# Comparing Means

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Published on May 31, 2007

Author: litdoc1999

Source: slideshare.net

## Description

Brief, simple introduction to comparing means for students in SCED 421L

Comparing Means Dr. Roger Passman Northeastern Illinois University SCED 421L

Scales of Measurement Nominal Scale Placing objects or individuals into categories that are qualitatively different. Age Gender Race Grade range Class membership Nominal scale NAMES things

Nominal Scale

Placing objects or individuals into categories that are qualitatively different.

Age

Gender

Race

Class membership

Nominal scale NAMES things

Scales of Measurement Ordinal Scale Ranks objects or individuals with respect to how much or how little of an attribute under consideration the object or individual possesses. Rank order Likert scale data The interval between A & B and B & C is unknown, unequal or unmeasurable. Non-parametric data

Ordinal Scale

Ranks objects or individuals with respect to how much or how little of an attribute under consideration the object or individual possesses.

Rank order

Likert scale data

The interval between A & B and B & C is unknown, unequal or unmeasurable.

Non-parametric data

Scales of Measurement Interval Scale (sometimes referred to as Scale Data) Not only orders objects or events according to the amount of the attribute they represent but also has an arbitrary origin and establishes equal intervals between units of measure. The measured distance between A & B is equal to the distance between B & C or C & D and so on. Parametric Data

Interval Scale (sometimes referred to as Scale Data)

Not only orders objects or events according to the amount of the attribute they represent but also has an arbitrary origin and establishes equal intervals between units of measure.

The measured distance between A & B is equal to the distance between B & C or C & D and so on.

Parametric Data

Validity & Reliability Validity The extent to which the scale in fact measures that which is intended to measure. Reliability The extent to which the measure yields consistent results each time it is used

Validity

The extent to which the scale in fact measures that which is intended to measure.

Reliability

The extent to which the measure yields consistent results each time it is used

Inferential Statistics The science of making reasonable decisions with limited information Use what is learned through sample data to make generalized predictions for larger populations Generalizations are understood to be fallible but reasonable due to a concept known as sampling error. Decisions are based on tests of significance.

The science of making reasonable decisions with limited information

Use what is learned through sample data to make generalized predictions for larger populations

Generalizations are understood to be fallible but reasonable due to a concept known as sampling error.

Decisions are based on tests of significance.

The Null Hypothesis The null hypothesis (H 0 )states that there is NO relationship between the variables; that any observed relationship is only a function of chance Researchers choose between two potential explanations Null hypothesis—observed difference is merely due to chance Research hypothesis—observed difference is due to research intervention

The null hypothesis (H 0 )states that there is NO relationship between the variables; that any observed relationship is only a function of chance

Researchers choose between two potential explanations

Null hypothesis—observed difference is merely due to chance

Research hypothesis—observed difference is due to research intervention

The t -Test Among the most widely used tests of significance to test the null hypothesis Often used when sample size is under 30 Compares two means for significance Significance is chart dependent

Among the most widely used tests of significance to test the null hypothesis

Often used when sample size is under 30

Compares two means for significance

Significance is chart dependent

The t -Test Table of Values

T -Test Sample

Analysis of Variance (ANOVA) ANOVA computes the F -ratio which employs the variance of a group means as a measure of observed differences among groups. The general rationale of ANOVA is that the total variance of all subjects can be subdivided into two sources Variance between groups Variance within groups The F- ratio is the calculation of the variance between groups/variance within groups As the variance between groups increases the F -ratio increases As the variance within groups increases the F -ratio decreases The F- ratio is influenced by the number of subjects

ANOVA computes the F -ratio which employs the variance of a group means as a measure of observed differences among groups.

The general rationale of ANOVA is that the total variance of all subjects can be subdivided into two sources

Variance between groups

Variance within groups

The F- ratio is the calculation of the variance between groups/variance within groups

As the variance between groups increases the F -ratio increases

As the variance within groups increases the F -ratio decreases

The F- ratio is influenced by the number of subjects

A sample ANOVA

What you NEED to Know Tests of significance allow one to accept or reject the null hypothesis ( H 0 ) Either the results can be attributed to random chance, or The results can be attributed to experimental intervention Tests of significance do not guarantee that the interpretation is correct or even appropriate Provide a probability value for one’s interpretative assumptions Leave open the possibility of inappropriate interpretation

Tests of significance allow one to accept or reject the null hypothesis ( H 0 )

Either the results can be attributed to random chance, or

The results can be attributed to experimental intervention

Tests of significance do not guarantee that the interpretation is correct or even appropriate

Provide a probability value for one’s interpretative assumptions

Leave open the possibility of inappropriate interpretation

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