Inferential statistics

Sampling

* The purpose of sampling is to select a set of elements (sample) from a population that we can use to estimate parameters about the population * The bigger the sampling, the more accurate our parameters will be. example:

In the experiment of deciding if CEGL girls are smarter that CEGL boys, which would be your statistical hypothesis?

Hypothesis testing

But now, you already gathered information about a sample

No, you will test if your hypothesis are true or not

Hypothesis testing involves testing the difference between a hypothesized value of a population parameter and the estimate of that parameter, calculated from the sample

example:

If you want to know if CEGL girls are smarter that CEGL boys, you ask a few girls/boys their grades and compare averages, we will use Excel to compare the population and sample means. If the difference is too high, we can’t compare.

In statistics, the hypothesis to be tested is called “null hypothesis” and has the symbol “Ho” The other option of the hypothesis is the “alternative hypothesis” and its symbol is “Ha”

1 Ho: “There is no difference between (independent variable) and (dependent variable)” 2 Ha: “There is a difference between (independent variable) and (dependent variable)”

example:

In the experiment of deciding if CEGL girls are smarter that CEGL boys, which would be your statistical hypothesis?

Ho: There is no difference between Gender and Grades

Ha: There is a difference between Gender and Grades

How to decide between Ho and Ha?

A decision must be made on how much evidence is necessary to accept a hypothesis. If a hypothesis is that the world’s average is 23 and you only choose one person of 58 years, you wouldn’t decide basen of that.. We use statistical tests (excel) to determine the correct hypothesis. The value we use to determine if we keep Ho or Ha is called the level of significance (ALPHA): If we choose alpha=1% or 0.01 we are saying that from our collected data, there is a probability of 1% that our values were by chance.

ALPHA WILL BE ALWAYS 5%

Excel, our savior

We are going to see two different tests to determine the correct hypothesis. The first one is the “t-Test”

When do we use the t-test?

1 t-test paired: you select this option when you only have one group, but that group was subject to a before/after treatment 2 t-test equal variances: you select this option when you have two groups and their variances are equal. 3 t-test unequal variances: you select this option when you have two groups and their variances are not equal

After Excel?

Excel gives us many things... we are going to use the “p” value. The p value is a measurement that tells us how the distributions of our groups compare to each other P-critical one-tail: if you interested in knowing if you groups are below or above a value. (Our example of grades) P-critical two tail: if you are interested in knowing if your groups are below AND above of a value.

How to decide then?

If p<alpha, you deny the null hypothesis

If p>alpha, you accept the null hypothesis

If you happen to accept the null hypothesis, then you can’t conclude anything about the population. You can only conclude about the samples.

If you happen to deny the null hypothesis, then you are able to use your samples’ mean, deviation, etc to conclude about the population.

ANOVA TESTS

(Analysis of Variance)

* Single factor: we use this test when there is only one factor affecting our data * Two-factor with replication: we use this test when our data is affected by two factors and the procedures were repeated * Two-factor without replication: we use this test when our data is affected by two factors and the procedures were not repeated

PRESENTING YOUR RESEARCH

REPORT:

* Scientific report is designed to explain in full detail your research * Scientific report’s target audience is not the general...