Statistical data analysis is a procedure of performing various statistical operations. The manually computed value of correlation between age and self-esteem, using the above formula as shown in Table 14.1, is 0.79. Missing data is an inevitable part of any empirical data set. Quantitative data analysis. Although we can see a distinct pattern of grade distribution between male and female students in Table 14.3, is this pattern real or “statistically significant”? Hypothetical data on age and self-esteem. The bivariate scatter plot in the right panel of Figure 14.3 is essentially a plot of self-esteem on the vertical axis against age on the horizontal axis. Another useful way of presenting bivariate data is cross-tabulation (often abbreviated to cross-tab, and sometimes called more formally as a contingency table). Whether this difference between expected and actual count is significant can be tested using a chi-square test . The range in our previous example is 36-15 = 21. The frequency distribution of a variable is a summary of the frequency (or percentages) of individual values or ranges of values for that variable. Wikibuy Review: A Free Tool That Saves You Time and Money, 15 Creative Ways to Save Money That Actually Work. In this example, df = (2 – 1) * (3 – 1) = 2. One of the main reasons is that statistical data is used to predict future trends and to minimize risks. The second measure of central tendency, the median , is the middle value within a range of values in a distribution. For instance, for measuring a construct such as “benefits of computers,” if a survey provided respondents with a checklist of b enefits that they could select from (i.e., they could choose as many of those benefits as they wanted), then the total number of checked items can be used as an aggregate measure of benefits. There are few certainties when it comes to data analysis, but you can be sure that if the research you are engaging in has no numbers involved, it is not quantitative research. In other words, do the above frequency counts differ from that that may be expected from pure chance? Note that many other forms of data, such as interview transcripts, cannot be converted into a numeric format for statistical analysis. The information such as date, time, location, and type of crime is quantitative in that statistics can be used to Simple Interactive Statistical Analysis SISA allows you to do statistical analysis directly on the Internet. Investors can use this type of statistical analysis to assess stocks, and researchers define hypotheses and businesses assess major decisions using this process. the chance of getting the same results if the null hypothesis were true. The p-value is compared with the significance level (α), which represents the maximum level of risk that we are willing to take that our inference is incorrect. Meta-analysis: methods for quantitative data synthesis What is a meta-analysis? The data is considered in three types: Time series data: A set of observations on the values that a variable takes at different times. The significance level defines how strong the support is or is not for the analysis. To calculate the value of this correlation, consider the hypothetical dataset shown in Table 14.1. In this chapter, we will examine statistical techniques used for descriptive analysis, and the next chapter will examine statistical techniques for inferential analysis. primarily statistical. If self-esteem increases, then we have a positive correlation between the two variables, if self-esteem decreases, we have a negative correlation, and if it remains the same, we have a zero correlation. One of the main reasons is that statistical data is used to predict future trends and to minimize risks. Data transformation. b. numerical data that could usefully be quantified to help you answer your research question(s) and to meet your objectives. If the two variables were uncorrelated, the scatter plot would approximate a horizontal line (zero slope), implying than an increase in age would have no systematic bearing on self-esteem. The arithmetic mean of these values is (15 + 20 + 21 + 20 + 36 + 15 + 25 + 15)/8 = 20.875. This figure indicates t hat age has a strong positive correlation with self-esteem, i.e., self-esteem tends to increase with increasing age, and decrease with decreasing age. The two broad groups of quantitative analysis process are interval estimates and hypothesis tests, which provide specific tools for use. Sometimes, data may need to be aggregated into a different form than the format used for data collection. A critical region represents values in which a researcher can reject the null hypothesis. Many businesses rely on statistical analysis and it is becoming more and more important. Each observation can be entered as one row in the spreadsheet and each measurement item can be represented as one column. Also note that H 1 is a non-directional hypotheses since it does not specify whether r is greater than or less than zero. These measures include mean, median, and mode, and they are used to describe how data behaves in a distribution. parametric tests are more accurate, but require the assumption to be made about the data, eg. Hence, the lower triangular matrix (values below the principal diagonal) is a mirror reflection of the upper triangular matrix (values above the principal diagonal), and therefore, we often list only the lower triangular matrix for simplicity. It refers to the data which computes the values and counts and can be expressed in numerical terms is called quantitative data. The most commonly used parameters are the measures of central tendencyCentral TendencyCentral tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. A codebook is a comprehensive document containing detailed description of each variable in a research study, items or measures for that variable, the format of each item (numeric, text, etc. Quantitative data is defined as the value of data in the form of counts or numbers where each data-set has an unique numerical value associated with it. In statistics, most of the analysis are conducted using this data. ... Other Quantitative Analysis. The formula for calculating bivariate correlation is: where r xy is the correlation, x and y are the sample means of x and y, and s x and s y are the standard deviations of x and y. Regarding qualitative and quantitative analysis of data, Kreuger and Neuman (2006:434) offer a ... but quantitative researchers use the language of statistical relationships in analysis. Note that any value that is estimated from a sample, such as mean, median, mode, or any of the later estimates are called a statistic . Figure 14.3. statistical analysis. For instance, if we have a measurement item on a seven-point Likert scale with anchors ranging from “strongly disagree” to “strongly agree”, we may code that item as 1 for strongly disagree, 4 for neutral, and 7 for strongly agree, with the intermediate anchors in between. Univariate statistics include: (1) frequency distribution, (2) central tendency, and (3) dispersion. The type of report or need for information dictates the tools necessary for the process. For instance, we can measure how many times a sample of respondents attend religious services (as a measure of their “religiosity”) using a categorical scale: never, once per year, several times per year, about once a month, several times per month, several times per week, and an optional category for “did not answer.” If we count the number (or percentage) of observations within each category (except “did not answer” which is really a missing value rather than a category), and display it in the form of a table as shown in Figure 14.1, what we have is a frequency distribution. Answering such a question would require testing the following hypothesis: H 0 is called the null hypotheses , and H 1 is called the alternative hypothesis (sometimes, also represented as H a ). In other words, not all the statistical tools available have a purpose in these studies. The median refers to the point distribution above which and below which 50% of the cases fall. Quantitative data refers to numbers and statistics, and is very useful in finding patterns of behaviour or overriding themes. Quantitative classification refers to the classification of data according to some characteristics, which can be measured such as height, weight, income, profits etc. Directional hypotheses will be specified as H 0 : r ≤ 0; H 1 : r > 0 (if we are testing for a positive correlation). What are the Different Data Analysis Techniques? Most statistical programs provide a data editor for entering data. Table 14.3. We are interested in testing H 1 rather than H 0 . Crime analysis employs both types of data and techniques depending on the analytical and practical need. For example, crime data can be used in various ways, both quantitatively and qualitatively. An analysis that involves only one variable (i.e. If p>0.05, then we do not have adequate statistical evidence to reject the null hypothesis or accept the alternative hypothesis. Data coding. Qualitative data analysis works a little differently from quantitative data, primarily because qualitative data is made up of words, observations, images, and even symbols. Let’s say that we wish to study how age is related to self-esteem in a sample of 20 respondents, i.e., as age increases, does self-esteem increase, decrease, or remains unchanged. The cross-tab data in Table 14.3 shows that the distribution of A grades is biased heavily toward female students: in a sample of 10 male and 10 female students, five female students received the A grade compared to only one male students. For example, descriptive statistics are among the most common for quantitative statistical analysis. During data entry, some statistical programs automatically treat blank entries as missing values, while others require a specific numeric value such as -1 or 999 to be entered to denote a missing value. Two methods that can produce relatively unbiased estimates for imputation are the maximum likelihood procedures and multiple imputation methods, both of which are supported in popular software programs such as SPSS and SAS. For our computed correlation of 0.79 to be significant, it must be larger than the critical value of 0.44 or less than -0.44. Univariate analysis, or analysis of a single variable, refers to a set of statistical techniques that can describe the general properties of one variable. There is no shortage of application for this analysis process. Coding is the process of converting data into numeric format. In the two -tailed table, the critical value of r for α = 0.05 and df = 18 is 0.44. In contrast, the distribution of C grades is biased toward male students: three male students received a C grade, compared to only one female student. Quantitative Data Analysis CHAPTER 13 “O h no, not data analysis and statistics!” We now hit the chapter that you may have been fearing all along, the chapter on data analysis and the use of statistics. In layman's terms, this means that the quantitative researcher asks a specific, narrow question and collects a sample of numerical data from participants to answer the question. 40-50 50 . As you see the difference between qualitative and quantitative data is significant, not only when it comes to the nature of data but also the methods and techniques for analysis are quite different. Both qualitative and quantitative data analysis have a vital place in statistics, data … In quantitative research, the sole approach to data is statistical and takes places in the form of tabulations. Such a curve is called a normal distribution. Statistical tests for quantitative data. Weight (in kgs) No of Studemts. Since our computed value of 0.79 is greater than 0.44, we conclude that there is a significant correlation between age and self-esteem in our data set, or in other words, the odds are less than 5% that this correlation is a chance occurrence. 50-60 200 . However, the distribution of B grades was somewhat uniform, with six male students and five female students. Quantitative data refers to: a. statistical analysis. The degree of freedom is the number of values that can vary freely in any calculation of a statistic. (iv) Quantitative classification. ), the response scale for each item (i.e., whether it is measured on a nominal, ordinal, interval, or ratio scale; whether such scale is a five-point, seven-point, or some other type of scale), and how to code each value into a numeric format. Business owners can now use quantitative methods to predict trends, determine the allocation of resources, and manage projects.Quantitative techniques are also used to evaluate investments. In the above example, the sorted values are: 15, 15, 15, 18, 22, 21, 25, 36. Standard deviation , the second measure of dispersion, corrects for such outliers by using a formula that takes into account how close or how far each value from the distribution mean: where σ is the standard deviation, x i is the i th observation (or value), µ is the arithmetic mean, n is the total number of observations, and Σ means summation across all observations. Rather, it is tested indirectly by rejecting the null hypotheses with a certain level of probability. Data preparation usually follows the following steps. Most research cases have a null hypothesis and an alternative hypothesis. For most statistical analysis, α is set to 0.05. This plot roughly resembles an upward sloping line (i.e., positive slope), which is also indicative of a positive correlation. Readers are advised to familiarize themselves with one of these programs for understanding the concepts described in this chapter. More often than not, it involves the use of statistical modeling such as standard deviation, mean and median. If the correlations involve variables measured using interval scales, then this specific type of correlations are called Pearson product moment correlations . Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test.Significance is usually denoted by a p-value, or probability value.. Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. Once data is collected, you may need to process it before it can be analyzed. Such pattern can also be seen from visually comparing the age and self-esteem histograms shown in Figure 14.3, where it appears that the top of the two histograms generally follow each other. What Are the Different Types of Quantitative Analysis Tools? numerical data that could usefully be quantified to help you answer your research question (s) and to meet your objectives. The term statistical data refers to the data collected form different sources through methods experiments, surveys and analysis. The purpose of applied statistical techniques is to either support or not support each hypothesis. There are two different statistical tables for one-tailed and two -tailed test. These statistics include mode, mean, and median along with standard deviation and variance, among other potential statistics. A simple cross-tabulation of the data may display the joint distribution of gender and grades (i.e., how many students of each gender are in each grade category, as a raw frequency count or as a percentage) in a 2 x 3 matrix. Weight (in kgs) No of Studemts. For example, in a survey regarding the election of a Mayor, parameters like age, gender, occupation, etc. Coding is especially important for large complex studies involving many variables and measurement items, where the coding process is conducted by different people, to help the coding team code data in a consistent manner, and also to help others understand and interpret the coded data. Statistical treatment of data greatly depends on the kind of experiment and the desired result from the experiment. Other types of means include geometric mean (n th root of the product of n numbers in a distribution) and harmonic mean (the reciprocal of the arithmetic means of the reciprocal of each value in a distribution), but these means are not very popular for statistical analysis of social research data. This data must be converted into a machine -readable, numeric format, such as in a spreadsheet or a text file, so that they can be analyzed by computer programs like SPSS or SAS. Qualitative data analysis is non-statistical, its methodological approach is primarily guided by the concrete material at hand. Click on one of the procedure names below, fill in the form, click the button, and the analysis will take place on the spot. Coded data can be entered into a spreadsheet, database, text file, or directly into a statistical program like SPSS. To answer this question, we should compute the expected count of observation in each cell of the 2 x 3 cross-tab matrix. Statistics is basically a science that involves data collection, data interpretation and finally, data validation. In some research reports, interval estimates or other quantitative methods may have inclusion. d. any data you present in your report. Once data is collected, you may need to process it before it can be analyzed. Such deletion can significantly shrink the sample size and make it extremely difficult to detect small effects. A codebook should be created to guide the coding process. What is the Difference Between Quantitative and Qualitative Research. There are parametric and non-parametric tests. Time series data means that data is in a series of particular time periods or intervals. Deriving absolute meaning from such data is nearly impossible; hence, it is mostly used for exploratory research. Ratio scale data such as age, income, or test scores can be coded as entered by the respondent. Quantitative analysis refers to a set of processes by which numerical data is analyzed. The alternative hypothesis indicates some changes exist from the initial null hypothesis. Secondary quantitative data is often available from official government sources and trusted research organizations.In the U.S., the U.S. Census, the General Social Survey, and the American Community Survey are some of the most commonly used secondary data sets within the social sciences. Statistical analysis is a study, a science of collecting, organizing, exploring, interpreting, and presenting data and uncovering patterns and trends. Age is a ratio-scale variable, while self-esteem is an average score computed from a multi-item self-esteem scale measured using a 7-point Likert scale, ranging from “strongly disagree” to “strongly agree.” The histogram of each variable is shown on the left side of Figure 14.3. Time series analysis is a statistical technique that deals with time series data, or trend analysis. Quantitative data analysis may include the calculation of frequencies of variables and differences between variables. The two middle values are 18 and 22, and hence the median is (18 + 22)/2 = 20. The range is the difference between the highest and lowest values in a distribution. Quantitative analysis refers to a set of processes by which numerical data is analyzed. 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