Explain the difference between descriptive and inferential statistics. Choose the correct answer below.
A. Descriptive statistics describes sets of data. Inferential statistics draws conclusions about the sets of data based on sampling.
B. Descriptive statistics is a characteristic or property of an individual experimental unit. Inferential statistics is the process used to assign numbers to variables of individual population units.
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Hire An Expert Tutor NowC. Descriptive statistics arc measurements that are recorded on a naturally occurring numerical scale. Inferential statistics are arc measurements that cannot be measured on a natural number scale; they can only be classified into one of a group of categories.
D. Descriptive statistics draws conclusions about the sets of data based on sampling. Inferential statistics summarizes the information revealed in data sets.
Answer; A. Descriptive statistics describes sets of data. Inferential statistics draws conclusions about the sets of data based on sampling.
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Define Inferential Statistics
Inferential statistics draws conclusions about the sets of data based on sampling and statistical inference.
The most common inferential statistics are correlation coefficients, confidence intervals, t-tests, and chi-squared tests in the sciences.
What Are The Types of Inferential Statistics?
The common types of inferential statistics include:
1. Hypothesis testing models
When it comes to hypothesis testing, formal hypotheses are created and then a statistical test is done to determine whether the hypothesis holds true or false. The test results are used to determine the probability that the outcome is caused by chance, not real and unique factors or significant differences between models. It is made up of the following tools:
A. Z-test
When the sample size is more than or equal to 30 and the data set has a normal distribution, the method is utilized to test the hypothesis that a population mean is given a specific value. The null hypothesis is the assumption of no difference between the population mean and sample mean. The alternative hypothesis represents the hypothesis that the population mean is different from a fixed value.
Z-test Formula
The z test formula determines whether there is a difference in the means of two populations by comparing the z statistic with the z critical value. The distribution graph’s acceptance and rejection zones are separated by the z critical value during hypothesis testing.
The null hypothesis may be rejected if the test statistic falls inside the rejection region; otherwise, it cannot. The z-test formula is provided below to set up the necessary hypothesis tests for one sample and a two-sample z-test.
One Sample Z Test
When the population standard deviation is known, a one-sample z test is performed to determine whether there is a discrepancy between the sample mean and the population mean. The following is the formula for the z-test statistic:
Z Test Statistic= Z Test = (x̄ – μ) / (σ / √n)
Here,
- x̄ = Sample Mean
- μ = Population Mean
- σ = Population Standard Deviation
- n = Sample Size
The following algorithm is provided to set a one sample z test based on the z test statistic:
Two-Tailed Test
Null Hypothesis: H0 : μ=μ0
Alternate Hypothesis: H1 : μ ≠ μ0
Decision Criteria: Reject the null hypothesis if the z statistic is greater than the z critical value.
Right-Tailed Test
Null Hypothesis: H0 : μ=μ0
Alternate Hypothesis: H1 : μ>μ0
Decision Criteria: Reject the null hypothesis if the z statistic is greater than the z critical value.
Left Tailed Test
Null Hypothesis: H0 : μ=μ0
Alternate Hypothesis: H1 : μ<μ0
Decision Criteria: Reject the null hypothesis if the z statistic is less than the z critical value.
B. T-test
T-test is employed when the sample size is below 30, and the data set exhibits a t-distribution. The researcher is unaware of the demographic variance. A t-test then is a test of whether or not the difference in means is significantly different from zero.
For example, if the mean grade of students who took two classes was higher than that of students who only took one class, you might conclude that adding two additional classes will probably lead to an increase in students’ grade point averages.
What is the difference between a one-sample t-test and a paired t-test?
A one-sample t-test is used to test whether the mean of a population is equal to a particular value, such as zero or the population parameter. A paired t-test compares the means of two groups. Ideally, for a valid comparison, each data point in one group should have an equal corresponding data point in another group.
T-test Formula
The formula for a two-sample T-test is: t = ( x̄1 – x̄2) / √ [(s21 / n 1 ) + (s22 / n 2 )]
Where:
- t = t-value
- x̄1 = Observed Mean of 1st Sample
- x̄2 = Observed Mean of 2nd Sample
- s1 = Standard Deviation of 1st Sample
- s2= Standard Deviation of 2nd Sample
- n 1 = Number of observations in 1st Sample
- n 2 = Number of observations in 2nd Sample
C. F-test
The F-test is a statistical procedure used to determine if there is or isn’t a difference in the variances of two samples or populations. This test can be used when you have two conditions, such as before and after treatment, and you want to know if one condition was more effective than the other. By using an F-test statistic, you can compare your data and decide if the variances between your groups are statistically significant.
F-test Formula
When evaluating hypotheses, the f test is used to determine whether variances are equal. For various hypothesis tests, the following is the f test formula:
Two-Tailed test:
Null Hypothesis: H0: σ12 = σ22
Alternate Hypothesis: H1: σ12 ≠ σ22
Decision Criteria: The null hypothesis is rejected if the f test statistic exceeds the f test critical value.
Right Tailed test:
Null Hypothesis: H0: σ12 = σ22
Alternate Hypothesis: H1: σ12 > σ22
Decision Criteria: Reject the null hypothesis if the f test statistic exceeds the f test critical value.
Left Tailed Test:
Null Hypothesis: H0: σ12 = σ22
Alternate Hypothesis: H1: σ12 < σ22
Decision Criteria: Reject the null hypothesis if the f statistic is greater than the f critical value.
D. Confidence interval
This is a value or range of values that is likely to contain the parameter of the average sample. The level of confidence for a specified confidence interval can be chosen. Typically, a 95% confidence interval is used when available data permits.
E. Analysis of Variance (ANOVA)
The analysis of variance tests the null hypothesis that the means of a group of independent populations are equal.
Example of ANOVA
Assuming you want to carry out a study on the effects of Corona Virus on education. You need to carry out the survey on different schools.
You also need to know if the education system is different between public schools and private schools. ANOVA will help you determine if the mean effects of coronavirus are different among different schools.
F. Analysis of Covariance (ANCOVA)
The analysis of covariance (ANCOVA) is an extension of the ANOVA where we allow for one or more covariates that are either covaried with one or more independent variables. Covariates can be removed during the analysis if there is a substantive reason to do so. The ANCOVA was developed to model and test the same information as ANOVA while also modeling and testing known factors that cause differences between groups.
An example of where ANCOVA can be used; ANCOVA can be used to check variation of the intention of a supplier to sell a given product while taking into account the price they are willing to sell at and the attitude that the consumers are likely to have on the product.
2. Regression Analysis
Regression analysis is used to find relationships between variables by fitting a suitable equation to a data set. The chosen equation is extended beyond the range of the sample to make predictions about future events. Regression analysis is used when there are two or more dependent variables that have linear and/or non-linear relationships with independent variables. It is employed when there are up to five independent variables that must be analyzed simultaneously, or over time.
What Are The Types of Regression Analysis?
The common types of regression analysis include:
1. Linear
2. Nominal
3. Logistic
4. Ordinal
In this article, we will only discuss linear regression analysis and logistic regression analysis.
A. Linear Regression Analysis
Linear regression analysis is a statistical technique used to determine the relationship between two or more variables by fitting a linear equation to the data set. One or more independent variables (X) and one dependent variable can be studied using this statistical technique. The independent variables (X) are the ones that might explain or help to predict changes in the dependent variable. These variables can be either quantitative or qualitative.
The purpose of linear regression analysis is to determine the strength and direction of the relationship between one dependent variable (Y) and one or more independent variables. Also, it helps determine if there is a relationship between the dependent and independent variable(s) of interest. This type of analysis helps in forecasting future values of a dependent variable based on the present values of an independent variable(s).
There are two types of linear regression analysis. They include:
1. Simple Linear Regression
Used when there is only one independent variable, X, changes in X cause changes in Y.
Y = B0 + B1X + ϵ
Where:
- Y – Dependent variable
- X – Independent variable
- B0 – Intercept
- B1– Regression coefficient
- ϵ – Residual (error)
2. Multiple Linear Regression
Used to illustrate the link between one dependent variable and two or more independent variables.
Y = B0 + B1X1 + B2X2 + …………. + BnXn + ϵ
Where:
- Y – Dependent variable
- X1, X2, X3, …., Xn – Independent variables
- B0 – Intercept
- B1, B2, Bn – Regression coefficient
- ϵ – Residual (error)
B. Logistic Regression Analysis
This type of regression analysis is used to determine the probability that an event will occur. This type of analysis allows prediction and evaluation of the dependent variable (Y) based on the occurrence of an independent variable (X), or predictor variables. The logistic regression equations are usually non-linear and can take on many different forms depending on the variables. The possible outcomes must be considered in all cases when using logistic regression analysis.
What Is An Example of Inferential Statistics?
Below is an example of inferential statistics:
Joy wants to open an ice cream shop in Minnesota, USA. A survey is carried out to determine the design for the appropriate menu. The study is carried out on 400 residents in order to gain a better understanding of their tastes and preferences. In order to get more accurate results, they include people of different gender, age groups, and income class. The results obtained were as follows:
- 60% of children love the strawberry flavor
- 80% of the total residents like chocolate ice cream
- Nearly 100% love fruit toppings on their ice cream
Following the nature of the results, Joy is sure that certain flavored ice cream will sell more in her shop. Also, she can use the results to come up with new kinds of flavors or ice cream toppings.
Define Descriptive statistics
Descriptive statistics describe sets of data as a collection of numerical values. Descriptive statistics can also be used to describe the distribution and generate graphs or charts of the data for easier interpretation. A statistic is considered descriptive if it is not used in any inferential analyses, which would include trying to determine whether any trends exist among the data for example.
The most common descriptive statistics are frequencies, means, medians, modes, ranges, and standard deviations. More complex statistics include confidence intervals, percentiles, and correlation coefficients in math courses or statistical analysis courses respectively.
What Are The Four Types of Descriptive Statistics?
The four common types of descriptive statistics include:
1. Measures of frequency
These are the least complex types of statistics. They provide a relatively quick assessment of data. The measurements can be either relative or absolute. The units of measure can be numbers, percentages, or arbitrary categories.
2. Measures of central tendency
These are the mathematical averages calculated by adding a group’s values and then dividing by the number of values in the group. It is used to depict a typical observation in measures such as mean, median, mode, and midrange
3. Measures of dispersion or variation
These are used to describe how far a data set is from the average. The extreme or central values are subtracted from the entire data set to produce standard deviation. Standard deviation shows the dispersion of a set of numbers. It is also known as variance, and it is used to describe the spread of a data set or signal. Variance is usually measured in relative terms:
4. Measures of position
Measures of Position are used to describe the spread of data in discrete categories. Two often used measures are percentile rank and z-score. Percentile rank shows the percentage of cases that fall into a particular percentile, and z-score is a scale that is between -1 and 1. It tells how far a specified data value lies from the mean or expected value on the scale.
Differences Between Inferential Statistics and Descriptive Statistics
| Inferential Statistics | Descriptive Statistics |
| Inferential statistics are used to test a hypothesis or to draw conclusions from sample data | Descriptive statistics are used to summarize and describe data. |
| Inferences are drawn from survey experiments or experimental data | Descriptive statistics deal with cross-tabulation data. |
| The measures of inferential statistics are linear regression, ANOVA, chi-square tests, and multiple regression | Descriptive statistics are measures of central tendencies, measures of dispersion, graphical representations, and correlation coefficients. |
| Inferential statistics analyze two or more variables as to the nature and strength of their relationship | Descriptive statistics deal with a single variable |
| Graphical displays of inferential statistics are limited to line graphs, bar charts, and curve graphs | Descriptive statistics can involve graphical representations in the form of histograms, pie charts, and scatter plots which show the distribution of values in patterns other than those of a straight line. |
What is the relationship between descriptive and inferential statistics?
Inferential statistics involves statistical inference based on the sample in terms of making inferences about the data. Descriptive statistics is usually presented in numeric form, also known as a data chart, and a sample/data set may be drawn from this chart.
When should you use descriptive and inferential statistics?
Descriptive statistics are used when the data set or sample is small. Inferential statistics are used when the data set or sample has relatively large numbers of observations.
When should inferential statistics typically be used?
Inferential statistics are usually used when the sample size is small and in situations where there is no possibility for a complete data set.
Is Mean descriptive or inferential?
Descriptive
What do inferential statistics allow researchers to do?
Since inferential statistics are based on the study of probability they can be used to investigate various questions. They help in obtaining a more accurate view of reality.
Why do researchers use inferential statistics?
The main advantage of using inferential statistics is that they are based on assumptions rather than empirical data. In contrast to descriptive statistics, inferential statistics employ statistical calculation to gain more reliable and extensive understanding of the population.
Is P value descriptive or inferential?
Inferential because we test a hypothesis based on the P value. P value tells us how likely it is to get the result by chance.
What is the role of hypothesis in inferential statistics?
Experiments and surveys are conducted to test if a specific hypothesis is correct or false. The hypothesis is also referred to as a research hypothesis.
What is the difference between population and sample in inferential statistics?
Population is the total number of items in the study sample. For example, if we are studying the height of US citizens aged 18-25, then those who fit this description would be our population.
Sample is a subset of a population that is studied to infer something about their underlying characteristics. A sample can be drawn from a population (called sampling) or can just exist as one within a given population (called non-sampling).
How would a test for differences in mean be performed?
Sometimes we need to test the null hypothesis that the mean of different groups are equal. The Analysis of Variance (ANOVA) is a way to do this by testing if there is enough evidence from our data to reject or not reject the assumption that there is no difference between two groups with respect to their means.
