# Stats 2 -topic 2

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zchilz's
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2017-01-24 10:53

## Section 1

Question | Answer |
---|---|

interger | rounded to nearest whole number |

VARIABILITY | Tendency to vary |

STATISTIC INFERENCE | Process of moving information about samples to statments about population |

Population parameters | statements we make about population |

interqualtitle range | away to get around problem of extremes |

histogram | display distribution of a data set in a graph. |

Possion distribution | common histogram when data see unusual things |

normal distribution | bell curve |

## Section 2

Question | Answer |
---|---|

STANDARD DEVIATION | a good measure of variation-- should increase as more variation in the data, tend not to chnage as a sample size changes, extreme data value should have a moderate influence on the statistics. |

DEVIATION positive | if the data is greater than the mean. (smaller is negative) |

to overcome the issue of of + and - cancelling each other out | either mean absoulute deviation or root mean square deviation |

sum of squares | add all together squared deviation |

variance of pop | once all add then divide gives variance of pop |

root mean pop | square root stage |

mean absoulute deviation | we drop the negative signs (from deviations that have them) and calculate the mean of these by dividing by how many there are. |

root mean square deviation | - square each number because the square of negative is positive. Then take mean of these squared deviations and take the square root of the results. |

DEGREES OF FREEDON | N-1 (sample size) - (number of parameters estimated from data) |

## Section 3

Question | Answer |
---|---|

NORMAL DISTRIBUTION | is the peaked distisribution in data |

the mean of normal distibution | defines ins central tendency- the peak |

tails of distibution | Are the bits of curve along way from the mean |

Z-CALCULATIONS | unit of variation.(usually a whole number) |

## Section 4

Question | Answer |
---|---|

central tendency | MEAN, MEDIAN, MODE- note doesn't give variation, which is more meaningful in stats anylisis |

range | max-min.. v crude estimate of variation and very sensitive to extreme values, so limited in use |

interquartile range | better than range but awkward to work with |

Standard deviation | better measurement of variation and once calculated can use in a number of other stat techniques |

## Section 5

Question | Answer |
---|---|

SAMPLING | Unrealibility and reliablity are key |

measurement error | values for measurements not recorded correctly |

rounding error | when approximations are made |

error | difference between true values and estimated values. |

Random | determined by chance without any order, purpose or dependence or other things. |

BIAS | exaggerate each others inaccuracies then measurements with only random errors |

sampling error | when sample doesnt represent the wider population.- but no sample will ever perfectly represent the wider population |

EFFECTS CAN OCCUR IN METHOLODOGLY | observer effect, history effect, testing effec, instrumentation effect, selection effects, mortality effect, particpant effect, macho effect. |

Nomenclature | difference between true value and estimated value. |

beneficent subject bias | particpants aware of research so may reponse in a may that supports it, |

maleficent subject bias | o aware of research and attempt to respond in a way that undermines it. |

RRP | Reciprocation, precision, randomisation - TRY TO AVOID PSEUORPLICATION |

## Section 6

Question | Answer |
---|---|

CENTRAL LIMIT THEOREM | distribution of sample means its nearly always normal, no matter what the distribution values are, as long as sample size not too small. |

RELIABILITY | is a measure of how reliable the sample mean estimates the population mean. |

UNRELIABILTY | SD/sqrt(N) or sqrt(varience/N) “standard error of the mean”. Most important measure in statistical methods. |

## Section 7

Question | Answer |
---|---|

CONFIDENCE INTERVALS | calculate a range within which we are confident that the true mean lies |

AS RANGE GETS WIDER... | more confidence...99% CI is wider than the 95% CI. |

factors that make a confidence interval wide | Sample size, student T, Standard error |

STUDNET T DISTRIBUTION | - W.S Gossett. Similar to normal distribution but one difference – width of distribution varies and is controlled by the degree of freedom. |

(ttab) = CRITICAL VALUE | CI=2 x ttab x SE (standard error). |

## Section 8

Question | Answer |
---|---|

CHARTS | display visually, summary satistics (boxplots), indivudal data (scatterplots) |

TABLES | show data in a numerical form, rows and columns |

GRAPHS | a TYPE Of graph where axis is plotted |

KEY FEATURES OF CHARTS | error bars, axis, labels, a legend, reduction in chart junk, links, annotation can add value. "maximise the ratio of information shown to ink use" |

KEY FEATURES OF TABLES | - should have minimum maximum, population mean, sample size. o No vertical lines, only 3 lines, thick above and below definition of table, title, caption, sensible decimal places. |

## Section 9

Question | Answer |
---|---|

HYPOTHESIS TESTING AND 1 SAMPLE T TEST | |

OCCAMS RAZOR | : if two explanations account for the facts equally well, the simpler is to be preferred. |

NULL HYPOTHESIS (Ho) | NO PATTERN to explian, reject alternative. its not within conifdence level |

TYPE 1 ERROR | if you accept the null hypoth when alternative is true, (false negative) |

TYPE 2 ERROR | If you accept alternative (more complex) explanation when the null hypothesis is actually true- FALSE POSITVE |

ALTERNATIVE HYPOTHOSIS (H1) | we reject the null, if its within the confidence level |

CRITITCAL LEVEL OF PROABABILTY IS KNOWN AS .. | ALPHA VALUE, alpha 0.001 (1%) --> MINIMUN DIFFERENCE |

P VALUE | measures the probability that the difference we find occured by chance alone, assuming no real difference. |

SMALL P VALUE | shows significance; leads us to reject the null. p-value below 0.05 indicates a significance |

IMPACT OF SAMPLE SIZE | standard error increases if sample size small, fewer DF means t distribution is slighly fatter. |

P-VALUES CANNOT BE REPORTED ALONE DUE TO.. | size difference (strength of pattern), sample size, variability of the data/ |

TWO SAMPLE T-TESTS | help to calculate the probabilty that there is no real difference between the two means. |

PARAMETRIC TESTS | estimate of population para |

## Section 10

Question | Answer |
---|---|

f tests | - Compares two variances to see whether one is significantly bigger than the other. R.A Fisher created F-distribution. |

T TEST COMPARES.. | mean |

F TEST COMPARES.. | variance. F=Variance 1 divided by variance 2 (excel-FDIST(DATA)*2 |

LEVENS TEST | compares variance- but more robust as does not require normality of the data being tested. |

T test and F test assumptions | o Normality (individuals in each pop are normally distributed) o Random sampling o Independence |

2 SAMPLE T-test assumption | HOMOGENEITY OF VARIANCE. |

IF assumption is voilated, you should | use NON PARAMETRIC TEST, random sampling, |

Non parametric alternatives | Mann-Whitney U test--> ranks data, calculates rank of data. Two sample Kolmogorov S mirnov test--> compared shapes of distribution of 2 samples. not good at comparing averages |

## Section 11

Question | Answer |
---|---|

ANOVA | Analysis of variance |

SST | total sun of squares |

Variance | SST/DF |

STATISTICAL MODELS | produces fitted values also known as PREDICTED VALUES for each sampling unit |

RESIDUAL | observed value fitted value. |

Coefficient of determination | SSM/SST |

ANOVA USED | to compare more than two means simultaneously. use it instead of t-test to avoid Type 1 and 2 errors |

Null hypothesis in ANOVA | all means are the same |

model complexity is meansured by | DF |

ANOVA assumptions | constant variance, normal distribution of residuals |

if assumptions are voilated | not random sampling, likely to be bias, if not independent- over confidence in results as sample size bigger than should be |

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