within 1 standard deviation. 95.00% fall within 1.96 standard deviations. 95.44% fall within 2 standard deviations.
99.74% fall within 3 standard deviations. A good rule for approximating the area within 1, 2, and 3 standard deviations is what we call the "68, 95, 99.7 percent rule." Purpose of INFERENTIAL STATISTICS - correct answer ✔✔In inferential statistics, researchers attempt to go beyond their data. In particular, they use the laws of probability to make inferences about populations based on sample data. In the branch of inferential statistics known as estimation, researchers want to estimate the characteristics of populations based on their sample data. They use random samples (i.e., "probability" samples) to make valid statistical estimations about populations. In the branch of inferential statistics known as hypothesis testing, researchers test specific hypotheses about populations based on their sample data. There are four important points about inferential statistics - correct answer ✔✔1. First, the distinction between samples and populations is essential. You will recall that a sample is a subset of cases drawn from a population, and a population is the complete set of cases.
- Second, a statistic (also called a sample statistic) is a numerical characteristic of a sample, and a parameter (also called a population parameter) is a numerical characteristic of a population. Here is the main idea: If a mean or a correlation (or any other numerical characteristic) is calculated from sample data, it is called a statistic; if it is based on all the cases in the entire population (such as in a census), it is called a parameter.
- Third, in inferential statistics, we study samples when we are actually much more interested in populations. We do not study populations directly because it would be cost prohibitive and logistically impossible to study everyone in most populations that are the focus of research studies. However, because we study samples rather than populations, our conclusions will sometimes be wrong. The solution provided by inferential statistics is that we can assign probabilities to our statements and we can draw conclusions that are very likely to be correct
smallest number is called the lower limit, and the largest number is called the upper limit. In other words, rather than using a point estimate (which is a single number), the researcher uses a range of numbers, bounded by the lower and upper limits, as the interval estimate. This way, researchers can increase their chances of capturing the true population parameter. Level of Confidence - correct answer ✔✔Researchers are able to state the probability (called the level of confidence) that a confidence interval to be constructed from a random sample will include the population parameter. We use the future tense because our confidence is actually in the long-term process of constructing confidence intervals. For example, 95% confidence intervals will capture the population parameter 95% of the time (the probability is 95%), and 99% confidence intervals will capture the population parameter 99% of the time (the probability is 99%). This idea is demonstrated in the figure below. The reason is that 99% confidence intervals are wider than 95% confidence intervals and wider intervals are less precise An effective way to achieve both a higher level of confidence and a more narrow (i.e., more precise) interval is to increase the sample size. Bigger samples are therefore better than smaller samples. As a general rule, most researchers use 95% confidence intervals, and as a result, they make a mistake about 5% of the time. Researchers also attempt to select sample sizes that produce intervals that are narrow (i.e., precise) enough for their needs. confidence interval = point estimate ± margin of error Hypothesis Testing - correct answer ✔✔As you may recall, hypothesis testing is another branch of inferential statistics; one that is concerned with how well the sample data support a particular hypothesis, called the null hypothesis, and when the null hypothesis can be rejected. Unlike estimation, in which the researcher usually has no clear hypothesis about the population parameter, in hypothesis testing, the researcher states his or her null and alternative hypotheses and then uses inferential statistics on a new set of data to determine what decision needs to
be made about these hypotheses. In hypothesis testing, the researcher hopes to "nullify" the null hypothesis (i.e., they hope to find relationships or patterns in the world, which means that they want to reject the null hypothesis). Null Hypothesis - correct answer ✔✔represented by the symbol H0, is a statement about a population parameter and states that some condition concerning the population parameter is true. In most educational research studies, the null hypothesis (H0) predicts no difference or no relationship in the population Please remember this key point: Hypothesis testing operates under the assumption that the null hypothesis is true. Then, if the results obtained from the research study are very different from those expected under the assumption that the null hypothesis is true, the researcher rejects the null hypothesis and tentatively accepts the alternative hypothesis. Again, the null hypothesis is the focal point in hypothesis testing because it is the null hypothesis, not the alternative hypothesis, that is tested directly. the null hypothesis is the hypothesis that the researcher hopes to be able to nullify by conducting the hypothesis test. Alternative Hypothesis - correct answer ✔✔represented by the symbol H1, states that the population parameter is some value other than the value stated by H0. The alternative hypothesis asserts the opposite of the H0 and usually represents a statement of a difference between means or a relationship between variables. The null and alternative hypotheses are logically contradictory because they cannot both be true at the same time. If hypothesis testing allows the researcher to reject the null hypothesis, then the researcher can tentatively accept the alternative hypothesis. The alternative hypothesis is almost always more consistent with the researcher's research hypothesis; therefore, the researcher hopes to support the alternative hypothesis, not the null hypothesis. The null hypothesis is like a "means to an end." The researcher has to use the null hypothesis because that is what must be stated and tested directly in statistics; several examples of research questions, null hypotheses, and alternative hypotheses are provided in the table below. Examining Probability Value - correct answer ✔✔After the researcher states the null hypothesis, collects the research data, and selects a statistical test using SPSS, the computer program analyzes the research data and provides something called a probability value as part of the computer output.
- When the probability value is less than or equal to the significance level, the researcher rejects the null hypothesis, and
- when the probability value is greater than the significance level, the researcher fails to reject the null hypothesis. Choosing a significance level of .05 means that if your sample result would occur only 5% of the time or less (when the null hypothesis is true, as indicated by the probability value), then you are going to question the veracity of the null hypothesis, and you will reject the null hypothesis. The significance level is the value with which the researcher compares the probability value. When you engage in hypothesis testing, you follow these two rules: - correct answer ✔✔Rule 1. If the probability value (which is a number obtained from the computer printout and is based on your research results) is less than or equal to the significance level (the researcher usually uses .05), then the researcher rejects the null hypothesis and tentatively accepts the alternative hypothesis. The researcher also concludes that the observed relationship is statistically significant (i.e., the observed difference between the groups is not just due to chance fluctuations). Rule 2. If the probability value is greater than the significance level, then the researcher cannot reject the null hypothesis. The researcher can only claim to fail to reject the null hypothesis and conclude that the relationship is not statistically significant (i.e., any observed difference between the groups is probably nothing but a reflection of chance fluctuations). Steps in Hypothesis Testing - correct answer ✔✔1. State the null and alternative hypotheses.
- Set the significance level before analyzing the data.
- Obtain the probability value based on the analysis of your empirical data
- Compare the probability value to the significance level and make the statistical decision.
Step 4 includes two decision-making rules: Rule 1: If: Probability value ≤ significance level (i.e., probability value ≤ alpha). Then: Reject the null hypothesis. And: Conclude that the research finding is statistically significant. In practice, this usually means the following: If: Probability value ≤ .05.* Then: Reject the null hypothesis. And: Conclude that the research finding is statistically significant. Rule 2: If: Probability value > significance level (i.e., probability value > alpha). Then: Fail to reject the null hypothesis. And: Conclude that the research finding is not statistically significant. In practice, this usually means the following: If: Probability value > .05. Then: Fail to reject the null hypothesis. And: Conclude that the research finding is not statistically significant.
- Compute effect size, interpret the results, and make a substantive, real- world judgment about practical significance. This means that you must decide what the results of your research study actually mean. Statistics are only a tool for determining statistical significance. If you have obtained statistical significance, you must now interpret your results in terms of the variables used in your research study. For example, you might decide that females perform better, on average, than males on the GRE Verbal test, that client-centered therapy works better than rational emotive therapy, or that phonics and whole language in combination work better than phonics only. You must also determine the practical significance of your findings. A finding is practi Significance Tests - correct answer ✔✔Researchers report statistical significance to add credibility to their conclusions. Researchers do not want to interpret findings that are not statistically significant because these findings are probably a reflection of chance fluctuations. There are number of statistical significance tests that are
Chi-square test for contingency tables - correct answer ✔✔determine whether a relationship in a contingency table is statistically significant categorical independent/dependent QUALITATIVE DATA ANALYSIS - correct answer ✔✔Data analysis begins early in a qualitative research study, and during a single research study, qualitative researchers alternate between data collection (e.g., interviews, observations, focus groups, documents, physical artifacts, and field notes) and data analysis (creating meaning from raw data). Segmenting and coding go hand in hand because segmenting involves locating meaningful segments of data and coding involves marking or labeling those segments with codes or categories Qualitative data analysis involves the analysis of text from interview or field note transcripts, or the examination of visual material. Some basic procedures in qualitative data analysis are transcribing data, reading and rereading transcripts (i.e., immersing yourself in your data to understand what is going on), segmenting and coding the data, counting words and coded categories (enumeration), searching for relationships and themes in the data, and generating diagrams to help in interpreting the data. The goal of data analysis is to be able to summarize your data clearly and generate inductive theories based on the data. Mixed methods analyses are highly dependent on the purpose and questions of a study. Once these are established an analysis strategy can be developed, along with specific analytical procedures that facilitate the combining of qualitative and quantitative data. segmenting - correct answer ✔✔involves dividing qualitative data into meaningful analytical units. When segmenting text data (such as the transcript from an interview or notes from observations), it is important to read the text line by line and continually ask the following kinds of questions: Do I see a segment of text that has a specific meaning that might be important for my research study? Is this segment different in some way from the text coming before and after it? Where does this segment start and end? A meaningful unit (i.e., segment) of text can be a word, a single sentence, or several sentences, or it might include a larger passage such as a paragraph or even a complete document. The segment of text must have meaning that the researcher thinks should be documented
coding - correct answer ✔✔Coding is the process of marking segments of data (usually text data) with symbols, descriptive words, or category names. Codes are tags or labels for assigning units of meaning to the descriptive or inferential information compiled during a study. Codes usually are attached to "chunks" of varying size—words, phrases, sentences, or whole paragraphs.... They can take the form of a straightforward category label or a more complex one. master list - correct answer ✔✔a master list is simply a list of all the codes used in the research study. The master list should include each code followed by the full code name and a brief description or definition of the code. A well- structured master list will enable other researchers working on the project to use the list readily. During coding, the codes on the master list should be reapplied to new segments of text each time an appropriate segment is encountered. For example, one category from the master list for the data in the below table would be "career choice." Therefore, when the data analyst for this research study encountered another segment of data in which the same or a different person being interviewed made a comment about career choice, the researcher would reapply the label "career choice." Every time a segment of text was about career choice, the researcher would use the code "career choice" to refer to that segment. intercoder reliability - correct answer ✔✔When you have high consistency among different coders about the appropriate codes. Intercoder reliability is a type of interrater reliability. Intercoder reliability adds to the objectivity of the research and reduces errors due to inconsistencies among coders. Achieving high consistency requires training and a good deal of practice. intracoder reliability - correct answer ✔✔Intracoder reliability is also important. That is, it is also important that each individual coder be consistent. To help you remember the difference between intercoder reliability and intracoder reliability, remember that the prefix inter- means "between" and the prefix intra- means "within." Therefore, intercoder reliability means reliability, or consistency, between or across coders, and intracoder reliability means reliability within a single coder. If the authors of qualitative research articles that you read address the issues of intercoder and intracoder reliability, you should upgrade your evaluation of their research.
transcript with codes listed that apply to the whole transcript. Demographic variables are frequently used as facesheet codes (e.g., gender, age, race, occupation, school). Researchers might later decide to sort their data files by facesheet codes to search for group differences (e.g., differences between older and younger teachers) or other relationships in the data. interim analysis - correct answer ✔✔this cyclical or recursive process of collecting data, analyzing the data, collecting additional data, analyzing those data, and so on throughout the research project is called interim analysis Interim analysis is used in qualitative research because qualitative researchers usually collect data over an extended time period and they continually need to learn more and more about what they are studying during this time frame. In other words, qualitative researchers use interim analysis to develop a successively deeper understanding of their research topic and to guide each round of data collection. This is a strength of qualitative research. By collecting data at more than one time, qualitative researchers are able to get data that help refine their developing theories and test their inductively generated hypotheses (i.e., hypotheses developed from examining their data or developed when they are in the field). Grounded theorists use the term theoretical saturation to describe the situation in which understanding has been reached and there is no current need for more data. Refer to Figure 15.1 for the qualitative data-collection process To analyze qualitative data carefully, most data should be transcribed Transcription - correct answer ✔✔Transcription is the process of transforming qualitative research data, such as audio recordings of interviews or field notes written from observations, into typed text. The typed text is called a transcript. If the original data source is an audio recording, transcription involves sitting down, listening to the tape recording, and typing what was said into a word processing file. If the data are memos, open-ended questionnaires, or observational field notes, transcription involves typing the handwritten text into a word processing file. In short, transcription involves transferring data from a less usable to a more usable form. After transcription, it is good practice to put original data somewhere for safekeeping. Some qualitative researchers use a voice recognition computer program, which can make transcribing relatively easy. These programs create transcriptions of data while you read the words and sentences into a microphone attached to your
computer. Two popular programs are IBM ViaVoice and Dragon Naturally Speaking. The main advantage of voice recognition software is that it is easier to talk into a microphone than it is to type. Time savings are not currently large in comparison with typing, but the efficiency of these programs will continue to improve over time. It is important to note that these principles also apply when your qualitative data do not directly lend themselves to text (e.g., videotapes of observations, still pictures, and artifacts). You cannot directly transcribe these kinds of data sources. What can be done, however, is to employ the principles of coding (discussed previously) and enter codes and comments into text files for further qualitative data analysis. Memoing - correct answer ✔✔A helpful tool for recording ideas generated during data analysis is memoing (writing memos). Memos are reflective notes that researchers write to themselves about what they are learning from their data. Memos can include notes about anything, including thoughts on emerging concepts, themes, and patterns found in the data; the need for further data collection; a comparison that needs to be made in the data; and virtually anything else. Memos written early in a project tend to be more speculative, and memos written later in a project tend to be more focused and conclusive. Memoing is an important tool to use during a research project to record insights gained from reflecting on data. Because qualitative data analysis is an interpretative process, it is important that you keep track of your ideas by recording insights as they occur and not relying strictly on memory. Analysis of Visual Data - correct answer ✔✔ Photo interviewing - correct answer ✔✔Photo interviewing is a method of data collection in which researchers show images to research participants during formal or informal interviews. What is unique in this approach is that the researcher has the participant "analyze" the pictures shown to him or her; the researcher records the participant's thoughts, memories, and reactions as "results." In this approach, the pictures are the stimulus and the participant is the analyst. The researcher reports these descriptive findings as the primary results. In addition to this photo- interviewing analysis, the researcher can interpret the results further. Semiotic visual analysis - correct answer ✔✔Semiotic visual analysis is based on the theory of semiotics. A researcher who conducts semiotic analysis is therefore very concerned with what the signs in visual images mean. Semiotic researchers are not concerned with
