SMCR Kap 4-6

Type 1 Error Rejecting a true null hypothesis

Left sided test 5% Rejection area fully in left tail

Null hypothesis A single value defined for the parameter which is tested

Rejection region All values of the sample result for which we reject the null

Sig. Level Maximum probability of making a type 1 error

Capitalization on chance Increasing the probability of a type 1 error by performing a lot of tests on the same data

P-value Probability of drawing a sample which is at least as different from the hypothesized value, if the null is true

One-sided test Rejecting null only for very low or high values

Two sided test Rejecting null for both sides of CI

Expectation Research hypothesis that must be translated into a statistical hypothesis (null and alternative)

Goal of statistical inference Increase knowledge about a population when we only have a random sample from that

Estimation (Type of statistical inference) Not using previous knowledge, can be ignorant about the topic

Hypothesis testing (Type of statistical inference) Based on previous knowledge, and requires researcher to formulate an expectation

Binary decision Reject/not reject. Believe that the population looks as it is described or not

Statistical tests determine Whether a statement about a population is plausible, from a sample drawn in the population

Sample mean is an unbiased estimator of the parameter Why hypothesized mean is the average of the SaDi

Null hypothesis is implausible if The sample we've drawn is among the samples that are unlikely if the null is true

When can we construct a SaDi If the hypothesis specifics one value for the population statistic

P-value Probability that a sample is drawn with a value for the sample statistic at least as different from the hypothesized value as the one in the observed sample

P low Null must be rejected, and test is statistically significant

P value meaning Probability under the assumption that the null is true (conditional probability)

'Media literacy is 5.5 in the pop' Example of null hypothesis

'Media literacy average is not 5.5' Example of alternative hypothesis

Nil hypothesis Hypothesis stating no effect/association/difference

'Population mean is 5.5 or higher' Example of one-sided null hypothesis

When can a one-sided hypothesis be rejected If the sample statistic is at one side on the spectrum

One-sided tests is half of the two-sided Can double the one-sided to obtain two-sided and vice versa

Bigger the sample Narrow critical values (confidence intervals)

Larger difference between observed and expected value equals A more extreme test statistic value, the less likely we are to draw a sample with observed outcome or one that is more different from the expected, the more likely we are to reject the null

Probability distributions dependent on Degrees of freedom (determined by sample size) Larger samples hav more degrees of freedom, and lower critical values

Sufficient plausibility Observed sample outcome is among the sample outcomes that are closest to the population value

Exact approach testing Binomial formula, for discrete outcomes

Way to test null if we bootstrap our SaDi Confidence interval

We risk to make X if we apply additional tests to a sample Type 1 errorx

Inflated type 1 error Creating a new rejection region, by going .95x.95

Correction test in SPSS Bonferroni

Do not apply correction when Specifying a hypothesis beforehand about the two groups

Type 2 Error Not rejecting a false null hypothesis

Test power Probability of not making a type 2 error

Effect size Difference between hypothesized value and the true (population) value or observed (sample) value

Significance level of our test Maximum probability of making a type 1 error

Smaller standard errors yield Larger test statistic values, which have smaller p-values

Effect of small sample, but non-significant result True effect can be absent, or substantial

Effect of large sample, with non-significant result True effect is probably small, or absent

Effect of small sample with significant result True effect is probably substantial

Effect of large sample with significant result True effect can be small or substantial

Difference between sample outcome and hypothesized value Unstandardized effect size

Standardized effect size for sample means (Cohen's d) Divide difference between sample mean and hypothesized population mean by the standard deviation in the sample

Cohen's d rule of thumb of standardized effect sizes 0.2-0.8 (can also be above 1)

Main tool to increase test power Increase sample size

Effect size relates to Practical relevance

80% rule Boundary of test power

We need test power Decide how confident we can be about the support that we have found, statistical significance is irrelevant

Small sample Power to reject null is small, we may retain the null even if it is not true

Large sample Small difference in what we expect according to the null, test can be stat.sig. even if the differences are too small for practical value

Inherent meaning of statistical significance Result only means that the null has to be rejected, says nothing about practical relevance

Effect size Magnitude of effect in the population

Significant test We conclude that an effect probably exists in the population

Low test power High probability of type 2 error

Continuous outcome in a two-sided test The hypothesis can hardly ever be true, the true population value is likely not as same as the hypothesized value

Strawman principle Nil hypothesis is too weak to withstand the statistical test we perform

Expectation after high test power Significant results, but can be practically irrelevant

Instead of rejecting/not rejecting hypothesis we should Estimate/assess precisions of statements, through confidence intervals

Confidence intervals display Uncertainty about result

Safest tool to check previous research results Replication

Combining results to increase understanding Meta-analysis

Frequentist inference Does not assume true population value, instead regards it as a random variable

Bayesian inference starting point Previous knowledge, and not so easily discarded

Theoretical population Imagining it, instead of sampling from an observable one

Data generating process Regards our observed data as a result of a theoretical x

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