intro to psychstats, collection of data and presentation of data, frequency distribution table, measures of central tendency & normal distribution

What Are Statistics?

These are formulas and calculations developed by statisticians that psychologists and other behavioral researchers employ when “analyzing” the results of their research. Also, some of the answers that we compute are called this

Statistics

is defined as a branch of Mathematics which deals with the collection, organization, presentation, analysis and interpretation of data which may be used for prediction or making decisions.

Educated guesses

decisions made by using statistical methods

Pure guesses

decisions made without using statistical methods and may prove to be unreliable

Descriptive Statistics

uses the data to provide descriptions of the population, either through numerical calculations or graphs or tables.

Number of votes of a senatorial candidate, Number of enrollees per semester

examples of descriptive statistics

Inferential Statistics

considered as a higher form of statistics, it makes inferences and predictions about a population based on a sample of data taken from the population in question.

A registrar staff would like to estimate based on the number of inquiries, the total number of enrollees for this coming 1st semester.

Examples of inferential statistics

Variable

is a characteristic or condition that can change or take on different values over time for different individuals or objects under consideration.

The cellphone load consumption, the number of hours in browsing facebook

Example of a variable

What are types of Variables?

Qualitative Variable Quantitative Variables

Qualitative Variable

it can be separated into categories that are distinguished by some non-numeric characteristics.

sex, birthplace, geographic location, religion, marital status, socio-economic status, educational attainment, eye color and etc.

Examples of qualitative variables

Quantitative Variables

Are numerical in nature and can be ordered or ranked. It indicates how much of a given characteristics an individual, object or event possesses.

Weight, height, age, test scores, body temperature and etc.

Examples of quantitative variables

Discrete

Variables whose values can be counted using integral value or those value that cannot be taken in decimal form

Number of siblings, number of students, number of trees in a certain mountain

Examples of discrete data

Continuous

Variables that can assume a numerical value over an interval

Height, Weight, Speed, Age, Monthly salary

Examples of continuous data

What is data?

The measurements obtained in a research study

what is the goal of statistics?

to help researchers organize and interpret the data.

Population

is the collection of all responses, individuals, measurements, or counts that are of interest.

Parameter

A number that describes a populations characteristics

The students of CvSU Bacoor, the customer of a particular bookstore, residents of the city of Bacoor

Examples of population

Sample

A portion or a subset of the population selected for study

The 500 students of CvSU Bacoor, first 100 customers of a particular bookstore, 300 residents of the City of Bacoor

Examples of sample

what is the population?

all of the individuals of interest

what is the sample?

the individuals selected to participate in the research study

what are the Levels of Measurements?

1. Nominal Level 2. Ordinal Level 3. Interval Level 4. Ratio Level

Nominal Level

It is the weakest level of measurement where numbers or symbols are used simply for categorizing subjects into different groups. The data cannot be arranged in an ordering scheme.

Marital Status, religion, sex, religion

Examples of nominal data

Ordinal Level

It contains properties of the nominal level and in addition, the numbers assigned to categories of any variable may be ranked or ordered in some low to high manner.

year level, ratings, job description, military rank, student grades

Examples of ordinal data

Interval Level

it has properties of the ordinal and in addition, the distance between any two numbers on the scale is known sizes but the unit of measurement is arbitrary and there is no true zero point

IQ level, Temperature

Examples of interval data

Ratio Level

It contains all the properties of the interval level, in addition, has a true zero point

Scores in a certain test, total votes received by pres. Duterte, Weight, Length, Volume, Density, price’

Examples of ratio data

Summation notation

is used to denote the sum of values.

what symbol is used to denote the summation notation?

The upper case Greek letter sigma ∑ is used to denote the sum of all the values.

Primary Data

These are data or information which were gathered from the original source.

Diary, Autobiography, result of an experiment

Examples of primary data

Secondary Data

These are data that were taken from published or unpublished materials.

Books, News, Magazine, internet, information in research conducted

Examples of secondary data

Direct or Interview Method

A face to face contact between the source of information and the one who gathers the information. This method will give us precise and consistent information because clarifications can be made.

Indirect or Questionnaire Method

To obtain the information or data needed in a research work. A questionnaire is prepared to solicit the information or data needed . This method requires less time and is inexpensive.

Registration Method

Data or information needed in the research study were properly kept and recorded by private and government agencies authorized by the law to be responsible for safe keeping

Observation Method

This is a method, which observes the behavior of individuals or organizations in the study. This method of data gathering oftentimes used when the subject cannot speak or write.

Experiment Method

This method of data gathering can only be succeeded by performing series of experiment on some controlled and experimental variable.

Probability Sampling

The method of choosing the sample where in each member of the populace was given the opportunity to be selected and become a part of the sample

• Simple Random - Stratified Random - Systematic Random - Cluster Random

examples of Probability Sampling

Simple Random Sampling

A process of selecting a sample size in the population through lottery sampling

samples were chosen by drawing lots or called the fishbowl method.

Lottery Sampling

Stratified Random Sampling

In this method, the population is first divided into groups according to similarity of characteristics in order to avoid selecting samples coming only from one group.

Systematic Random Sampling

When samples are randomly chosen following some rules set by the researchers. This involves choosing the kth member of the population, but there should be a random start. We say we choose every kth member in this example, K= 3 Every third member of the population is selected.

Cluster Random Sampling

Also known as area sampling and usually applied when population is large. The group or cluster instead individual units or groups and randomly select one or more units

Non-Probability Sampling

This methodology does not give equal opportunity for all members of the population to be chosen to form part of the sample

• Purposive Sampling - Quota Sampling - Convenience Sampling - Snowball Sampling - Voluntary Sampling - Judgement sampling

Examples of non-probability sampling

Purposive Sampling

The samples were chosen based on the purpose of the research work.

Quota Sampling

This is very inexpensive and quick. Once the quota is reached the sampling procedures automatically terminates

Convenience Sampling

where the researchers find it most easy and convenient in choosing his samples.

Snowball Sampling

it is a technique in which one more members of the population are located and used to lead the researchers to other members of the population.

Voluntary Sampling

Sample are composed of respondents who are self-select to the study who have strong interest in the topic of the study.

Judgement Sampling

This sampling technique is applied when the researcher relies on his/her personal judgement in choosing to participate in the study.

what are the Methods of Presenting Data?

Textual Form of Presentation Graphical Form of Presentation Tabular Form of Presentation

Textual Form of Presentation

Makes use of words, sentences and paragraphs in presenting data collected.

The Philippine population reached 100 million persons in the last quarter of 2015, according to figures released by Philippine Statistics Authority.

Example of textual form of presentation

Graphical Form of Presentation

An illustrative description of the data by using graphs, symbols or visual aids.

Bar Graph, Line Graph, pie graph

Examples of graphical form of presentation

Bar Graph

it is a graph applicable to nominal or ordinal scale of grouped data. The horizontal axis represents the grouped data. While the vertical axis represents the frequencies.

Line Graph

it is a line segment applicable to nominal or ordinal scale of grouped data. The horizontal axis represents the grouped data while the vertical axis represents the frequencies

Pie Chart

it is used to describe the parts of a whole. The pieces of pie represent the proportions of the total that fall into each category

Tabular Form of Presentation

A way of classifying related numerical facts in horizontal arrays called lines or rows and vertical arrays

The frequency distribution table (fdt)

is a statistical table showing the frequency or number of observations contained in each of the defined classes or categories.

what are the Parts of a frequency distribution table?

Table Heading Stub or Classes Caption or Box Heading Body

Table Heading

includes the table number and the title of the table

Stub or Classes

They give the classifications or categories into which the figures fall and usually found at the left most side of the table

Caption or Box Heading

This gives the designation of the columns or identifies the figures found in that column. Usually found at the top most of the column

Body

Constitutes the main part of the table and contains figures to be presented.

Types of frequency distribution table

Qualitative or Categorical Frequency Distribution Table Quantitative Frequency Distribution Table

Qualitative or Categorical Frequency Distribution Table

a frequency distribution table where the data are grouped according to some qualitative characteristics. Data are grouped into non-numerical categories

Quantitative Frequency Distribution Table

a frequency distribution table where the data are grouped according to some numerical or quantitative characteristics.

Lower Class Limits

are the smallest numbers that can actually belong to different classes

Upper Class Limits

are the largest numbers that can actually belong to different classes

Lower Class Boundaries

Lower Class limits + 0.5

Upper Class Boundaries

Upper Class limits + 0.5

CLASS MIDPOINT/CLASS MARKS (X)

can be found by adding the lower class limit to the upper class limit and dividing it into 2.

Percentage (P)

The proportion of observation falling in a class and is expressed in % P= Class Frequency/Sum of all frequencies

CUMULATIVE FREQUENCY

Less than cf (cf) Greater than cf (cf)

CLASS BOUNDARIES

a. Lower Class Boundaries b. Upper Class Boundaries

Less than cf (cf)

Total number of observations whose values do not exceed the upper limit of the class

Greater than cf (cf)

Total number of observations whose values are not less than the lower limit of the class.

Measures of Central Tendency

Mean, Median, and Mode

what are 3 different ways of describing the average?

The mean, median and mode

what do you do to find the mean?

add up all the numbers and divide by the number of numbers.

what do you do to find the median?

place all the numbers in order and select the middle number.

The mode

is the number which appears most often.

The range

gives an idea of how the data are spread out and is the difference between the smallest and largest values.

5, 6, 2, 4, 7, 8, 3, 5, 6, 6 in this set of data, what is the mean?

5.2

5, 6, 2, 4, 7, 8, 3, 5, 6, 6 in this set of data, what is the median?

5.5

5, 6, 2, 4, 7, 8, 3, 5, 6, 6 in this set of data, what is the mode?

6