Hypothesis Testing

Charity I. Mulig

Variable

• A variable is any property or quantity that can take on different values.• Variables may take on

discrete or continuous values.

More on Variables…Types of Variables Levels of

Measurement1.Dependent2.Independent3.Extraneous

1.Nominal2.Ordinal/Ranked3.Interval4.Ratio

• Derived/ Transformed

Branches of Statistics

Descriptive Statistics

• Refers to the methods of data collection, organization, classification, summarization and presentation

Inferential Statistics

• Refers to the process of arriving at a conclusion about a population based on the information obtained from a sample.

Descriptive Statistics

Data Collection and Organization

1. Array is an arrangement of data from highest to lowest or lowest to highest.

2. Ungrouped Frequency Distribution (aka single-value grouping)

3. Grouped Frequency Distribution

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Measures of Central Tendency1. Mean2. Median3. Mode

Measures of Variability

1. Range2. Mean Deviation

3. Variance4. Standard Deviation

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Inferential Statistics

Parameter

–Is a number that describes a characteristic of a population

Statistic

–Is a number that describes a characteristic of a sample

Hypothesis Testing

Note:Hypothesis is a prediction

based on a body of knowledge, scientific theory or observations.

Note:

After the hypothesis is formulated, it has to be tested to find out whether it is true or false.

Note:In hypothesis testing, we test our

prediction about one or more of the population parameters that will either be accepted or rejected on the basis of the information obtained from the sample.

Steps in Hypothesis Testing

1. State, very clearly, the question you are attempting to answer.

2. Identify the characteristic of the sample and the variable in question.

3. Determine what appropriate statistical test is to be used.

Steps in Hypothesis Testing

4. State the null and alternative hypothesis. Determine the level of alpha at or below which you will reject the null hypothesis.

5. Determine whether it is a two-way or one-way test, for comparison of two means.

Steps in Hypothesis Testing

6. Make the appropriate calculation. If the probability (p-value) of obtaining this calculated value is equal or smaller than the preselected value of alpha, reject the null hypothesis and accept the alternative hypothesis.

Parametric Non-parametricCharacteristics • normally distributed (mean

median)•Continuous•Interval or ratio scale

If any of the conditions in the middle column is not met.

Inferences on Two Means

1. Unpaired T-test (compares 2 different groups)

1. Mann-Whitney Test

2. Paired T-Test (comparing results after an intervention on a group)

2. Sign Test (used if data are not numerical)

3. Wilcoxon Signed Rank Test (used if data is numerical)

Inference on Three or More Means

1. One-way ANOVA (for 1 independent variable)

1. Kruskal Wallis Test

2. Two-way ANOVA (2 independent variables)

2. Friedman Test

• data must be homogeneous with respect to other characteristics that may affect the results.•Use post-hoc to compare each pair of groups

Parametric Non-parametricCorrelation Pearson’s r (needs numerical

data; indicates strength of relationship)

• Random sample• Normally distributed• Interval or ratio

Spearman’s r (needs numerical data; indicates strength of relationship)

Other Tests

Chi-square Goodness Test

Chi-Square Test Association Fisher Exact Probability Test

•For all levels of measurement•Determine if the distribution is normal or binomial

•Uses a contingency table

•No zero value in the contingency table•Not more than 20% have values less than 5

•Used when there is a zero value in the contingency table•Used when more than 20% of the values in the contingency table is less than 5.

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Assumptions of ANOVA

• Each group is a random sample from the population of interest.

• The measured variable is continuous.• Measurement is in ratio or interval scale.• The error variances are equal.• The variable is approximately normally

distributed.Back

More on Kruskall Wallis Test• The sampled population have the same but

unspecified distribution with the possible exception that one or more of the sampled populations tend to have larger values than one or more of the others.

• The sample represent random sample from their respective populations.

• Measurement is on at least on an ordinal scale.• The samples can be obtained from independent

populations.Back

More on Correlation• Used to determine if an association and

strength of association between two variables exist

• Used to determine how strong an association is

• Does not assume a cause-and-effect association between variables.

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