Quantitative Methods- Assessment

 POPULATION AND SAMPLE

A population is an entire group or complete set of individuals or elements about which some specific information is required or in other words something you want to draw conclusions about.

So far researchers are interested in answering general questions of interest such as:

·       Architects are interested in understanding the design preferences of all homeowners in a specific urban area.

·       Computer scientists are interested in exploring the efficiency of all algorithms used in a specific category of software applications.

·       Economists are interested in studying the spending habits of all households in a particular country.

·       Environmental scientists are interested in monitoring the pollution levels of all water bodies within a designated region.

·       Psychologists are looking for general rules about all people (how do people learn a language?)

·       Statisticians are interested in analyzing the salary distribution of all employed statisticians in the field of academia.

 

Whatever it is you want to make generalizations about, you have to make a large collection of data either individuals or objects that you are interested in. This is known as population. Reaching the whole population might be cumbersome due to time or resources, so researchers often make use of samples drawn from the population to make a conclusion about the larger population. This is known as a sample.

A sample is a subset of a population in which true inferences about the population can be made. Note that a sample can be used to make a good guess about the population. Therefore, the larger the sample size the better our confidence level.

There are 2 types of sampling methods

1.     Probability sampling- This is a sapling technique where every member of the population and a known and equal chance of being selected for a sample.

Types of Probability Sampling Techniques

·       Random Sampling

·       Stratified Sampling

·       Systematic Sampling

·       Cluster Sampling 

2.     Non-probability sampling- This is a sapling technique where not every member of the population has a known and equal chance of being selected for a sample.

Types of non-probability sampling technique

·       Convenient Sampling

·       Purposive Sampling

·       Snowball Sampling

·       Quota Sampling

All statistical techniques are divided into two broad categories: descriptive and inferential statistics.

https://www.blogger.com/blog/post/edit/1781268278613007246/5860578026225684807

Experimental Design

Experimental designs represent systematic research methods conducted objectively and under controlled conditions. These approaches involve manipulating one or more independent variables to examine their impact on a dependent variable. By carefully controlling variables and ensuring objectivity, experimental designs aim to maximize precision, facilitating the drawing of conclusions regarding the stated hypotheses.

 

Questionnaire Design

Designing an effective questionnaire means creating reliable, meaningful, and valid questions in a research study capable of achieving the research objectives.

An important element in writing good questions

·       Question clarity and short- Keep language simple if explaining anything. Ensure jargon, ambiguity, and complex terms that are capable of confusing the respondents are avoided.

·       Avoid a leading question- Ensure questions are not leading the respondents to a particular answer.

·       Question structure- Ensure questions are organized logically. Non-threatened and simple questions can be begun with, this is capable of building the respondents' confidence before bringing in more sensitive and complex topics.

·       Avoid bias questions- The questions should be neutral and unbiased. Objectivity must be maintained throughout the questions.

·       Avoid lengthy questions- The questionnaire must maintain a reasonable length to ensure respondent engagement. Too lengthy questions can lead to fatigue or receiving inadequate responses from the respondents.

·       Avoid phrasing in the negative- Negative phrasing can lead to confusion and increase the likelihood of respondents misinterpreting the intended meaning.

 

DESCRIPTIVE STATISTICS

Descriptive statistics are informational and help to summarise and describe the actual characteristics of the data set. Descriptive statistics provides an initial understanding of the data distribution.  Descriptive statistics has three (3) basic categories.

1.     Measure of central tendency (mean, mode, median)

2.     Measure of variability i.e. spread of the data set (variance, standard deviation)

3.     Measures of frequency distribution, count of occurrence of each value (count)

To obtain descriptive statistics on your variables, the first step is to gather all relevant background information before conducting any statistical analyses. These descriptive statistics include the range, mean, standard deviation, skewness, and kurtosis.

https://www.blogger.com/blog/post/edit/1781268278613007246/4839363183018201007

Let's interpret each statistic in the table one by one:

1.     N (Sample Size):

·       The number of observations in the dataset for the variable "age" is 439.

2.     Range:

·       The difference between maximum and minimum values is referred to as range.

·       The range of “age” is 80 (82 - 2).

3.     Minimum:

·       In the dataset, the lowest value for the variable "age" is 2.

4.     Maximum:

·       The largest value in the dataset for the variable "age" is 82.

5.     Mean (Average):

·       The average age in the dataset is 37.39.

6.     Standard Deviation:

·       Standard deviation measures the amount of dispersion in the dataset.

·       For the variable "age," the standard deviation is 13.293.

7.     Variance:

·       The square of the standard deviation.

·       For the variable "age," the variance is 176.695.

8.     Skewness:

·       Skewness measures the asymmetry of the distribution.

·       When the distribution is skewed to the right, it is referred to as a positive skewness (0.564).

9.     Kurtosis:

·       A measure of the "tailedness" of the distribution.

·       A positive kurtosis (0.117) indicates that the distribution has heavier tails than a normal distribution.

10.  Std. Error of Mean:

·       Standard error related to the mean.

·       The standard error of mean for variable "age," is 0.634.

11.  Std. Error of Skewness:

·       Standard error associated with skewness.

·       For the variable "age," the standard error of skewness is 0.157.

The second step is to check whether any assumptions of the individual tests are not violated. To ensure data meets the required requirement, an assumption check is important for any statistical procedures.

1. Normality Assumption:
• Visualizing the shape of our distribution kurtosis and skewness provides insight, and helps in assessing the normality assumption.
2. Homogeneity of Variance:
• The homogeneity of variance assumption is important. The variance of the residual should be the same between the independent variable and the predicted scores.
3. Linearity:
• This is an important assumption in regression analysis. This can be achieved by scatterplots. It is used in assessing the linearity between variables. There should be a straight-line relationship between the residual and the predicted dependent variable score.
4. Independence:
• Descriptive statistics give an insight into the assumption of independence between our predictor variables. In statistical tests, the assumption of independence should not be violated.
5. Outlier Detection:
• Descriptive statistics, such as the identification of extreme values (outliers), are important for assessing the impact of outliers on statistical analyses.
6. Sample Size:
• The sample size is important for determining whether the sample size is adequate for the statistical method being applied.

Understanding the relationship between Sample Mean and Population Mean

When samples are taken repeatedly, we do not get the same mean value every time, there will always be a discrepancy between the true and the estimated population mean, (i.e. ) because of sampling variation.

But in most cases, the population mean (μ, ‘mu’) is unknown

INFERENTIAL STATISTICS

Inferential statistics involves drawing inferences on the broader population based on inferences made on the sample. For an estimation to be meaningful, we need to understand our measuring scale. To measure is to know https://quotestats.com/author/lord-kelvin-quotes/ . This is simply a way to categorize and understand the nature of the data we are dealing with. The four primary types of measurement scales are:

1.       Nominal: Nominal scales are the most basic of measurement where variables are named or labeled in no specific order. The categories have no inherent order. For example, Gender (Male or Female) and colors (Red, Yellow, Green, Blue).

2.       Ordinal: The ordinal scale has all its variables in a specific order or rank. However, the interval between the categories is not uniform or meaningful. The categories have a relative order indicating which is higher or lower and the differences between the categories are not measurable nor consistent. For example, educational levels (PhD, Master’s, Bachelor’s), social class (Upper, Middle, Lover), and customer satisfaction (Excellent, Good, Fair, Poor).

3.       Interval: Interval scales have labels, orders, as well as uniform intervals between them, but they lack zero true points. The intervals between them are consistent and measurable.

4.       Ratio Scale: Ratio scales have the same features as interval scales except that they have a true zero point.

It is important to understand the level of measurement and data types. If you cannot measure it, you cannot improve it https://quotestats.com/author/lord-kelvin-quotes/.

For Summary statistics: To measure average and measure of spread

1.     Continuous     

2.     Categorical    

To select appropriate statistical methods: Dependent Variable

1.     Continuous     

2.     Categorical    

 Demonstrate some Quantitative Analysis using SPSS

In this case, I will analyze this dataset by making use of binary logistic regression in evaluating the impact of all the independent variables (age, highest education level, weight, height, general health, alcohol drinks per day, caffeine drinks per day, physical fitness, current weight, hours sleep/weekends, how many hours sleep needed) on the dependent variable (problem with sleep), because my outcomes are binary/dichotomous, and binary logistics only assumes two possible outcomes i.e YES or NO. Binary logistic regression tries to predict whether someone has a problem with sleep (score = 1) or someone does not have a problem with sleep (score = 0).

Some assumptions need to be met in logistic regression analysis.

·       In logistic regression a linear relationship between dependent and independent variables is not required.

·       Homoscedasticity of variance, linearity, and interval of the independent variable are not required.

·       The residuals (error term) need not be normally distributed.

·       The binary logistic regression typically requires little or no multicollinearity among independent variables.

·       Larger samples are required for logistic regression.

The whole Demonstration of quantitative Analysis using SPPS can be found in my blog

https://twinniegrace.blogspot.com/2024/01/demonstrating-quantitative-analysis.html