Research Methods, 9th Edition

Theresa L. White and Donald H. McBurney

Chapter 15Data Exploration Part 2:

Inferential Statistics

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Some basic terms

Empirical data Facts derived from experience

Population All members of some group

Sample A subset of a population

Statistic A quantity computed from a sample

Parameter A quantity computed from a population

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Statistics

Descriptive Statistics Summarize a set of data Chapter 14

Inferential Statistics Assist in drawing conclusions about

populations by examining a sample drawn from the population.

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Sampling Distributions

Distribution of means of samples from a population

Standard Error of the Mean Standard

Deviation of a sampling distribution

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Sampling Distributions

Three properties: The sampling distribution has the same

mean as the original distribution. The sampling distribution has a smaller

standard deviation than the population distribution.

The larger the size of the samples that are drawn from the population, the smaller the standard deviation of the sample distribution.

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Sampling Distributions

The standard error of the mean is the standard deviation of the population divided by the square root of the sample size

The sample size becomes larger, the shape of the distribution approaches a normal distribution, regardless of the shape of the population from which the samples are drawn.

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Hypothesis Testing

H1 (Alternative) vs H0 (Null)

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Hypothesis Testing

H1 (Alternative) vs H0 (Null)

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Hypothesis Testing

H1 (Alternative) vs H0 (Null)

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Hypothesis Testing

H1 (Alternative) vs H0 (Null)

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Hypothesis Testing

Directional hypothesis An alternative hypothesis that predicts that the results of

one condition will be greater (or less) than another, rather than a prediction that they will simply differ.

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Hypothesis Testing

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Hypothesis Testing

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Hypothesis Testing

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Hypothesis Testing

One-tailed hypothesis test Statistical test of a directional hypothesis

Two-tailed hypothesis test Statistical test of a nondirectional hypothesis

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Hypothesis Testing

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Hypothesis Testing

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Hypothesis Testing

Statistical significance is the probability that a result happened by chance

Alpha is the probability of deciding that the null hypothesis is false when it’s actually true. Probability of a Type I error

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Hypothesis Testing

2020

Hypothesis Testing

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Hypothesis Testing

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Hypothesis Testing

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Significance

Probability that an experimental result happened by chance

Generally alpha less than .05 (statistical significance)

Does not necessarily mean that the result was important or large

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Significance

The significance of significance Size of result is measured with Effect Size

Effect size shows the strength of the relationship between the independent and dependent variables.

Be measured by practice or by Cohen’s d (eta-squared)

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Significance

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Power of the Test of the Null Hypothesis Against the Alternative

Power is the probability of rejecting the null hypothesis when it actually IS false

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Power of the Test of the Null Hypothesis Against the Alternative Power

Three things influence the power of a test The value of alpha

The smaller your alpha level, the smaller your power. Experimental error Sample sizes

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Chi Square Statistic

Tests Frequency Data to determine whether two categorical variables are related.

Expected Frequency vs Observed Frequency

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Chi Square Statistic

contingency table also referred to as cross tabulation or crosstab In statistics, a contingency table is a type of table in a 

matrix format that displays the (multivariate) frequency distribution of the variables. 

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Chi Square Statistic

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ANOVA

Compares more than two conditions For only two, use a t-test

Tests the significance of a difference among several conditions in an experiment by making two different estimates of the variability that would be expected if the null hypothesis is true. Between variability Within variability

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T test

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ANOVA

Ha: at least two means differ(Note the alternative hypothesis is sometimes stated as "at least one mean differs")

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ANOVA

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ANOVA

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How to Read an ANOVA Table

Between Subjects Single Factor Design

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How to Read an ANOVA Table

Within Subjects Single Factor Design

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How to Read an ANOVA Table

Between Subjects Factorial Design