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Hypothesis Testing

How to Transform a set of raw scores into a set of z-scores

  • STATISTICS
To transform the set of raw scores into a set of z-scores in order, you will need to convert them into a standard normal distribution with a mean of 0 and a standard deviation of 1. Transforming raw scores into standard distribution helps us to compare the two raw scores from two different distributions. In this blog post, we will discuss, why would you want to transform a set of raw scores into a set of z-scores with examples as given below.
3 min Read 1

Negative Z Score Table

  • STATISTICS
A negative Z score value indicates the raw score value is either left or below the mean of the standard normal distribution. The negative z score in the z-table represents the area under the bell curve to the left of z. If the z score value is negative, use the negative z table to find an area on the left of the mean of the distribution. You can refer Z score calculator article which explains how to calculate the Z score using the z score formula below.
4 min Read 3

One Sample Proportion z-test

  • STATISTICS
The one-sample proportion Z-test is a statistical tool used to conduct a hypothesis test about population proportions(p). It is used to estimate the difference between the proportion of responses(or number of successes) in sample data and the actual proportion in the population data from which we draw the sample. What are the conditions required for conducting a one-sample proportion z test? Assumptions for the one sample proportion z-test are as follows:-
4 min Read 2

One Sample Z-Test in R

  • STATISTICS
The one-sample Z-test is a statistical hypothesis test used to determine whether the mean of a single sample is significantly different from a known population mean. It is used to draw conclusions about a population based on sample data. In this article, we will discuss the concept of a one-sample z-test in R with practical examples. Why Use the One-Sample Z-Test The one-sample z-test statistical tool can be used: Hypothesis Testing: It helps you to assess whether your sample data provides enough evidence to support or reject a hypothesis about a population parameter.
4 min Read 2

Z Score Calculator – How to use Z-Score calculator

  • STATISTICS
Z score allows a comparison between two scores that are from different normal distributions of raw scores to standardized scores. Z Score Formula If the population mean and population standard deviation are known, the Z score is calculated using the below formula z = (x -μ )/σ Where: μ = is the population mean for the unstandardized value σ = is the population standard deviation for the unstandardized value x = is the raw score value z = is the calculated z-score value.
4 min Read 2

Z Score Table and Chart

  • STATISTICS
Z table or the Z-score table also called the standard normal table is a mathematical table used to find the probability that the z-score value is below, above, or between the values on the standard normal distribution. Standard scores are most commonly called z-scores. In this post, equivalent terms like z-values, standardized variables, and normal scores are used. The standard normal distribution table is the normal distribution having a mean value of 0 and a standard deviation of 1.
9 min Read 7

Z-Score - Definition, Formula, and Calculation

  • STATISTICS
What is a Z-Score? Z-score is the distance of the raw score value from the mean in terms of standard deviation. Raw scores above the mean have a positive Z-score value, while a raw score below the mean has a negative z-score value. Z-Score is also known as the standard score because it allows the comparison of scores on different kinds of data by standardizing the distribution. Z-Score value can be positive, negative, or zero.
6 min Read 5

Chi-square Test for variance

  • STATISTICS
Testing variance or standard deviation In this tutorial we will discuss a method for testing a claim made about the population variance $\sigma^2$ or population standard deviation $\sigma$. To test the claim about the population variance or population standard deviation we use chi-square test. In this tutorial we will explain the six steps approach used in hypothesis testing to test hypothesis about the population variance or population standard deviation. Chi-square Test for Variance Let $X_1, X_2, \cdots, X_n$ be a random sample from a normal population with mean $\mu$ and variance $\sigma^2$.
3 min Read 1

Chi-square Test for variance examples

  • STATISTICS
Chi-square Test for the Variance In this tutorial we will discuss a method for testing a claim made about the population variance $\sigma^2$ or population standard deviation $\sigma$. To test the claim about the population variance or population standard deviation we use chi-square test. In this tutorial we will discuss some numerical examples using six steps approach used in hypothesis testing to test hypothesis about the population variance or population standard deviation.
5 min Read 3

F test for two variances

  • STATISTICS
Testing equality of two variances Many times it is desirable to compare two variances rather than comparing two means. F test is used to compare two population variances or population standard deviations. In this tutorial we will discuss six steps approach used in hypothesis testing to test whether two population variances are same or not. F-Test for equality of two variances Let $X_1, X_2, \cdots, X_{n_1}$ be a random sample of size $n_1$ from a population with variance $\sigma^2_1$ and $Y_1,Y_2, \cdots, Y_{n_2}$ be a random samples of sizes $n_2$ from a population with variance $\sigma^2_2$.
3 min Read 2

F test for two variances examples

  • STATISTICS
F test for two variances In this tutorial we will discuss some examples on F test for comparing two variances or standard deviations. Example 1 A professor from a graduate school claims that there is less variability in the final exam scores of students taking the statistics major than the students taking the mathematics major. Random samples of 13 mathematics majors and 10 statistics majors are selected from the his large class, and the following results are computed based on the final exam scores:
6 min Read 4

paired t-test

  • STATISTICS
Paired $t$-test (Dependent Sample) Let $X_1, X_2, \cdots, X_n$ and $Y_1, Y_2, \cdots, Y_n$ be two dependent samples each of size $n$ with respective means $\mu_1$ and $\mu_2$. Define $d_i = X_i - Y_i$, $i=1,2,\cdots, n$. Then $\mu_d= \mu_1 - \mu_2$. Let $\overline{d}=\frac{1}{n} \sum d_i$ be the mean of the difference and $s_d=\sqrt{\frac{1}{n-1}\sum (d_i - \overline{d})^2}$ be the sample standard deviation of the difference. Assumptions a. The samples are dependent (matched pairs).
3 min Read 1