# Descriptive Research Methods

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Intro and Descriptive Research Methods

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Such a curve is called a normal distribution. Central tendency is an estimate of the center of a distribution of values. There are three major estimates of central tendency: mean, median, and mode. Consider a set of eight test scores: 15, 22, 21, 18, 36, 15, 25, 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. The second measure of central tendency, the median , is the middle value within a range of values in a distribution. This is computed by sorting all values in a distribution in increasing order and selecting the middle value.

In case there are two middle values if there is an even number of values in a distribution , the average of the two middle values represent the median. In the above example, the sorted values are: 15, 15, 15, 18, 22, 21, 25, Lastly, the mode is the most frequently occurring value in a distribution of values. In the previous example, the most frequently occurring value is 15, which is the mode of the above set of test scores.

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. Dispersion refers to the way values are spread around the central tendency, for example, how tightly or how widely are the values clustered around the mean. Two common measures of dispersion are the range and standard deviation. The range is the difference between the highest and lowest values in a distribution.

The range is particularly sensitive to the presence of outliers. 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:. The square of the standard deviation is called the variance of a distribution. Bivariate analysis examines how two variables are related to each other.

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. To calculate the value of this correlation, consider the hypothetical dataset shown in Table The two variables in this dataset are age x and self-esteem y. The formula for calculating bivariate correlation is:. The manually computed value of correlation between age and self-esteem, using the above formula as shown in Table This figure indicates t hat age has a strong positive correlation with self-esteem, i.

Such pattern can also be seen from visually comparing the age and self-esteem histograms shown in Figure Note here that the vertical axes in Figure The bivariate scatter plot in the right panel of Figure This plot roughly resembles an upward sloping line i. If the two variables were negatively correlated, the scatter plot would slope down negative slope , implying that an increase in age would be related to a decrease in self-esteem and vice versa. 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.

After computing bivariate correlation, researchers are often interested in knowing whether the correlation is significant i. 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. Although they may seem like two hypotheses, H 0 and H 1 actually represent a single hypothesis since they are direct opposites of each other. We are interested in testing H 1 rather than H 0.

Also note that H 1 is a non-directional hypotheses since it does not specify whether r is greater than or less than zero. Significance testing of directional hypothesis is done using a one-tailed t-test, while that for non-directional hypothesis is done using a two-tailed t-test. In statistical testing, the alternative hypothesis cannot be tested directly.

Rather, it is tested indirectly by rejecting the null hypotheses with a certain level of probability. Statistical testing is always probabilistic, because we are never sure if our inferences, based on sample data, apply to the population, since our sample never equals the population. The probability that a statistical inference is caused pure chance is called the p-value. The easiest way to test for the above hypothesis is to look up critical values of r from statistical tables available in any standard text book on statistics or on the Internet most software programs also perform significance testing.

The degree of freedom is the number of values that can vary freely in any calculation of a statistic. In case of correlation, the df simply equals n — 2, or for the data in Table There are two different statistical tables for one-tailed and two -tailed test. For our computed correlation of 0. Since our computed value of 0. Most research studies involve more than two variables. Such correlations are easily computed using a software program like SPSS, rather than manually using the formula for correlation as we did in Table A correlation matrix is a matrix that lists the variable names along the first row and the first column, and depicts bivariate correlations between pairs of variables in the appropriate cell in the matrix.

The values along the principal diagonal from the top left to the bottom right corner of this matrix are always 1, because any variable is always perfectly correlated with itself. Further, since correlations are non-directional, the correlation between variables V1 and V2 is the same as that between V2 and V1. 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.

If the correlations involve variables measured using interval scales, then this specific type of correlations are called Pearson product moment correlations. Another useful way of presenting bivariate data is cross-tabulation often abbreviated to cross-tab, and sometimes called more formally as a contingency table. A cross-tab is a table that describes the frequency or percentage of all combinations of two or more nominal or categorical variables. As an example, let us assume that we have the following observations of gender and grade for a sample of 20 students, as shown in Figure A simple cross-tabulation of the data may display the joint distribution of gender and grades i.

This matrix will help us see if A, B, and C grades are equally distributed across male and female students. The cross-tab data in Table 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. However, the distribution of B grades was somewhat uniform, with six male students and five female students. The last row and the last column of this table are called marginal totals because they indicate the totals across each category and displayed along the margins of the table.

Although we can see a distinct pattern of grade distribution between male and female students in Table In other words, do the above frequency counts differ from that that may be expected from pure chance? To answer this question, we should compute the expected count of observation in each cell of the 2 x 3 cross-tab matrix. The researcher not only explores the surface level, but also attempts to explore the research problem at a deeper level. A researcher who conducts a descriptive research collects detailed information from the participants.

He can use a number of techniques for this purpose. Some of the widely used techniques in the social sciences are surveys , interviews , case study , and even observation. For an example, a researcher who wants to explore the attitudes of teenagers towards the commodification of language education can conduct a descriptive research. This is because his research aims at understanding the attitudes of a particular age group on the phenomenon of commodification of language. For this particular research, he can use survey method and also in-depth interviews as data collection methods. However, correlational research is different.

Unlike in the case of descriptive research where the focus is on collecting descriptive data, in correlational research the researcher attempts to identify associations that exist between variables. The researcher also makes an effort to understand the nature of the relationship as well. However, it is vital to point out that although the researcher identifies whether there is a relationship between factors, he does not manipulate the variables to come to conclusions. He can neither predict which variable influences the other. For an example, a researcher who studies on suicide can come up with an idea that there is a relationship between teenage suicide and love affairs.

This is a prediction that he makes. However, in a correlational research to identify the connection between variables, the researcher needs to find patterns in his data corpus. This highlights that there exist a clear difference between these two types of research. Now let us summarize the difference as follows.