· **Quantitative Data Analysis: Statistics**

**Introduction**

Understanding the use of basic statistical strategies is part of being a critical consumer of published research literature. Unless they plan to conduct research themselves, it is not as important for counselors to understand the mathematical calculations of the statistical techniques as it is to be able to recognize the names of the common ones and what kind of information they provide. There are several commercially-available software packages for analyzing quantitative data, one of which is described in detail in Chapter 14 of Counseling Research: Quantitative, Qualitative, and Mixed Methods.

**Descriptive and Inferential Statistics**

In quantitative studies, statistical techniques are used for data analysis. The two main categories of statistics are descriptive and inferential. Descriptive statistics are used to summarize the data. Some common descriptive statistics are the measures of central tendency: the mean, median, and mode. They provide information about where the middle is in distribution of scores. On the normal distribution, the mean, median, and mode are the same. Distributions are said to be skewed when extreme scores draw the mean away from the middle of the distribution. Measures of variability, such as the range, variance, and standard deviation, provide information about how widely a distribution of scores is dispersed (Erford, 2015, p. 250). The standard deviation is a measure of how the scores cluster around the mean. The greater the standard deviation, the greater the spread of scores.

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Inferential statistics are used to make inferences from the sample to the population. All inferential statistical procedures are based on probability theory. They are used to test hypotheses. Three commonly used inferential statistics are chi square, t-test, and analysis of variance (ANOVA). Chi square is used with nominal data to determine if the observed expected frequency differs significantly from the expected frequency. A t-test is used to determine whether there is a statistically significant difference between the means of two groups. ANOVA is used to determine whether there is a statistically significant difference between the means of three or more groups.

**Statistical Significance **

When a quantitative study tests a hypothesis, it is technically the null hypothesis being tested. The null hypothesis says there is no difference between the groups, or relationship between the variables (depending on the research design). If the statistical procedure indicates there is statistical significance, the null hypothesis is rejected, meaning that the probability is high that there really is a group difference or strong relationship between the variables.

Rejecting the null hypothesis is not equivalent to proving the research or alternative hypothesis. Researchers can embrace the research hypothesis as one plausible explanation, but because only the null hypothesis can be tested, the researcher cannot be completely certain. That is why it is inaccurate to say that a study proves something. It is more prudent and correct to state that the findings from this study lend support to the theory, or the results fail to support the theory.

**Validity**

The concept of validity has several applications to research. External validity is the extent to which the research findings can be generalized from the sample to the population. Internal validity is the extent to which we can trust that the changes in the dependent variable are due to the effect of the independent variable. There exist multiple threats to external validity and internal validity. One of the threats to internal validity has to do with instrumentation, which is the quality of the measurement instrument being used to collect data.

When instruments are used to assess one or more variables, consideration must be given to their validity and reliability. These are some of the concepts with which to be familiar: face validity, content validity, criterion validity, construct validity, inter-rater reliability, internal consistency reliability, equivalent forms reliability, and test-retest reliability.

**Reference**

Erford, B. T. (2015). Research and evaluation in counseling (2nd ed.). Stamford, CT: Cengage.

**Objectives**

To successfully complete this learning unit, you will be expected to:

1. Describe descriptive and inferential statistical concepts in a research study

Assignment **Quantitative Data Analysis: Statistical Techniques**

**Resources**

After studying the introduction to this unit and completing the study activities, summarize the quantitative research article you selected. Include enough detail to provide the context for the main focus of this post, the statistical techniques that were used in the study. Identify a descriptive statistic from the study. Also, describe the statistical technique that was used to answer the research question or test the hypothesis. The description should be in your own words, not direct quotes from the article. Cite and reference the course text to demonstrate that you are incorporating material from an authoritative source on research methods.

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