Stats Chapter 12 : Testing Hypothesis

effect size

a statistical measure that quantifies the magnitude or strength of a relationship between variables or the impact of an intervention in a study. It provides a standardized way of expressing the size of an observed effect, making it easier to compare across different studies or contexts.

EX: if a new teaching method results in a statistically significant improvement in student scores, the effect size would tell you how much of a practical difference that improvement makes in comparison to the variability observed. It aids researchers and practitioners in understanding the real-world importance of their findings.

Hypothesis (H0)

a model or proposition that we adopt in order to test

Alternative Hypothesis (Ha or H1)

This is a statement that suggests a specific effect, difference, or relationship between variables. It represents what researchers aim to support if the data provide enough evidence to reject the null hypothesis.

Null hypothesis

ia statement in statistical hypothesis testing that suggests there is no significant difference, effect, or relationship among the variables being studied. It represents a default or initial assumption that any observed differences or effects are due to random chance or sampling variability.

the null hypothesis typically states that there is no effect or no difference, and any apparent differences observed in the data are simply due to random fluctuations.

One-proportion z-test

a statistical method used to assess whether the proportion of successes in a sample is significantly different from a hypothesized population proportion. This test is commonly applied in situations where you want to evaluate whether a sample proportion suggests a meaningful departure from a known or assumed population proportion.

formular : z=

• ^​p is the sample proportion,

• p0​ is the hypothesized population proportion under the null hypothesis,

• n is the sample size

One-sample t-test for the mean

a statistical method used to determine whether the mean of a sample is significantly different from a known or hypothesized population mean. It's commonly employed when working with small sample sizes and the population standard deviation is unknown.

Formula : t=s/n​xˉ−μ

• x is the sample mean,

• μ is the population mean under the null hypothesis,

• s is the sample standard deviation,

• n is the sample size.​
  

One sided -alternative or one-tailed

refers to a type of hypothesis test where the researchers are interested in detecting an effect or difference in one direction only. In other words, they are concerned with whether a parameter is significantly greater than or less than a specific value, rather than simply determining if it is different.

—> Right-tailed : The alternative hypothesis is formulated to detect if the parameter is significantly greater than the specified value.

• example:H0​:μ=10 (null hypothesis)

• H1​:μ>10 (alternative hypothesis)

—> left-tailed: The alternative hypothesis is formulated to detect if the parameter is significantly less than the specified value.

For example:

• H0​:μ=10 (null hypothesis)

• H1​:μ<10 (alternative hypothesis)

P-value or probability value

a measure in statistical hypothesis testing that helps researchers assess the evidence against a null hypothesis. It quantifies the likelihood of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true.

In simpler terms, the p-value helps researchers decide whether the observed data provide enough evidence to reject the null hypothesis. A smaller p-value indicates stronger evidence against the null hypothesis, while a larger p-value suggests weaker evidence.

Two sided alternative or Two tailed

a type of hypothesis test where researchers are interested in detecting whether a parameter is significantly different from a specified value in either direction.

Here's how it's typically formulated:

1. Null Hypothesis (H0): States that there is no significant difference; the parameter is equal to a specified value.

2. Alternative Hypothesis (Ha): States that there is a significant difference; the parameter is not equal to the specified value.

   For example:

   • H0​:μ=10 (null hypothesis)

   • �1:�≠10H1​:μ=10 (two-sided alternative hypothesis)