## Example of a Statistical Tests Based on Newspaper Articles

• 16th Mar, 2020
• 19:54 PM

## Inference Hypothesis Testing

It is almost impossible for us to perform analysis using data of entire population, so we take small samples from the population and make inferences based on the analysis performed on that sample. Inferential statistics are used to learn about or draw conclusions about a population larger than a particular sample represents.
Obesity Rate change over the years: https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight

Hypothesis Testing: Hypothesis is the idea that might be true and which can be tested.

• Null Hypothesis: The hypothesis that there is no statistically significant difference between two specified variables, any observed difference being due to sampling or experimental error. Like our two variables weight and height of a person are related with each other -  As a statistician our goal is to reject the Null-Hypothesis.
• Alternative Hypothesis: An alternative hypothesis is one that states there is a statistically significant relationship between weight and height of a person.
• P-value: is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. If p-value is 0.012 it means that probability of null hypothesis to be true is 1.2%.
• Decision Rule: On general our significance level is .05 and we reject the null hypothesis, if the p-value of our test is lesser than our significance level.

## Chi- Square:

Chi-square goodness of fit test : is used to check whether the given sample is are preventative of original population.

Does height can be traced to the genes inherited from mom and dad - https://time.com/4655634/genetics-height-tall-short/

• Null hypothesis: There is no relationship between the height and genes
• Alternative hypothesis: There is relationship between the height and genes
• Chi-square test for independence: it tests whether distributions of categorical variables differ from each another.

Do Men and Women Prefer Different Types of Pets: https://www.psychologytoday.com/us/blog/canine-corner/201904/do-men-and-women-prefer-different-types-dogs

• A chi-square test of independence could be used to examine the relationship between gender (male or female) and pet (dog or cat).
• Null Hypothesis: There is no relationship between gender (male or female) and pet (dog or cat).
• Alternate Hypothesis: There is relationship gender (male or female) and pet (dog or cat).

## T-test:

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. A t-test is used when the population parameters mean and standard deviation are not known, or we can say where sample size is not larger i.e. n < 30>

Omega-3 fatty acids decreased irritability of patients with bipolar disorder: https://nutritionj.biomedcentral.com/articles/10.1186/1475-2891-4-6

• Null- Hypothesis: There is no difference between the means of Pre- irritability levels and Post- irritability levels.
• Alternative-Hypothesis: There is difference between the means of of Pre- irritability levels and Post- irritability levels.

## Z-test

Z-test is used to determine whether two sample’s means are different taken from one population when variances and standard deviation are known. The z-test is best utilized for more than-30 examples on the grounds that, under the central limit theorem, as the sample size of tests gets bigger, the samples are considered to be approximately normally distributed.

Decrease in “Hamilton Rating Scale for Depression” Following Isotretinoin Therapy in Acne: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4601412/

• Null-Hypothesis: There is no decrease in “Hamilton Rating Scale for Depression” Following Isotretinoin Therapy in Acne.
• Alternate-Hypothesis: There is decrease in “Hamilton Rating Scale for Depression” Following Isotretinoin Therapy in Acne.

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