# Is the relationship statistically significant

## Is the relationship statistically significant

UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE

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Explain how researchers use inferential statistics to evaluate sample data

Distinguish between the null hypothesis and the research hypothesis

Discuss probability in statistical inference, including the meaning of statistical significance

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Describe the t test, and explain the difference between one-tailed and two-tailed tests

Describe the F test, including systematic variance and error variance

Distinguish between Type I and Type II errors

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Discuss the factors that influence the probability of a Type II error

Discuss the reasons a researcher may obtain nonsignificant results

Define power of a statistical test

Describe the criteria for selecting an appropriate statistical test

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Inferential statistics are necessary because

the results of a given study are based on data obtained from a single sample of researcher participants and

Data are not based on an entire population of scores

Allows conclusions on the basis of sample data

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Allow researchers to make inferences about the true differences in populations of scores based on a sample of data from that population

Allows that the difference between sample means may reflect random error rather than a real difference

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Null Hypothesis

H0: The means of the populations from which the samples were drawn equal

Research Hypothesis

H1: The means of the populations from which the samples were drawn equal

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Probability: The Case of ESP

Are correct answers due to chance or due to something more?

Sampling Distributions

Sample Size

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t value is a ratio of two aspects of the data

The difference between the group means and

The variability within groups

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t= | group difference |

within-group difference |

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Degrees of Freedom

One-Tailed

Two-Tailed Tests

The F Test (analysis of variance)

Systematic variance

Error variance

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Calculating Effect Size

Confidence Intervals and Statistical Significance

Statistical Significance

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Type I Errors

Made when the null hypothesis is rejected but the null hypothesis is actually true

Obtained when a large value of t or F is obtained by chance alone

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Type II Errors

Made when the null hypothesis is accepted although in the population the research hypothesis is true

Factors related to making a Type II error

Significance (alpha) level

Sample size

Effect size

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Researchers traditionally have used either a .05 or a .01 significance level in the decision to reject the null hypothesis

The significance level chosen is usually dependent on the consequences of making a Type I vs. Type II error.

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- Power is a statistical test that determines optimal sample size based on probability of correctly rejecting the null hypothesis

Power = 1 – p (probability of Type II error)

- Effect sizes range and desired power
- Smaller effect sizes require larger samples to be significant
- Higher desired power demands a greater sample size
- Researchers usually strive power between .70 and .90

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- Scientists attach little importance to results of a single study
- Detailed understanding requires numerous studies examining same variables
- Researchers look at the results of studies that replicate previous investigations

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- Is the relationship statistically significant?
- H0: r = 0 and
- H1: r ≠ 0
- It is proper to conduct a t-test to compare the

r-value with the null correlation of 0.00

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Software Programs include

SPSS

SAS

Minitab

Microsoft Excel

Steps in analysis

Input data

Rows represent cases or each participant’s scores

Columns represent for a participant’s score for a specific variable

Conduct analysis

Interpret output

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One Independent Variable

Nominal Scale Data

Ordinal Scale Data

Interval or Ratio Scale Data

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IV | DV | Statistical Test |

Nominal Male-Female | Nominal Vegetarian – Yes / No | Chi Square |

Nominal (2 Groups) Male-Female | Interval / Ratio Grade Point Average | t-test |

Nominal (3 groups) Study time (Low, Medium, High) | Interval / Ratio Test Score | One-way ANOVA |

Interval / Ratio Optimism Score | Interval / Ratio Sick Days Last Year | Pearson’s correlation |

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Multiple Independent Variables

Nominal Scale Data – Factorial Design

Ordinal Scale Data – no appropriate test is available

Interval or Ratio Scale Data – Multiple Regression

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