# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-probabilities-statistics-statistical%20tests.html


## Statistical Tests

"A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions. " Michael J. Moroney


#### Statistical Tests


##### What you have to know:

- You must be able to solve linear equation. (If not, check this lesson)
- How to plot linear graphs (If not, check this lesson)

##### Pearson's correlation coefficient (PMCC)

- 1. Watch the video:
- 2.Show how the data spread in an interactive Applet 3.Read this solved problem how to use your calculator TiNspire and with Ti84
- 3.Read this solved problem how to use your calculator TiNspire and with Ti84
- 3.Read this solved problem how to use your calculator TiNspire and with Ti84

#### Spearman's rank correlation coefficient


##### What you have to know:

- You must be able to calculate Pearson's correlation momentum coefficient. For Spearman's test is noted as rs
- Remember that when I have the same value in my raw data I take the average of the ranks
- Spearman's correlation shows the extent to which one variable increases or decreases as the other variable increases.

##### Key Points

- 1. Watch the video:
- 3.Read this solved problem how to use your calculator TiNspire and with Ti84

#### Chi-Square test


##### What you have to know:

- The null hypothesis is rejected if either the statistic is more than the critical value or the p-value is less than the significance level.
- If the null hypothesis is rejected we say the result is significant
- The hypothesis test for the population correlation coefficient rho (ρ) will have H0 :ρ=0. The p value can be obtain from GDC.
- Chi squared test for independence can be performed to find out if two data sets are independent of each other or not.The GDC will produce a table of expected frequencies and a p-value . If any expected frequencies are less than 5 then adjacent rows or columns need to be merged.
- In a Chi squared goodness-of-fit-test , the degrees of freedom are v=n-1
- To obtain the number of degrees of freedom, take the number of cells minus one, and then subtract one for each of the parameters estimated

##### Key Points

- 1. Watch the video:
- 3.Read this solved problem how to use your calculator TiNspire and with Ti84

#### T-Test


##### What you have to know:

- When testing for a population mean, use z-test if the population standard deviation is known and the t-test if not
- When testing for the differences between two means use the pooled t-test.
- When two groups are paired find the difference between each pair and test H0 : μ=0

##### Key Points

- 1. Watch the video:
- 2. IB exam question on T-test and Chi square GOF test video

#### Type I and Type II error.


##### What you have to know:

- A probability of a type I error is the probability of rejecting H0 when H0 is true. For the normal distribution this will be equal to the significance level, for a discrete distribution this will be the probability of the statistic falling in the critical region.
- In order to find the probability of a type II error, first find the critical region under the null hypothesis.
- The probability of a type II error is the probability of the statistic not being in the critical region. This is calculated using a value for the parameter chosen from the alternative hypothesis.

##### Key Points

- 1. Watch the video:

### IB Past Paper Problems

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