Basic Stat Midterm 1

Regression Model

Relationship between Response Variable and Predictor Variables

Correlation Coefficent

r: -1 to +1

0 = no linear relationship

• + correlation = one variable goes up, so does other

P-Value

0-1

Larger the p value, less statistically significant (cut off is 0.05 or 5%)

• Small p value = evidence AGAINST null hypothesis

Error Bars

Standard Deviation

Z Score

(data point - mean) / (std)

*Put $ in the constants (mean and std)

How to check if did z score right

• Mean of z scores = 0

• Standard Deviation of z scores = 1

Function for standard deviation

stdev.s (sample) the p is for population

What does a positive/negative z score mean

Positive z score: group is above class average

Negative z score: group is below class average

How to set up bar graph

• Insert blank bar graph

• Label legend, press series value arrow to select data, using comma between

• Horizontal axis should be categorical value, to add label press on 1 and write it out with comma between

How to correct error bars

To make them show the standard deviation:

• Double click

• Custom

• standard deviation of female plank hold, standard deviation of female max grip (SAME for both positive and negative) this is only for 1 of 4 bars

What does it mean when someone says they collected data?

They have anwsers whos qualities allow them to be analyzed

Types of Categorical Data

• Nominal: no order (eye color)

• Binary: 2 categories (male vs female)

• Ordinal: there is natural order (grades)

Quantitative Data

NUMBERS

• Discrete: whole numbers

• Continuous

Purpose of Protocol

Makes sure you have good data (protocol is a set of rules)

Variables, items, construct, idea relation

Idea is structured into a construct (makes idea measurable)

Constructs need to be broken down into simpler ideas called items

Items become our variable

Idea: question, construct: interest, items: influencing factors, variables: data

Cross Sectional vs Longitudinal

Cross sectional: one and done

Longitudinal: collect data from multiple points

Is retrospective or prospective data more reliable?

Prospective because can be measured in a controlled experiment, retrospective is prone to bias and relies on individual memory

Validity

About RELEVANCE (NOT precision)

Can be measurement validity (is what we are measuring appropriate?) or study validity (is how we measure something appropriate?)

Can be valid but NOT precise

Internal Validity vs External Validity

Internal: does the dependent variable get caused by the independent variable?

• Truth in study

External: can results be generalizable? (REPRESENTATIVE SAMPLE)

• Truth in real life

Types of Measurement Validity

Looks at if tools are appropriate to answer question

• Face: does it make sense on the surface?

• Content: cover all items

• Convergent: measure using different tools should still converge around an idea (ARE THINGS RELATED?)

  • Gold Standard: VO2max testing

• Discriminate: not accidently measuring something similar (ARE THINGS UNRELATED?)

Reliability

How precise (REPEAT)

The test-retest method

Steps of Descriptive Statistics

1. Find central tendency (similarities- usually mode for small range, median for large range or mean which is last resort)

2. Find variance (differences within group)

Measures of Variability

• Range

• Standard Deviation

What shows amount and pattern of variability

Curve Bell (normal distribution)

• 68 (1std) - 95 (2std) - 99.7 (3std)

• Mean = median = mode

Based on variance, if not clustered around midpoint = NOT NORMAL

Common Misconception about what’s the center of a graph

• Median = ALWAYS center

• Mean = only center if the data has a normal distribution

Kurtosis

Data is too tall around average (leptokurtic) or too far from average with big tails (platykurtic)

Need a normal distribution for

Inferential statistics

• correlation

• regression

• T-test

• ANOVA

What does a z score do

It transforms 2 variables so that they can directly be compared so that mean = 0 and standard deviation = 1

What graph to use for:

• 1 continuous variable

• 1 continuous + 1 categorical OR 2 continuous variables

• 2 continuous + categorical

1 continuous variable = HISTOGRAM

1 continuous + 1 categorical OR 2 continuous variables = SCATTERPLOT

2 continuous + categorical = LINE GRAPH

Excel Annoying thing with column graph vs histogram

Column graph (BAR GRAPH) = different color bar vs. histogram = same color bar

What are you testing in terms of hypothesis?

Attempt to reject null hypothesis: cannot say rejection means alternative hypothesis is true, just that the null is unlikely

Type 1 vs Type 2 Error

Type 1: false positive (delusional, think a difference but not there)

Type 2: false negative (think there is no difference when there is)

Significance level

Half infinity sign: sets the bar for false positives (type 1 error)

Always set at 0.05 (5% you are wrong)

What is considered statistically signifiant?

When alpha (half infinity) or p is less than 0.05

Beta + Power

Beta = type 2 error (false negative)

• Always set at 0.2

Power = true positive

• Reduce type 1 but increase type 2 probability

1- Beta = Power

What makes power go up?

• Decrease beta (type 2 error)

• high differences in central tendencies

• Low variability

• Increase sample size

Inferential tests for categorical independent & continuous dependent

• T test

• ANOVA

Inferential Tests for continuous independent & dependent

• Correlation

• Regression

Critical Value

Minimum distance that a sample distribution must be from null hypothesis for statistic significance

What does it mean to reject and fail to reject null hypothesis

Reject (p less than OR EQUAL TO 0.05) = observed difference is probulary due to chance

Fail to Reject (p is bigger than 0.05) = observed difference is probulary not just chance

Cannot prove a relationship, only that its MORE likely to exist