Descriptive Statistics, Significance Levels, and Hypothesis Testing PDF

CHAPTER NINE Descriptive Statistics, Significance Levels, and Hypothesis Testing Chapter Checklist After reading this chapter, you should be able to: 8. Accurately calculate descriptive statistics. 1. Explain the concept of the normal curve. 9. Accurately report descriptive s...

CHAPTER NINE Descriptive Statistics, Significance Levels, and Hypothesis Testing Chapter Checklist After reading this chapter, you should be able to: 8. Accurately calculate descriptive statistics. 1. Explain the concept of the normal curve. 9. Accurately report descriptive statistics. 2. Assess data for its distribution and compare it to 10. Choose an appropriate level of significance the normal curve. for each statistical test used in your research project. 3. Create a frequency distribution and polygon for each variable in a dataset. 11. Make a decision about a hypothesis based on the stated level of significance. 4. Compute and interpret the mean, median, and mode for each variable in a dataset. 12. Explain the relationship among sampling techniques, significance levels, and hypothesis 5. Compute the range and standard deviation for testing. each variable in a dataset. 13. Identify when an alternative hypothesis is 6. Explain the relationship between the mean and accepted and when a null hypothesis is retained. standard deviation for scores on a variable. 7. Use frequencies and percentages to provide a summary description of nominal data.  NUMBERS INTO STATISTICS 169 Numbers are just one tool researchers can use to col- they are often applied or adapted to other forms of lect data, or information about communication phe- quantitative communication research, such as surveys. nomena. In their most basic function, numbers can To begin, let’s examine how data are used to create capture the quality, intensity, value, or degree of the descriptive statistics. variables used in quantitative communication studies. Recall from Chapter 5 on measurement that numbers have no inherent value. Rather, a numerical value is meaningful and can be interpreted only within the NUMBERS INTO STATISTICS context in which the number was collected. Also recall that each variable must be operationalized, meaning The numerical data, or raw data, collected from each that the researcher must specify exactly what data participant is compiled into a dataset or collection of were collected and how. These processes are valuable the raw data for the same variables for a sample of to scholarly research because they help researchers participants. A dataset is shown in Figure 9.1. In this indicate precisely what is being studied and what is not. dataset, except for the first column, the columns rep- In addition to descriptive statistics, this chapter resent variables in the study, while the rows represent also explains two concepts critical to quantitative the responses of individuals. In this dataset, there are communication research: statistical significance and eight variables (train through beh3) and the responses hypothesis testing. These scientific traditions are so of 15 participants. Using the numbers in the dataset, strong and so widely accepted among communication researchers compute another set of numbers, called researchers who use quantitative research designs that descriptive statistics, which convey essential basic Participant identification number Variable names id train tolerate livesup type1 type2 beh1 beh2 beh3 703 1 0 5 3 3 0 0 1 704 1 0 3 3 3 0 0 0 706 1 0 4 1 2 0 0 0 707 1 0 2 3 3 1 1 1 708 1 0 4 3 3 1 1 1 709 1 0 4 1 4 1 1 1 710 1 0 3 1 2 1 1 1 711 1 0 4 3 3 1 1 1 712 1 0 2 1 2 1 0 1 713 1 1 3 3 0 1 1 1 714 1 0 3 0 2 0 0 1 715 1 0 4 3 2 1 1 1 716 1 0 4 1 2 1 1 1 717 1 0 5 3 3 1 1 0 901 1 0 4 1 2 0 1 1 Raw data Descriptive statistics for the variable livesup: N (or number of cases) = 15 mean = 3.6 (sum of 54 divided by 15, the number of cases) standard deviation = 0.91 range = 2 to 5, or 3 FIGURE 9.1 Example of a Dataset 170 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing information about each variable and the dataset as a normal curve is less likely to occur in the measurement whole. of communication phenomenon (Hayes, 2005), the Look at the data in Figure 9.1. From the raw data, normal distribution is used as the basis of hypothesis a researcher can compute four numbers to summarize testing and inferential statistics. and represent each variable in the dataset regardless. The normal curve, or bell curve, is a theoreti- The mean, standard deviation, range, and number of cal distribution of scores or other numerical values. cases are commonly used to provide a summary inter- ­Figure 9.2 illustrates the normal curve. The majority pretation of each variable. Each of these is discussed in detail in this chapter. Besides their descriptive, or summarizing, function, numbers are also used in more complex ways to provide information about the relationships between or among variables in the study and to help researchers draw con- clusions about a population by examining the data of the sample. This use of numbers is known as inferential statistics; several types of inferential statistics, or statis- tical tests, are covered in Chapters 10 and 11. Regardless of which statistical test may be called for by a hypothesis or research question, researchers must x mean interpret and report basic information about the partic- median ipants and each variable in a research study. Having a mode ­basic understanding of how researchers use numbers as a Normal distribution tool in collecting and interpreting data can help you make an independent assessment of a researcher’s conclusion. But before we can turn to those summary descrip- tive statistics, we need to introduce the properties of median the normal curve. Descriptive statistics and their inter- mode pretation are inextricably linked to it. NORMAL CURVE x It is not meaningful to analyze or interpret a score from mean one individual on one variable. Without other data to Positively skewed distribution compare the score to, the researcher would be left with an isolated data point. Interpreting and reporting indi- vidual scores is neither practical nor meaningful. More interesting and useful is the comparison of median mode data collected from many individuals on one variable. For example, knowing how individuals in one sample scored on a leadership assessment provides the oppor- tunity to examine one score against other scores in the sample and the opportunity to examine the set of scores as a whole. As scientists over time and across x disciplines have collected data from natural sources, mean they have discovered that frequency distributions of Negatively skewed distribution ­datasets tend to have a particular shape (see Stahl, 2006). This shape is the normal curve and represents FIGURE 9.2 Distribution of Scores one of the primary principles of statistics. While the  NORMAL CURVE 171 of cases are distributed around the peak in the middle, their communication apprehension decreases signif- with progressively fewer cases as one moves away from icantly. As a result, very few students in the depart- the middle of the distribution. That is, in this theoreti- ment have very high communication apprehension cal distribution, more responses are average or near- scores. average than extremely high or extremely low. The Alternatively, a negatively skewed curve represents normal curve is recognizable because of its distinct bell a distribution in which there are very few scores on shape and symmetry—one side of the curve is a mirror the left side of the distribution (see Figure 9.2). Thus, image of the other side. there are very few very low scores. The long tail point- The horizontal axis represents all possible values ing to the left indicates this. In a negatively skewed of a variable, whereas the vertical axis represents the curve, most of the scores are lumped together on the relative frequency with which those values occur. right side of the curve, above the mean. If we return to In a normal curve—and remember that it is a theo- the example of communication students, this sample retical model—the mean (the average score), median of students is also likely to have a negatively skewed (the score in the middle of the distribution), and mode distribution of communication competence scores. As (the score that occurs most frequently) would have the students complete the skill or performance element in same value and would divide the curve into two equal each class, they become more competent in their inter- halves. Although it is highly unlikely that data for a actions. As a result, very few students in the depart- variable would be represented as a true normal curve, ment would have very low communication competence scientists look for the normality of their data and the scores. degree to which the distribution of their data deviates Notice the relative positions of the mean, median, from the normal curve. and mode on the skewed distributions. The mean is always pulled to the skewed side (or side with the tail) of the distribution. Thus, the mean will always be the Skewed Distributions largest value of the three measures of central tendency in a positively skewed distribution and the smallest in a When a distribution of scores is not normal, it is negatively skewed distribution. When distributions are ­referred to as a skewed distribution. One side is not a skewed, the median is a better measure of central ten- mirror image of the other. Rather, the curve is asym- dency than the mean. metrical; one side is different from the other. Thus, the mean, median, and mode will not be at the same point. Skewness, or the degree to which the distribu- Distributions of Data tion of data is bunched to one side or the other, is a direct ­reflection of the variability, or dispersion, of the Anytime you collect data, your first step should be to scores. develop a frequency distribution for each variable in the A positively skewed curve represents a distribu- dataset for which you have collected quantitative data. tion in which there are very few scores on the right Creating a frequency distribution is simple. List the side of the distribution (see Figure 9.2). Thus, there scores in order, from highest to lowest, and then iden- are very few very high scores. The long tail point- tify the number of times each score occurs (Figure 9.3). ing to the right indicates this. In a positively skewed With these steps completed, you can create a polygon curve, most of the scores are lumped together on the to get a good sense of the normality of the distribution. left side of the curve, below the mean. For exam- In this type of diagram, the range of possible scores for ple, students from a communication department the variable is displayed on the horizontal axis. The with a strong focus on practicing communication frequencies with which those scores occur are listed on skills would likely have a positively skewed distribu- the vertical axis. With the axes defined, plot each data tion of communication apprehension scores. Why? point according to its frequency of occurrence. Now The department’s curriculum requires each course draw a line to connect each of the points you plotted. to include a communication skill or performance How would you interpret the polygon in Figure 9.3 for element. As students take communication classes, this dataset? Is it normal? Or is it skewed positively or they become more comfortable communicating, and negatively? 172 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing Data as they Data ordered from Scores Frequency were collected highest to lowest x f 73 83 83 1 82 82 82 1 76 81 81 1 75 80 80 2 83 80 79 3 79 79 78 4 77 79 77 4 76 79 76 4 69 78 75 3 78 78 74 3 71 78 73 1 78 78 72 1 80 77 71 1 77 77 70 1 74 77 69 1 81 77 74 76 79 76 80 76 78 76 78 75 77 75 77 75 74 74 76 74 79 74 75 73 76 72 70 71 72 70 75 69 4 3 Frequency ( f ) 2 1 0 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 Scores FIGURE 9.3 Developing a Frequency Distribution  DESCRIPTIVE STATISTICS 173 DESCRIPTIVE STATISTICS Number of Cases Descriptive statistics are those numbers that supply Generally, the greater the number of cases, or data information about the sample or those that supply points, the more reliable the data. One way for con- information about variables. They simply describe sumers of research to make this determination is to what is found. Having this information, researchers look for this information in the method or results sec- and consumers of research reports can make value tion of the written research report. The number of judgments or inferences about what the data mean. cases for which data are reported is represented by the Researchers describe data for each quantitative letter n or N (e.g., N = 231). Although styles vary by variable in three ways: the number of cases or data journals, generally N refers to the total number in a points, central tendency, and dispersion or variabil- sample, whereas n refers to a subsample, or a group of ity. Each of these descriptions provides information cases drawn from the sample. about the frequency of scores. The number of cases Remember that the number of cases may not simply indicates the number of sources from which always be the number of people. Rather, cases may be data were collected. Measures of central tendency the number of speaking turns, arguments, conflict epi- describe how the majority of participants responded sodes, or commercials—virtually any type of communi- to a variable. Dispersion describes the spread of cation phenomenon that a researcher has identified in scores from the point of central tendency. Each of a research question or hypothesis. these concepts is described in the following sections. Figure 9.4 shows abbreviations commonly used in Measures of Central Tendency ­descriptive statistics. Descriptive statistics provide a standardized method Measures of central tendency are the primary summary and procedure for summarizing and organizing all form for data. One of the most common summaries is cases of one quantitative variable. In a research study, the average. One number, the average, can represent the descriptive statistics are computed for each variable. sample of data on one variable. In other words, this one When this step is complete, researchers use this infor- number acts as a summary of all the scores on one vari- mation to assess differences and relationships ­between able. Research reports do not report the data collected variables. for every case on every variable. Instead, researchers Recall from Chapter 5, on measurement, that data report summary statistics for each variable. But there can be captured in four levels: nominal, ordinal, inter- are several measures of central tendency in statistics. In val, and ratio. Data must be collected at interval or research, we must specify which one we’re using. ratio levels for the mean and median to be computed. Of course, the number of cases and the mode can be Mean The arithmetic mean, or simply the mean, is the computed for data at any level. most common measure of central tendency. Commonly Number of cases n N Frequency f Mean M X Median Mdn Mode Mo Standard deviation sd SD FIGURE 9.4 Symbols Used to Represent Descriptive Statistics 174 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing TRY THIS! Are the Data Normal or Skewed? One of the best ways to learn about the normal curve, and potentially skewed distributions, is to collect data and diagram the data. Collect data from at least two of the following popu- lations (admittedly, you will not be conducting a random sample) and plot the data as a frequency distribution. Try to get at least 50 cases in your sample. Shoe sizes of other students (do not mix men and women) Number of contacts in the address book on students’ cell phones Number of pets students have Number of times students have been issued a traffic violation ticket After plotting your data on a frequency distribution, assess the normalcy of the curve. Does it look more like the normal curve or like a skewed distribution? If it is skewed, what could account for that type of distribution? referred to as the average, the mean is computed by add- This total is divided by 2 (151/2 = 75.5) to find the ing up all the scores on one variable and then dividing by median of the dataset, or 75.5. the number of cases, or N for that variable. In this and other statistics, the mean should be calculated to include Mode A third measure of central tendency is the two decimal points. Because all the scores are added mode. The mode is the score that appears most often together, the mean depends upon each and every score in a dataset. If datasets are large, it is common for the available. If one score is changed, the mean will also dataset to be bimodal or multimodal, which means change. The mean is the most sensitive to extremely high that more than one score has the largest frequency of or extremely low values of the distribution, and it is the occurrence. In fact, most distributions of scores are most commonly reported measure of central tendency. bimodal or multimodal, making it impossible for a researcher to use the mode to represent the average in Median Another measure of central tendency is later statistical calculations. the median. The median is the middle of all the scores Looking at the dataset in Figure 9.5, you can see on one variable. To compute the median, the data (or that the value of 78 is the most frequent score. Thus, scores) must be arranged in order from smallest to larg- 78 is the mode for this dataset. est. If there is an uneven number of cases, the median If a distribution of scores is normal, or completely is the score exactly in the middle of the distribution. If symmetrical, the mean, median, and mode will be the there is an even number of scores, the median is found by same number. But data are seldom this perfect. It is counting equally from the smallest and largest numbers far more likely that a distribution of scores will be to the midpoint where no number exists. Take the num- somewhat asymmetrical. Thus, the mean, median, and bers above and below this midpoint, add them together, mode will be different. and divide by 2. This calculation is the median. It may Most researchers report and use the mean in or may not be the same as the mean for a set of scores. ­describing the data for a variable. It is an appropri- Because the median is always in the middle, scores in the ate choice if the distribution is relatively normal. dataset can change without the median being affected. But if a set of scores is skewed, it may be better to Look at Figure 9.5. Notice the line between 76 report the median and use it in later calculations and 75 on the numbers in the ordered list. This is the because it better reflects the middle of the distri- midpoint of the dataset. Because a researcher cannot bution. Computing the variability in the scores can report the midpoint as “between 76 and 75,” he or help you determine whether the mean or median she adds the two numbers together (76 + 75 = 151). is most appropriate. Mode scores are infrequently  DESCRIPTIVE STATISTICS 175 Data in its raw order form Data in order from highest to lowest 73 83 83 83 75 80 83 80 79 79 69 78 78 78 71 78 62 78 78 76 80 75 74 75 73 74 80 73 78 73 56 71 78 69 64 64 76 62 75 56 Descriptive statistics for the dataset: mean = 74.25 standard deviation = 7.00 median = 75.5 (the two middle scores of 76 and 75 are averaged) mode = 78 range = 27, from 56 to 83 N = 20 FIGURE 9.5 The Data from a Measure of Communication Competence reported. When they are, the mean or median scores report the high and low scores on questionnaires. For accompany them as well. example, for the data shown in Figure 9.5, the range of 27 is the result of subtracting 56, the lowest score, from 83, the highest score. The range is a crude measure of Measures of Dispersion dispersion because changing any values between the highest and lowest score will have no effect on it. To fully describe a distribution of data, a measure of The range can also be used to describe demographic dispersion, or variability, is also needed. Two distribu- characteristics of the research participants. In these tions can have the same mean but different spreads instances, however, the lowest value is not subtracted of scores. Whenever a measure of central tendency is from the highest value. Rather, the researcher simply used, a measure of dispersion should also be reported. reports the highest and lowest values. For example, The two most commonly reported are the range and Hesse and Mikkelson (2017) describe their partici- the standard deviation; both provide information pants in the following way: about the variability of the dataset. A total of 401 individuals participated in the study, Range The simplest measure of dispersion is the range, with 213 males and 188 females. The sample ranged or the value calculated by subtracting the lowest score in age from 18 to 72, with a mean age of 31.67 years from the highest score. Generally, the range is used to old (SD = 10.10). (p. 26) 176 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing Some scholars might report the range for females in direction from convex to concave. These are the inflec- age here simply as a range of 54 years (e.g., 72 − 18 = tion points at which the +1 and −1 standard devia- 54). However, reporting just the distance between the tions are placed. The perpendicular lines to the right smallest and largest value does not tell us what part of of the mean are positive standards of +1, +2, and the age continuum participants represent. It is more +3. The perpendicular lines to the left of the mean are effective to report the smallest and largest value, as negative standards of −1, −2, and −3. The distances Hesse and Mikkelson demonstrate. between the perpendicular lines are equal and, in turn, divide the horizontal axis into standard deviations. Standard Deviation Even when the range is reported, Regardless of what your data are measuring or it is impossible to determine how close or how far the range of scores in your dataset, the normal curve apart the scores are from one another. Thus, research- and this set of standards are always the same. This is ers use standard deviation as the standard calculation a property of the theoretical normal curve. The more and representation of the variability of a dataset. The normal a distribution of scores, the more this property, formula for computing a standard deviation is avail- or rule, applies. The less normal the distribution, the able at the link for Chapter 9 at www.joannkeyton less accurate this rule. Using the normal curve as a.com/research-methods. Of course, you can use any base and the standard deviation for a set of scores, the spreadsheet or statistical software program to calcu- distribution of scores for a variable can be compared late the standard deviation. Each time a mean score is to the normal curve. Thus, researchers use the theo- reported, the accompanying standard deviation should retical normal curve to assess the distribution of the also be reported. In fact, the mean reported by itself data they obtained. When a distribution is not normal, is not interpretable. For instance, the larger the stan- researchers should provide some explanation for this dard deviation, the greater the degree the scores differ phenomenon. from the mean. Alternatively, if the standard deviation The area of the curve between the +1 and −1 is small, this indicates that the scores were very similar standards is identified in a variety of ways, includ- or close to one another. Or, if the standard deviation is ing “within one standard deviation of the mean” and zero, all the scores are the same. “one standard deviation above and below the mean.” Notice the vertical markers in the normal distri- According to the theoretical normal curve, 68.26% of bution in Figure 9.6. The middle marker is the point the cases in a dataset will fall within the +1 to −1 at which the mean exists. Now notice the two points standards (see Figure 9.6). on either side of the mean where the curve changes To find the range of scores from a dataset that would fall within the +1 to −1 standard deviations, simply add the standard deviation to the mean (or sub- tract it). When researchers refer to the typical partici- pant or typical score, they are referring to the range of scores within this area. For example, if your score on a measure of communication apprehension fell within these standards, you would be considered as average, 2.14% 2.14% or someone for whom apprehension is not exceptional 13.59% 34.13% 34.13% 13.59% in either direction. –3 –2 –1 x +1 +2 +3 For the set of scores used in Figure 9.5 (M = 74.25; Md SD = 7.00), the following would represent the range Mo of scores within the +1 to −1 standard deviations: standard deviation 68.26% M = 74.25: Add the standard deviation of 7.00 95.44% to equal 81.25, or the score at the +1 standard 99.72% ­deviation. FIGURE 9.6 Standard Deviations of the Normal M = 74.25: Subtract the standard deviation of 7.00 Curve to equal 67.25, or the score at the −1 standard ­deviation.  APPLICATION OF DESCRIPTIVE STATISTICS 177 Thus, in this case, scores from 67 to 81 would be researchers (Mikucki-Enyart & Reed, 2020) report within the +1 to −1 standards and considered typi- this information: cal for this sample. To check, count the frequency of PIL’s [parents-in law] satisfaction with the in-law scores with values from 67 to 81. That count should be relationship was assessed with a modified version of 15 out of 20, or 75% of total number of cases. When Huston et al. (1986) Marital Opinion Questionnaire the curve is normal, about 68% of the cases should (MOQ). Participants reported the extent to which lie between these two values. The remaining cases are they agreed or disagreed (1 = strongly disagree, above and below these values. 7 = strongly agree) with eight anchor items describ- The further out a score on the distribution, the more ing the in-law relationship (e.g., rewarding, miserable) extreme the score. The area between the +2 and −2 and a final item assessing the overall quality of standard deviations would contain 95.44% of the scores the relationship (1 = completely dissatisfied, in that dataset. The area between +3 and −3 standards 7 = completely satisfied). Negatively valenced items would contain 99.72% of the scores in the dataset. were reverse scored. The final, global item of the Notice that the normal curve does not touch the hori- MOQ was averaged with the mean score of the first zontal axis. Rather, it extends infinitely to the right and eight items to create an overall in-law satisfaction the left. Remember that the normal curve is theoretical score: M = 6.26, SD = 0.93, α = 0.90 (Huston et al., and must allow for the most extreme cases, even those 1986; Morr Serewicz & Canary, 2008). (p. 866) that fall outside +3 or −3 standard deviations. With this information, the mean and standard devi- ation can be interpreted to reveal the normalcy of the APPLICATION OF DESCRIPTIVE scores for the extent of their regret. In this case, it is STATISTICS easy to see that the variable had a positively skewed distribution, or very few very high scores. One reason the mean, median, and standard devia- Alternatively, when the distribution of scores appears tion are reported in the method section of a writ- normal, researchers indicate this by phrases such as ten research report is so the reader can assess the “The distribution of scores approximated the normal normalcy of the data. Descriptive findings also help curve” or “The distribution of scores appeared normal.” the reader interpret the conclusions drawn from Frequencies and percentages are also commonly data (Levine et al., 2008). The following excerpt used to provide summaries of nominal data. Examples from a research report characterizes one way of each will demonstrate their utility. AN ETHICAL Mistakes in Calculations ISSUE Whether you collect data by yourself or with the help of others, whether you calculate with a spreadsheet or statistical program, and whether you interpret data by yourself or with the help of an expert, as the researcher who reports the data, you are ultimately responsible for all aspects of data collection. Why? Because the researcher is the author of the research report. Thus, double-checking the procedures for data collection, the validity of the data as it is entered, and the results are all responsibilities of the researcher—no one else. Failing to take the time to double-check and failing to correct mistakes when they are found are ethical viola- tions of scientific standards. People trust what they read to be accurate. In fact, they may use reported results to develop a communication training program to help others or to alter their own communication behaviors. A researcher’s credibility—past, present, and future—rests on the extent to which consumers trust what they read. If you are collecting data for a project, you should double-check everything. 178 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing Frequencies researchers report indicates what interactive strategies corporate Facebook pages are more likely to include. A commonly used descriptive statistic is frequency, or the number of times a particular value of a variable ­occurs. Communication researchers often use fre- Percentages quency data to report on the occurrence of communica- Most commonly, we think of a percentage as being tion events. This type of data is actually at the nominal a number that represents some part of 100. But not level, because the researcher is making a decision for all variable scores use 100 as the base or foundation. each occurrence—did this communication phenom- Thus, it is more accurate to describe a percentage as a enon occur or did it not? comparison between the base, which can be any num- For example, Kim et al. (2014) explored what inter- ber, and a second number that is compared to the base. active strategies Fortune 100 companies use on their Look again at the previous example for the frequencies Facebook pages. As Table 9.1 demonstrates, the most and percentages reported in Table 9.1. The number of frequently used strategy was messages that triggered times an interactive component was used is the basis users’ general behavioral actions. For example, a com- for the percentages in the far right column. pany’s Facebook page would include a button to “learn Percentages are also frequently used to describe more about it”! When clicked, Facebook users would ­attributes of participants or characteristics of their be taken to a page with more information about the communication behavior. For a study that examined product. Table 9.1 shows that of the 1,486 corporate how parents mediate their tweens’ (e.g., ages 8 to Facebook postings examined by the research team, 655 14) disclosure of information online (Wonsun et al., or 44.1% used a general behavioral action strategy. 2012), the following percentages are reported: The table provides basic descriptive information about what the researchers discovered. Across the 1,486 Two hundred and thirty adults (116 men and 114 Facebook sites coded in this content analysis study, six women) completed a survey on transgression and different strategies of interactivity were present and forgiveness in their friendships. They were recruited coded. Both the n, or number or frequency, and the using convenient sampling, and questionnaires were percentage of the total are reported. By looking at the administered across several undergraduate courses. frequencies in Table 9.1, you can also tell which interac- The average age of participants was 21 (M = 21.61; tive strategy was used the least. In this study, Facebook SD = 4.98). Approximately 74% of participants self- pages that allowed users to chat or virtually interact identified as Caucasian, 18% as African American, 3% with a company representative were used less fre- as Asian American, 2% as Hispanic, and the remain- quently (n = 39, 2.6%). Examining the frequencies, the der (3%) did not select these racial categories. (p. 297) TABLE 9.1 Number and Percentage of Interactive Components Used on Facebook Corporate Pages n % 1. Messages seeking fans’ feedbacks/opinions 390 26.2 2. Messages providing live chat/virtual online opportunities 39 2.6 3. Messages seeking fans’ specific action-based participation 160 10.8 4. Messages triggering fans’ general behavioral action 655 44.1 5. Messages about seasonal/holiday greetings 66 4.4 6. Messages about fans’ daily life/personal life 160 10.8 Total 1,486 100.0 SOURCE: Kim, S., Kim, S-Y., & Sung, K. H. (2014). Fortune 100 companies’ Facebook strategies: Corporate ability versus social responsibility. Journal of Communication Management, 18(4), 343–362. https://doi.org/10.1108/JCOM-01-2012-0006  CRUNCHING THE NUMBERS 179 By putting data from the study’s participants in and provide a result—but it will be the wrong result or percentage form, the researchers make it easy for the a noninterpretable result! If you are going to use any of reader to get an idea of how research participants iden- these programs, you need basic instruction on how to tified their race. With that information, readers can set up the spreadsheet or statistical program, how to make an assessment about the degree to which the enter data, and how to appropriately run and interpret sample is relevant and appropriate for the study. the statistical tests. Despite the obvious advantages, the use of spread- sheet or statistical software can create a false sense CRUNCHING THE NUMBERS of security. There are five issues that you should con- sider if you use these programs for data entry and sta- In research, enough data are collected that comput- tistical computation (Pedhazur & Schmelkin, 1991). ing statistics by hand is generally out of the question. First, computers can fail. Programs can stall. Never But for small datasets, you will be able to perform the trust all your data to one file on one storage device. needed calculations with a calculator, as long as it has Second, results can only be as good as the data a square root function. The square root function is indi- entered. Whereas a spreadsheet or statistical package cated by the symbol √  . may decrease the number of computational errors, With medium or large datasets, you will need to use data-entry errors can still occur. Errors such as enter- a spreadsheet program (such as Excel) or a statistics ing the wrong value or omitting a value are common. program (such as SAS or SPSS). A spreadsheet pro- Because your conclusions and interpretations rest on gram works just fine for simple data analysis projects the validity of the data, it is wise to double-check all and is easy to use. Programs specifically designed for data entered. statistical use require a more specialized knowledge of Third, researchers—even experienced ones—tend to statistics and programming. limit their thinking to statistical procedures they know One caution, however, about using any software they can do on the computer. Researchers always need program to help compute statistics is that although to be mindful of this and periodically stretch their sta- programs compute the statistical tests, the program tistical knowledge and expertise. Fourth, the power of relies on you to request the appropriate test and to computing makes it possible to create an abundance of make the appropriate interpretation of the outcome. analyses. Do not be tempted to “see what will happen” Likewise, the program relies on you to indicate which by running any and all statistics. Rather, the techniques data should be included in the test. If you specify the and statistics chosen should be driven by your research wrong test or indicate the wrong data to be used for that questions and hypotheses. Finally, as the researcher, test, the software program will still do the calculation you are the person responsible for the results and their DESIGN Describing Variables CHECK When reading a research report, look for the descriptive statistics for each variable in the method section or in a table. Here you should find: 1. The number of cases for this variable 2. The mean or median 3. The standard deviation 4. The range of scores possible or the range of scores obtained With this information, you can make a determination of the normalcy of the data even if the researcher omits this description. 180 CHAPTER 9 / Descriptive Statistics, Significance Levels, and Hypothesis Testing interpretations, even if someone else does your statisti- to the population, or larger group from which the cal programming. sample was pulled. Accepting the conclusions derived For quantitative research, descriptive statistics from the sample and assuming that those conclusions simply describe the data. To provide answers to are also applicable to the population is known as hypotheses and research questions, researchers then ­population ­inference. More commonly in communica- set significance levels. tion research, studies are designed to test the predic- tions of a theory (Hayes, 2005). In other words, are the data consistent with the predictions the researcher SIGNIFICANCE LEVELS drew from the theory? If so, then the researcher can claim that the theory would likely work in similar A significance level is a criterion for accepting or reject- situations. This is known as process inference. Social ing hypotheses and is based on probability. Probabil- scientists base this inference on the probability level ity is a scientific term to identify how much error the computed for each statistical test. The probability level, researcher finds acceptable in a particular statistical or significance level, which is established for each sta- test. But you are also familiar with the concept of prob- tistical test prior to computing the statistical test, is the ability in a less scientific sense. You have made many level of error the researcher is willing to accept. You decisions in your life based on the degree of probability will find this symbolized in written research reports for some event occurring. Did you ever drive to the as the letter p or referred to as the alpha level. If the beach even though rain clouds were approaching? probability level of the statistical test is acceptable, or Have you ever gambled that you had enough gas to get within the traditions of the discipline, then the find- you to your destination? Did you choose to ask either ings are believed to be real, not random, and the infer- your mother or your father for money based on the like- ence can be presumed to be valid. If the probability lihood of which one would give it to you? In these deci- level is unacceptable, no conclusion can be drawn sions and others similar to them, you were basing your (Boster, 2002). actions on your informal rules of probability. In other Generally, the probability level of 0.05 is accepted words, you accepted a certain degree of risk, or error, as the standard in the communication discipline. This in making these decisions. It probably would not rain, means that 5 out of 100 findings that appear to be valid but what if it did? The last time your fuel gauge was will, in fact, be due to chance. When the probability close to empty you drove another 50 miles without a level of a statistical test is 0.05 or less, the finding is real, problem. And you knew it was better to ask your mom and labeled as statistically significant. Setting the stan- than ask your dad, as your mom usually said yes. dard as a 0.05 probability level is arbitrary; generally, In scientific research, probability is an estimate communication researchers have adopted this stan- of “what would happen if the study were actually dard (0.01 and 0.001 are other common standards). You repeated many times, telling the researcher how should note, however, that the selection of a 0.05 prob- wrong the results can be” (Katzer et al., 1978, p. 60). ability level was not based on mathematical, statistical, In other words, probability is a calculation about the or substantive theory (Henkel, 1976). validity of the results. Researchers could choose to If the probability level of a statistical test is greater conduct the same survey or experiment many times, than 0.05 (e.g., p = 0.15, p = 0.21), the finding is labeled but calculating the probability, or significance, of a nonsignificant. This means that the difference could statistical test for a sample of data has become the easily be caused by chance or random error. What accepted manner in which scientists deal with this causes the probability level to be unacceptable, or issue. As a result, the level of probability provides an higher than 0.05? Many things can contribute to high estimate of the degree to which data from a sample probability levels. would reflect data from the population the sample Items on a survey or questionnaire intended to was drawn from. measure a construct may be poorly written such that Perhaps you are thinking, “Why wouldn’t the participants respond inconsistently to them. The results of a study be valid?” In some cases, research- researcher or assistants conducting an experiment can ers are looking to make inferences from the sample, also create bias that generates unacceptable levels of or people who participated in their particular study, probability. For example, male participants may be  HYPOTHESIS TESTING 181 treated differently from female participants. Research privileges the alternative hypothesis in the writing of assistants may unconsciously smile at participants they journal articles, it is technically the null hypothesis know and ignore those with whom they are unfamil- that is statistically tested. Hypothesis testing relies on iar. Or, the theory, which was the foundation of the two scientific techniques, significance testing and sam- study, is not accurate or the theory was not adequately pling (Chapter 6). or appropriately tested (Hayes, 2005). It is important Testing the null hypothesis is, in essence, an act to remember that setting the significance level at 0.05 is of decision making. Do you accept the alternative arbitrary. There can be good reasons to make the prob- explanation, or do you retain the null hypothesis? ability level more rigorous, setting it, for example, at Most researchers rely on the conventions of hypoth-.01. In their study of the effectiveness of message strat- esis testing because, combined with random sampling egies for talking about AIDS and condom use, Reel and significance testing, they can be effective in sepa- and Thompson (1994) set the level at