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Statistics > Statistical Inference > Flashcards

Statistical Inference Flashcards

1
Q

Inferential procedures allow us to…

A

generalize from a sample to a population

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2
Q

Inferential procedures are based on what two things?

A
  • Probability
  • Sampling Error
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3
Q

Probability definition

A
  • likelihood that any one event will occur, given all the possible outcomes
  • likely to be representative to the population differences or if they could have occurred by chance.
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4
Q

Sampling Error

A
  • Likeliness that sample characteristics will be different from population characteristics
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5
Q

Central Limit Theorem

A
  • If one was able to infinitely sample a population and plot the means they would take the shape of the normal curve.
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6
Q

If the population is bigger this means…

A

the SD is smaller

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7
Q

Standard Error

A
  • The standard deviation of the sampling distribution of means is called the standard error of the mean.

Based on sample size (more is better) and sampling error (accuracy of population characteristics)

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8
Q

Hypothesis testing

A
  • Inference also used to answer questions concerning comparisons or relationships
  • Way to decide if an observed effect reflects chance only or if we can argue with confidence that these are real effects

Examples:
* Is treatment A more effective than B?
* Is there a relationship between the length of time a treatment A is applied and the amount of change in variable X?

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9
Q

In hypothesis testing, why do we still expact change wven if the treatment is not effective?

A

Due to chance differences in subject characteristics

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10
Q

Paired t-test

A

Sample people tested twice

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11
Q

Independent t-test

A

Different groups of people tested

Ex: Compare two groups

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12
Q

Null Hypothesis

A
  • Observed differences due to chance as a result of sampling error (aka no difference, means are equal)
  • Goal is to reject the goal in research. P-value <0.05.
  • Rejecting the null means that it is unlikely that chance is involved – there is a significant effect
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13
Q

independent variable

A

The thing we manipulate

Ex: BFR, No BFR

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14
Q

Dependent Variable

A

Values measured

Ex: Knee Extension Strength (Nm)

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15
Q

We want the ____ hypothesis, as it shows a difference has been found.

A

alternative

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16
Q

Decision to reject or not reject the null are based on ____

A

the results of objective statistical procedures

This does not guarantee that a correct decision has been made

17
Q

Alpha

A
  • Probability of chance occuring
  • Often 0.05 or 0.02
  • This is used to control type 1 error
18
Q

Type 1 Error

A
  • Rejecting the null when it is true
  • Conclude a true difference exists when differences were due to chance
19
Q

Levels of Significance

A
  • Significant or Not
  • Significant = <0.05

Thus is why we say may as there is always a possibility of chance

20
Q

Type II Error

A
  • Conclude differences were due to chance when they were true differences
  • Find no difference but a real difference exists.
  • This is when effect size is crucial as there could be a different but was just not seen in the statistical tests; likely due to a small sample size
21
Q

Standard for rejecting the null hypothesis is called…

A

the level of significance

22
Q

How do we choose Alpha?

A
  • Generally 0.05
  • Although, the smaller the alpha means less likely Type 1 error to occur (Alpha = 0.01)
23
Q

Power

A
  • 1-beta
  • Is like sensitivity; The more power the better chance of seeing a difference.
  • Should be .8, some say higher .9
24
Q

What influences Statistical Power?

A
  • Lower Alpha makes it harder to find differences
  • Variance
    – Less variance, increases power
    – less variance with repeated measures
  • Sample size
    – Larger sample, greater power
  • Effect Size (difference between groups)
    – Greater effect size = greate group differences
25
Q

What is a power analysis used for?

A
  • To determine sample size
  • Determine probability of type II error
26
Q

Too many people in a study can result in…

A

a small effect size

27
Q

More precise data =

A

likeliness to find significant differences

28
Q

In order to deem a study had true differences due to treatment, what must we see with effect size and p-value?

A
  • Effect Size >0.8
  • P-value <0.05
29
Q

If you see a study with an effect size of >0.8 and a p-value of >0.05 (not significant), what does this mean?

A
  • The study is underpowered! They needed more samples!
  • There is a difference but wasn’t found in stats
  • Type II Error
30
Q

Effect size <0.8 and P-value of >0.05 means…

A

Study is a wash. Nothing found with intervention.

31
Q

Practical vs Statistical Significance

A

Difference = 0.04
* Practical: 400m small change in n is a large differences
* Statistical: Large n, small difference

Relate findings to application

32
Q

What is the critical region of rejection?

A
  • T value is a number we calculate and tells use where we are in distribution and tells us if we are in the tail and if they are different or not.
  • Alpha is related to t value
33
Q

One tailed vs two tailed tests

A
  • One tail: distribution on one tail (more powerful to find a difference)
  • Two tailed: .025 on both ends for total of 0.05
34
Q

Degrees of Freedom

A
  • Degrees of Freedom based on size of sample that gives probability distribution to give us the 0.05 distribution for sample size.
  • Number of components that are free to vary
  • (n-1)
35
Q

Parametric Statistics

A
  • random sample.
  • group variances approximately equal (homogeneous) or called “homogeneity of variance”
  • interval or ratio data
Example of unequal homogenous
36
Q

Non-parametric

A
  • normality and homogenity of variance not satisfied
  • nominal or ordinal data
37
Q

Parametric vs Nonparametric - which is more powerful

A

Parametric

Statistics (13 decks)

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