Unit – 1: Introduction to Descriptive Statistics
Lesson – 1: Relevance of Statistics in Psychology

• Introduction

Psychology is a scientific discipline that relies on systematic research to understand human behavior and mental processes. Statistics are essential in psychology for organizing, analyzing, and interpreting research data.

Without statistics, psychological research would lack objectivity and scientific credibility.

• Breakdown
→ Psychology is a scientific discipline that studies behavior and mental processes.

→ Research is a systematic way to gather data and draw conclusions.

→ Statistics help psychologists to organize, summarize, and interpret data.

• Psychological Research

Psychological research refers to the process of systematically collecting, analyzing, and interpreting data about psychological variables such as behaviors, emotions, thoughts, and experiences.

– Process

a. Formulating a hypothesis

b. Collecting data

c. Analyzing data

d. Drawing conclusions

e. Reporting results

• Key Points

-Research is not limited to laboratories. It can happen in schools, offices, homes, clinics, etc.

-Psychological research can be basic (theoretical) or applied (practical).

-Without research, psychology would be based only on personal opinion and bias.

-Research helps psychologists build and test theories.

• Why do Psychologists carry out Research?

There are five main reasons why a psychologist carries out research:

i) Exploration: To address the “What” question when little is known about a phenomenon.

ii) Description: To describe a detailed phenomenon and its context—social, cultural, and historical—by addressing the “Who” and “How” questions.

iii) Explanation: To find the reason why a phenomenon occurs, focusing on the “Why” question.

iv) Prediction: To determine when a phenomenon or behavior is likely to occur again, answering the “When” question.

v) Control: To change or influence behavior to improve the quality of life by making constructive changes.

• What are the different types of Research?

Research can be classified along four dimensions:

1.Basic vs. Applied research

2.Laboratory vs. Field research

3.Quantitative vs. Qualitative research

4.Cross-sectional vs. Longitudinal research

1. Basic (or pure research)

Aims to advance our understanding of psychological phenomena by discovering something new or refining existing theories.

1:1 Applied research

Is carried out to find a solution to a practical problem and utilizes already well-established theories.

2.Laboratory research

Is carried out in a controlled environment, giving the researcher control over the variables.

2:2 Field research

Is carried out in natural settings where the researcher has less control over the environment.

3.Quantitative research

Involves the use of numbers to gather, analyze, and present data, often collected through questionnaires and reported as means, percentiles, standard deviations, and correlation coefficients.

3:3 Qualitative research

Involves the use of words and images to gather, analyze, and present data, collected through case studies, interviews, and observations, and analyzed using content analysis, thematic analysis, etc.

4.Cross-sectional research

Is carried out at one point in time to capture the level of a variable at that time.

4:4 Longitudinal research

Is carried out over an extended period of time to capture the process of change.

• Relevance of Statistics in Psychological Research

Statistics is a branch of Mathematics that involves the collection, presentation, and analysis of data.

It helps in finding out trends and patterns in data, which are used to identify the probability of whether an event or behavior is going to take place or not.

The proper use of statistical methods and techniques can help in diagnosing patients, making better decisions to improve mental health and well-being, identifying suitable job candidates, and improving organizational efficiency and productivity.

*The two primary types of statistics used in psychology are descriptive and inferential statistics.

• Descriptive and Inferential Statistics

– Descriptive statistics

Describes and summarizes data, helping researchers clearly identify the nature of the information available after data collection.

Examples include: mean, median, mode, standard deviation, range, percentiles, percentile ranks, and correlation coefficients.

– Inferential statistics

Used to draw conclusions about a population by collecting data from a sample statistic (such as mean).

For example, to understand if the performance of first-year psychology students at University of Delhi is the same as the average performance of first-year psychology students at Ambedkar University, we can collect sample data from students at University of Delhi and then test our hypothesis.

Inferential statistical techniques include t-tests, ANOVA (Analysis of Variance), and chi-square tests.

• Levels of Measurement

A researcher includes many different variables in research, and for statistical analysis, assigns a number to a particular variable.

Psychologist S. S. Stevens (1946) identified four different ways of assigning numbers to observations (known as measurement scales):

i) Nominal Scale

ii) Ordinal Scale

iii) Interval Scale

iv) Ratio Scale

⇒ Nominal Scale

Used for variables that are qualitative in nature (rather than quantitative), such as gender (male or female).

The categories must be mutually exclusive (one category need to be completely independent of the other) and exhaustive (there must be enough categories to accommodate all the observations).

⇒ Ordinal Scale

Used in cases where the categories are mutually exclusive and exhaustive.

A higher level of measurement than the nominal scale, as it assigns ranks to the categories, making it easier to identify which category comes first and last.

⇒ Interval Scale

Represents the next level of complexity than the nominal and ordinal scales.

Has all the properties of an ordinal scale with the additional feature that the difference between points on this scale is the same across the scale.

On this scale, zero is just an arbitrary point.

⇒ Ratio Scale

Includes all the characteristics of the interval scale and has a true zero point.

For example, the Kelvin scale to measure temperature has a true zero point or absolute zero temperature, implying an absolute absence of heat.

• Grouped Frequency Distribution (Excluded from Syllabus)

• Frequency Distribution

Data collected comes in a variety of forms and needs to be organized for accurate interpretation.

Frequency distribution helps organize data by showing the number of observations for each category.

• Grouped Frequency Distribution

When there is a wide range of scores, it is better to combine them into groups.

These groups are called class intervals.

Example: Instead of listing every possible score, scores of students in a statistics paper can be grouped into intervals (e.g., 64–65, 66–67).

Grouped frequency distribution makes data easier to visualize and understand.

Guidelines (Qualities) / Guidelines for Creating Class Intervals:

• Class intervals must be mutually exclusive (no overlap).
• Intervals must be continuous (include intervals even with no scores).
• Interval containing the highest score should be at the top.
• Intervals should have the same width.
• Interval width should be a convenient number (e.g., 2, 3, 5, 10).
• More class intervals lead to better accuracy of interpretation.
• The lower score of an interval should be a multiple of the interval width.

Steps Involved in Creating a Grouped Frequency Distribution:

1. Find the highest and lowest scores.

2. Calculate the range (highest score minus lowest score).

3. Divide the range by 10 and 20 to find the largest and smallest interval width and select a convenient width between these values.

4. Find the score where the interval width should begin (highest or lowest), and it should be a multiple of the interval width.

5. List the class intervals with the highest value at the top, making continuous intervals of equal width.

6. Use a tally system to count scores within each interval, then convert the tally into frequency.

Real Limits vs Apparent Limits

In real situations, scores might be in decimals (e.g., 70.5), which can be hard to place in intervals with discrete values.

Real limits extend half a unit below the smallest value and half a unit above the largest value.

Apparent limits extend from the smallest unit to the largest unit of measurement in the interval.

Relative Frequency Distribution

Shows the proportion or percentage of scores within each interval.

Cumulative Frequency

Is the total number of scores at or below a given value.

Graphical Representation of Data

Histogram

A diagram that uses rectangles to represent the frequency of variables, where the area of the rectangle is proportional to the frequency, and the width equals the class interval.

Frequency Polygon

A graph created by connecting data points with lines to show frequency distribution.

Cumulative Percentage Curve

A graph that shows the percentage of data falling below a certain value.