# Statistical Methods in the Context of Psychological Research

## Statistical Methods in the Context of Psychological Research

**Introduction**

Psychology originally started out as a branch of philosophy but has since acquired an independent status. It employs scientific methodology in the studies of human behavior and emotions. This means that the basic scientific procedure of postulating a hypothesis and then proceeding to validate these with the use of empirical tests is the standard approach. Psychology is both an academic and practical subject. An academic subject, it studies in depth all topics under personality and related topics like social behavior and human development and emotions. As a practical subject, it carries out investigations in respect of practical problems associated with every life of a human being. Psychology draws from various fields of knowledge in analyzing psychological problems and in particular it assumes the validity of certain concepts in philosophy such as deduction, induction and abduction. It uses the concepts of deductive nomological reasoning and inductive reasoning extensively in explanandums. This study is designed to introduce the student to the use of statistical methods as one of the main tools in the acquisition and synthesis of knowledge in Psychology.

**Types of Research**

Research in Psychology is usually conducted by using either qualitative or quantitative methods in accordance with scientific methods. The qualitative methods involve the use of interviews and observations. Creswell (2003) explains that there are five types of qualitative research, namely narrative, phenomenology, ethnography, case study, and grounded theory. Creswell also held that quantitative methods include practical experiments in real life situation, cross-sectional study, case-control study, and longitudinal study. The quantitative methods are the ones that are readily open to statistical analysis.

**Types of Statistical Methods**

The nature of most psychological enquiries involves extracting information from data obtained by observing a population or individual members of a population. The psychological parameters under scrutiny on many occasions do not lend themselves to direct measurements and the most optimal way of studying the characteristics is to resort to statistical methods. These methods can be classified into two broad categories namely:

**Descriptive statistics**

This involves the use of mathematical concepts to collect, classify and summarize data with the purpose of describing the set of data in an unambiguous manner. Objective statements can then be made about psychological phenomena after representing the set of data with quantities known as measures of central tendency and measures of variability.

**Inferential Statistics**

In contrast to the above, Inferential statistics tries to make judgment and reach conclusions beyond the data by making inferences on the nature of the general population that the set of data came from. Statistical theory is used to select a test statistic and a hypothesis is then tested to decide whether or not there is a significant statistical variation. Inferential Statistics is a method of moving from a particular case to a general case. Many of the Inferential Statistical methods are based on the General Linear Model however there are more sophisticated methods available including the Multivariate Analysis Method.

**Research Process in Psychology**

Basically Research Psychologists engage in studies in order to:

1. Test the validity of a particular concept or theory in the field of psychology

2. Test an application in a real life situation

3. Make propositions about the existence of some characteristics in a sample or population

4. Make propositions about relationships between characteristics identified

5. Test or develop a technique in psychology

In all cases, the design of the experiment is of paramount importance. It should lead to an unambiguous conclusion and must not leave room for alternative interpretation of the results. Usually an ideal design is available but the problem is that the nature of psychological issues makes it impracticable to use. Therefore researchers have to resort to real life designs that are as near as possible to the ideal design. (Kirk, 1995)

An ideal experiment will have at least one independent variable usually referred to as variable X, and a dependent variable Y. Ideal experiments in psychology feature two groups or samples from the set of possibilities, the population. The first group, the control group, is the set in which the characteristic variable X is kept constant. The second set is known as the experimental group.

Such an experiment should have the following properties:

1. The experimental group should be identical to the control group in the choice of membership.

2. The sample chosen should be a perfect representation of the population.

3. Both the control and experimental groups should be subject to identical conditions.

4. The measurement of the output variable Y must be precise and accurate for both groups.

These conditions are very difficult to meet in real life situations and researchers have to device means to get as close as possible. One such device is the method of assignment to group known as random sampling. There are many other types of statistical sampling that may prove appropriate for each particular type of experiment (Smith, 2001). Other strategies that can be employed include random assignment to groups, matched-group designs, repeated-measures designs, correlational research designs, and single-subject research. (Goos & Bradley, 2011)

**Contemporary Statistical Methods**

Before starting out on any psychological research, it is important to select in advance the statistical method to be employed and to design the experiment to fit the statistical model.

**Descriptive Statistics**

The underlying concept in descriptive statistics is the use of measures of central tendency and variability to describe the data. The method involves the use of the following definitions and formula.

**Measures of Central Tendency**

The mean is defined as the arithmetic average of a set of data. In describing the set, it is necessary to include both the population mean and the sample mean. The population mean is derived by summing up all the scores in the population and dividing the figure obtained by the total number (N) of scores in the population. The sample mean is the average for the particular sample drawn.

These are represented as follows:

μ = ΣX / N (where μ is the population mean)

x = Σx / n (x is sample mean)

Sometimes when the set of scores is skewed the mean can be misleading and the median is then used as a better description.

The median is described as the score in the middle when all the scores are ranked in order of magnitude. A third statistic frequently in use is called the mode. It is simply the score that occurs the most number of times in the data. It is possible to have more than one mode and such a set of data is said to be multimodal.

**Measures of Variability**

The measures of variability enable psychologists to determine how representative of the population the sample obtained is. This is important when making generalized statements about the population. The most commonly used measures of variation are the range, variance and the standard deviation. The range is defined as the difference between the greatest and the smallest scores. It is calculated by subtracting the lowest score from the highest score. The range only gives a rough guide to the variability and the researcher in addition usually has to calculate the variance and the standard deviation. These are better representations.

The variance is the sum of the squared deviations of each score from the means. The formula for calculating the variance (σ2) is as follows:

σ2 = Σ (Xi - μ)2 / N

Xi are the values of the variables in the set of data.

The standard deviation is defined as the square root of the variance and is calculated as follows:

σ = sqrt [σ2] = sqrt [Σ ( Xi - μ )2 / N ]

As an example let us take a population consisting of five observations: 1, 4, 7, 10, 13

The mean would be μ = (1+4+7+10+13)/5 = 7

The Variance σ2 = (36+9+0+9+36)/5 = 18

The Standard Deviation σ = sqrt [18] = 4.24

**Inferential Statistics**

The researcher uses methods in inferential statistics to make pronouncements about the population in which the sample is drawn from. A good example is when a population mean is estimated by calculating the mean and standard deviation of a sample. Most of the methods currently available in inferential statistics rely heavily on the General Linear Model. This model assumes a linear relationship between a variable and the true population values. Thus in the general linear model:

Y = Β0 + Β1X

Β0 is a constant and Β1 is known as the regression coefficient. Β0 and Β1 are then estimated by taking samples and using statistical methods such as Regression Analysis, t-Test, ANOVA and ANCOVA depending on type of experiment (Howell, 324-325).

**Regression analysis**

The regression analysis method uses the concept of random samples and what is known as the least squares regression line. It states that the population regression line can be estimated by the linear relationship (least squares regression line) that is calculated from the scores using the following formula: ŷ = b0 + b1x where ŷ is the regression line

b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]

b0 = y - b1 * x

Note that y is the mean of the observed values and x is the mean of the variables in the sample.

**Hypothesis testing**

In Hypothesis testing a proposition about some characteristics of the population is made and the researcher’s task is to determine whether it is true or false. The ideal situation is to examine all members of the population but this is usually impracticable and so the psychologist has to resort to a sample of the population and look for any inconsistency with the hypothesis. (Lehmann & Romano, 2005)

The technique involves the use of two disjoint hypotheses. The first one is referred to as the Null Hypothesis H0 while the second one is called the Alternative Hypothesis H1. The Null Hypothesis assumes that the data obtained is by chance while the Alternative Hypothesis states that there is more to it than meets the eye. Therefore the researcher has to frame his enquiry in such a way that there is no possibility of overlap between the two hypotheses. Rejecting one implies accepting the other. It is only then that a test statistic can be used to obtain a meaningful result. Test statistics that are in common use include t-score, z-score and the mean.

Example:

H0 : Dogs are intelligent

H1: Dogs are not intelligent

We could choose a random sample of 50 dogs and test for intelligence and use a t-score to accept or reject H0 .

**Measurements and Data Collection**

It is important to understand that there four different types of measurements that are encountered in real life psychological research. These are nominal, ordinal, interval, and ratio. (Thompson, 2006)

• Nominal measurements are figures that cannot be ranked in any order because they are just identifiers.

• Ordinal measurements return figures that can be ranked but have no value associated with the differences between any two figures.

• Interval measurements are distances between two points or figures.

• Ratio measurements are the most useful in statistical analysis and are best employed for comparison of data.

Research Scientists employ several methods of data collection depending on the experiment at hand. These methods include case studies, questionnaires, interviews, observations and an appeal to authoritative sources.

**Professional Research Software**

There are many professional software packages that are currently available for the statistical design and analysis of experiments. The SPSS software is one of the most popular. Others include MedCalc and SAS/STAT® Software. All of these match the requirements of the psychologist in the analysis of results associated with behavioral enquiries. They have all the functions required for both descriptive and inferential statistics and can be used for both parametric and non parametric statistical analysis. They provide standard distributions such as Normal and Poisson and Frequency Tables. They can also be used for Regression Analysis and Time Series Analysis and have a wide collection of statistical charts

**Conclusions**

The knowledge and the application of statistical methods are very essential in the research endeavors of Psychologists. It is impracticable in real life to obtain an ideal experimental situation and the researcher has to resort to statistical methods of choosing not only the best design but also in applying the relevant concepts to counter skeptical arguments that will inevitably arise in the scientific community.

**References**

Creswell, J.W., 2003. Research Design: Qualitative, Quantitative, and Mixed Method. Saga Publications

Goos, Peter and Jones, Bradley (2011). Optimal Design of Experiments: A Case Study Approach. Wiley. ISBN 978-0-470-74461-1.

Howell, David (2002). Statistical Methods for Psychology. Duxbury. pp. 324–325.

Kirk, RE (1995). Experimental Design: Procedures For The Behavioral Sciences (3 ed.). Pacific Grove, CA, USA: Brooks/Cole.

Lehmann, E.L.; Romano, Joseph P. (2005). Testing Statistical Hypotheses (3E ed.). New York: Springer. ISBN 0-387-98864-5.

Smith, T. M. F. (2001). "Biometrika centenary: Sample surveys". In D. M. Titterington and D. R. Cox. Biometrika: One Hundred Years. Oxford University Press. pp. 165–194. ISBN 0-19-850993-6.

Thompson, B. (2006). Foundations of behavioral statistics. New York, NY: Guilford Press.

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