Dentistry

?Assignment Topic: – Inferential Statistics

?Course Title: – Statistics

?Course Code: – SGS116

?Lecture Group: – A

?Submitted to: – ?Dr. Ahmed Refaat

?Prepared by: Mohamed emad hamday – 180013

?

Definition

Statistics have two main branches, first one Descriptive statistics and second one is Inferential statistics.

Inferential statistics have a lot of definitions. Inferential statistics is the way to use simple of group (population) to make inferences about that group (population).

Also in another way it means that we use a little part of people to make prediction about the whole people itself.

Also it can define as a decision take from simple of the all data

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Main types of Inferential statistics

1. T-test

2. ANOVA (Analysis of variance)

3. Regression

1-T-test

Used to:Used to:

1) Compare between two individuals (means) to know if they came from same group or no.

2) It makes you know how significant the difference between two variables is.

Also, it is called (Student’s T-test).

The types of t-test are

1-One-sample t-test is used to decide if a sample of observations could have been shown up by a process with a specific mean or no.

There two types:-

I. The alternative hypothesis suppose that some difference exists between the true mean (?) and the comparison value (m0)

II. The null hypothesis suppose that no difference exists. The aim of the one sample t-test is to acknowledge if the null hypothesis should be rejected, given the sample data.

There are 3 forms:-

If the aim is to measure any difference without lock to direction a two-tailed hypothesis is used.

If the direction of the comparison between the sample mean and the comparison value are important, either an upper-tailed or lower-tailed hypothesis is used

• H1: ? ? m0 (two-tailed)

• H1: ? > m0 (upper-tailed)

•

2

H1: ? < m0 (lower-tailed)
2-unpaired t test (independent-samples t-test):- consists of tests that compare mean value of continuous-level. The independent sample t-test compares two means. It suppose a model where the variables in the analysis are split into independent and dependent variables.
3-paired t test (dependent samples t-test):- it is the kind of test that process on connected data.
Example: - make two test on the same person before and after workout.
The t-test has two camping hypotheses, the null hypothesis and the alternative hypotheses
The null theory suppose that the true mean difference between the paired sample zero (difference is observe at random variation)
•?H0: ?d = 0
On the other hand, the alternative theory suppose that the true mean difference between the paired samples is not equal to zero, the alternative hypotheses can take different shape that depend on the result.
Firstly, if the direction of the difference does not matter, a two-tailed hypothesis is used.
Secondly, an upper-tailed or lower-tailed hypothesis can be used to increase the power of the test.
Notice: - The null hypothesis remains the same for each type of alternative hypothesis it not effect on it.
• H1: ?d ? 0 (two-tailed)
• H1: ?d > 0 (upper-tailed)

• H1: ?d < 0 (lower-tailed)
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2-ANOVA (Analysis of Variance)
ANOVA: - is a potential difference in a dependent variable by a nominal-level variable which holds two or more categories.
General focus of ANOVA:-
Researchers and students use ANOVA in many w