CHAPTER 13: UNDERSTANDING RESEARCH RESULTS- STATISTICAL

INFERENCE

SAMPLES AND POPULATIONS

•Inferential statistics are necessary because the results of a given study are based on data

obtained from a single sample of research participants.

•If researchers ever study entire populations; their findings are based on sample data.

•In addition to describing sample data, we want to make statements about populations.

oWould the results hold up if the experiment were conducted repeatedly, each time

with a new sample?

Definition of Inferential Statistic: statistics designed to determine whether results based on

sample data are generalizable to a population

•Used to determine whether we can, in fact, make statements that the results reflect what

would happen if we were to conduct the experiment again and again with multiple

samples.

oWhether we can infer that the difference in the sample means reflects a true

difference in the population means.

Example: People in one state might tell you that 57% prefer the Democratic candidate and that

43% may favor the Republican candidate for office.

•Reports say that these results are accurate to within 3 percentage points, with a 95%

confidence level.

•The researchers are very confident that if they were able to study the entire population

rather than a sample, the actual percentage who preferred the Democratic candidate

would between 60% and 54%

•The percentage preferring the Republican would be 46% and 40%

•Researcher could predict with a great deal of certainty that the Democratic candidate will

win because there is no overlap in the projected population values.

INFERENTIAL STATISTICS

•Equivalence of groups is achieved by experimentally controlling all other variables or by

randomization.

•The assumption is that if the groups are equivalent, any differences in the dependent

variable must be due to the effect of the independent variable. (usually valid)

•It is also true that the difference between any two groups will almost never be zero.

oThere will be some difference in the sample means, even when all of the

principles of experimental designs are utilized; this happens because we are

dealing with samples rather than populations.

•Random or chance error will be responsible for some difference in the means even if the

independent variable had no effect on the dependent variable.

•THE POINT IS THAT THE DIFFERENCE IN THE SAMPLE MEANS

REFLECTS ANY TRUE DIFFERENCEIN THE POPULATION MEANS, PLUS

ANY RANDOM ERROR.

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•Inferential statistics give the probability that the difference between means reflects

random error than a real difference.

NULL AND RESEARCH HYPOTHESIS

•Statistical inference begins with a statement of the null hypothesis and a research (or

alternative) hypothesis.

Null Hypothesis: The hypothesis used for statistical purposes that the variables under

investigation are not related in the population, that any observed effect based on sample

results is due to random error.

•

(null hypothesis) : the population mean of the no-model group is equal to the

population mean of the model group

•Independent variable had no effect

• Used because it is very precise

oThe population means are exactly equal

oPermits us to know precisely the probability of the outcome of the study

occurring if the null hypothesis is correct.

oThe null hypothesis is rejected when there is a low probability that the obtained

results could be due to random error.

This is what is meant by statistical significance.

•

Statistical significance: Rejection of the null hypothesis when an

outcome has a low probability of occurrence (usually .05 or less) if, in

fact, the null hypothesis is correct.

•Significance is a matter of probability.

•

•Research Hypothesis: The hypothesis that the variables under investigation are related in

the population- that the observed effect based on sample data is true in the population.

•(research hypothesis): The population mean of the no-model group is not equal to the

population mean of the model group

•Independent variable did have an effect.

•

•LOGIC OF THE NULL HYPOTHESIS

•If we can determine that the null hypothesis is incorrect, then we accept the research

hypothesis as correct.

•Acceptance of the research hypothesis means that the independent variable had an effect

on the dependent variable.

•

•PROBABILITY AND SAMPLING DISTRIBUTIONS

•Probability- The likelihood that a given event (among a specific set of events) will occur.

We all use probabilities frequently in everyday life.

oExample: the weather forecaster says there is a 10% chance of rain today; this

means that the likelihood of rain is very low.

Probability in statistical inference is used in much the same way.

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The probability that an event (in this case, a difference between means in the sample) will

occur if there is no difference in the population.

•

•PROBABILITY: THE CASE OF ESP

The use of probability in statistical inference can be understood intuitively from a simple

example;

oExample: you test your friend on their ESP (extrasensory perception)

You test your friend by doing 10 trials and of showing them 5 cards with

different symbols on each card; you show these cards twice in a random

order in 1 trial

The null hypothesis is that only random error is operating

The research hypothesis is that the number of correct answers shows more

than random or chance guessing

You can reasonably say that that the person will get 1/5 answers right

•You can expect small deviations away from the expected 2 answers

correct per trial

oHow unlikely does a result have to be before we decide it is significant?

A decision rule is determined prior to collecting the data

oThe probability required for significance is called the alpha level

Most common alpha level probability is used is 0.05

•The outcome is considered significant when there is a 0.05 or less

probability of obtaining the results; only 5/100 chances that the

results were due to a random error

•

•Sampling Distribution

•You can infer using intuition that getting 7/10 answers vs. 2/10 answers correct on the

ESP experiment is unlikely

oThe probabilities shown were derived from a probability distribution called the

binomial distribution

oAll statistical significance decisions are based on probability distributions such as

this one

•Called sampling distributions

•The sampling distributions are based on the null hypothesis

•All statistical tests rely on sampling distributions to determine the probability that the

results are consistent with the null hypothesis

oWhen the results are very unlikely according to the null hypothesis expectations

the null hypothesis is rejected

•

•Sample Size

•The total number of observations on determinations of statistical significance

•In the ESP example; let’s say you tested your friend on 100 trials instead of 10 and

observed 30 correct answers

o30/100 is less likely then 3/10

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## Document Summary

Inferential statistics are necessary because the results of a given study are based on data obtained from a single sample of research participants. If researchers ever study entire populations; their findings are based on sample data. Example: people in one state might tell you that 57% prefer the democratic candidate and that. Reflects any true differencein the population means, plus. Inferential statistics give the probability that the difference between means reflects random error than a real difference. Null and research hypothesis: statistical inference begins with a statement of the null hypothesis and a research (or alternative) hypothesis. this is what is meant by statistical significance. Independent variable did have an effect: logic of the null hypothesis. we all use probabilities frequently in everyday life: example: the weather forecaster says there is a 10% chance of rain today; this means that the likelihood of rain is very low.