KIN 206 Final Review

what is empirical research?

when we go and collect data

• any activity in which data (quantitative or qualitative) are concluded from some area of experience and then conclusions are drawn from the data about that area of experience.

statistics

a branch of mathematics

• involves both the collection, analysis, interpretation, and presentation in relation to numerical data (quantitative)

any quantitative research question requires what?

stats

identify the steps to the scientific method:

1. developing a research hypothesis

2. collecting data

3. analyzing data

4. conclusions about research hypothesis

5. communicating findings

what is a variable?

a property or characteristic that can take on different values

are constructs variables?

constructs are special types of variables that you cannot directly measure because they are theoretical in nature

how do we determine what the research hypothesis is?

1. identifying a question or issue to be examined

2. reviewing and evaluating relevant theories and research

define the independant variable (IV):

the varible manipulated by the reseacher

define the dependant variable (DV):

the variable measured by the researcher

what do research hypothesis specify (as precisely as possible)?

the nature and direction of the relationship between variables

what are different types of research hypotheses?

1. directional vs. non-directional

2. research vs. statistical

define a directional research hypothesis:

states that there is a relationship between the IV and the DV, and which group will score higher or lower on the DV

ex. youth soccer players who wear head protection will have fewer concussions than those who do not wear head protection

define a non-directional research hypothesis:

states that there is a relationship between the IV and the DV but no direction, dont say how the IV would score on the DV

ex. there will be a difference in the number of concussions between youth soccer players who wear head protection and those who do not

research hypothesis vs. statistical hypothesis?

research hypothsis

• A is related to B

• A causes B

statistical hypothesis: mathematical expression

• null hypothesis

• alternative hypothesis

what is the null hypothesis

• this is the statistical hypothesis to be rejected

• it says nothing will happen; that there is no relationship

define population

the total number of possible units or elements that could be included in a study

• this is the theoretical population

define sample

a subset of the population used to represent the population

what is the main assumption when drawing a sample from a population?

sample characteristics = population characteristics

what is the assumption with random sampling? what are limitations to this?

that there is an equal probability of any unit or element in the population being selected into the sample

• but, you have to know who everybody in the population is in order to do this

• the people who decide to particpate in the study are often different from those who dont

define measurement:

concerned with the methods to provide descriptions of the degree (value to which an individual (or place, thing, etc.) possesses a defined characteristic (property)

what are the different levels of measurement?

• discrete:

  • categorical nominal

  • ordinal

• continuous

  • interval

  • ratial

what is catagorical nominal?

values differ in catagory or type

• a numerical value is used to denote a category but the actual number itself isn’t meaningful

• ex. basketball = 1, football = 2

what is ordinal

values that can be placed in order to other values

• nhl draft prospect ranking

what is interval level of measurement

values are equally spaced on a numeric contiuum with no absolute 0

• likert type scale

• tempurature

what is ratio level of measurement

values are equally spaced on a numeric continuum, true 0 point

• distance

how many response options do you need to move from discrete ordinal to continuous interval

if you have a likert type scale:

• 4 or less = ordinal

• 5 or more = interval

what is a likert type scale?

where there is a statement, you are asked to agree - disagree

• then, we assign values to those responses

why does the level of measurement matter?

1. what we can do statistically with the data

2. the mathematical operations that can be performed

3. how we interpret data

4. weather differences between individuals or groups are meaningful

descriptive statistics?

organise, summarise, and describe the data that has been collected

inferential statistics:

• test hypotheses and draw conclusions about the data collected from the sample

• inferences from samples to populations

• ex. mean arm hang of this sample could be used to represent the mean arm hang of all female canadians aged 20-29

why does use of language matter when drawing conclusions about research hypotheses

we are wanting to know whether the results support the research hypothesis

• there is an important distinction between support and prove

what is communicating findings

how researchers communicate and interpret the results — important within the field

reasons as to why examine data?

1. to gain a initial sense of the data

2. detecting data entry errors or data coding errors

3. to identify outliers

• rare, extreme scores that are outside the range of most other scores in the data set

4. to evaluate research methodology

• very similar scores may indicate problems with measure used

5. to determine whether data meet statistical criteria and assumptions

what is a frequency distribution table?

summarizes the number and percentage of participats for the different values of the variable

how do we create a frequency distribution table

• identify all possible values for the variable

• determine the frequency of participants who report each value

• calculate the percentage for each value

in a frequency distribution table what is the difference between percent and valid percent

Sometimes there is missing values in a data set (ex. someone didnt state the province they were from) and so '“percent” accounts for the missing people in the total number of scores:

ex. out of 150, if 3 didnt state they are still included in the total and would account for 2%

In “valid percent” the missing people are excluded from the total number of scores and make up for nothing as the new total is 147

what is cumulative percent and when would we use/not use it? why

it doesnt make a whole lot of sense for categorical/nominal variable

• because its not ranked data

because its the added percent for each sequential variable, for ranked data, its good to know how many people score under this value:

ex. if 15% of people in the data are 20 and they all smoke, then it could show us that 30% of people under 30 smoke. this is because they added the percentages of 20 yo (15%) and 30 yo (15%) to make 30% so we can say that that is the amount of people under that variable who engage in smoking because its ranked

• makes sense for ordinal, interval, or ratio

what are the ways that frequency tables can identify “problem data”

• incorect entry ex. BMI = 333

• restricted range

• highly skewed data

• missing data

what do you do with problem data?

in real world we have algorithms that are extremely good at predicting what the outcome would have been but for the purposes of this class, if you do not know what happened delete the value

what is a grouped frequency distribution table:

a table that groups interval or ratio values of a variable into smaller numbers of intervals

• frequencies and percentages are calculated within the intervals

• not based on how you collected the data but grouped afterwards

what is a real lower limit?

the smallest value of a variable that would be grouped in a particular interval

what is a real lower limit?

the largest value of a variable that would be grouped into a particular interval

what type of charts might we use for discrete; ordinal or nominal data?

• bar chart

• pie chat

bar chart

use bars to represent the frequency or percentage of values

• bars do not touch, not a continuum

pie chart

represent the percentage of the sample corresponding to the value

what charts do we use for continuous levels of measurement such as interval and ratio data

• histogram

• frequency polygons

histograms

• use bars to represent the frequency of values

• bars touch - indicate an interval variable

• bars touch indicating an underlying numerical continuum

• you can take a grouped frequency distribution table and plot it into a histogram

frequency polygons

• are line graphs that use data points to represent frequencies

• still on a continuum

what are the implications with poorly designed figures when drawing conclusions from figures

poorly designed figures might lead to inappropriate or misleading conclusions

• ex. same data but differently scaled y axes (could make the results look way more exaggerated than they are

what is important to note when describing distributions?

• modality

• symmetry

• variability

modality

different types of modality are based on how many times a value has the highest frequency.

NEED to have a gap between those actual values

ex.

• unimodal

• bimodal

• multimodal

symmetry

symmetric distributions have frequencies that change in similar manner moving away from the mode

• asymmetric distributions have outliers that skew the shape of the distribution

  • negative skey

  • positive skew

• doesnt always mean that there is outliers

• skewness statistic

how do we quatify skewness? explain:

skewness statistic

• posiitive statistic = positive skew

• negative statistic = negative skew

• 0 = perfectly normal distribution

  • the further the skewness statistic is from 0 the more skewed the distribution

variability

• the amount of differences in the distribution of a variable

• are there scores different from or similar to one another?

• the flatter the distribution the MORE variability

• kurtosis statistic

leptokurtic distribution

the tallest, most peaked

• least variable

mesokurtic

in the middle

• the variability of a normal distribution

• a perfectly mesokurtic distribution has a kurtosis statistic of 0

• neither peaked nor flat

platykurtic

• the flattest

• most variable

kurtosis statistic

• positive statistic = indicates a leptokurtic distribution

• negative statistic = indicates a platykurtic

• 0 = perfectly (mesokurtic) normal distribution

  • the further the kurtosis statistic is from 0 the more likely the distribution is to be not normal

what are the measures of central tendancy

• mean

• median

• mode

mean

the average of all the values in the data set

• sum all of the values and devide by the number of values you have

median

the exact number that sits in the middle of the data set when arranged in ascending to descending order

• if there is an even number of values, calculate the mean of the two middle numbers

mode

the value that appears most frequent in the dataset

what does it mean to say the mean as a balancing point?

if we subtract the mean from each score, and add up those values, it would equal 0.

• the sum of the negative differences will always be equal to the sum of the positive differences

in a perfectly normal distribution, the mean and the median will be…?

the same value

in a positively skewed distribution the mean will be… compared to median

higher value than the median

in a negatively skewed distribution the mean will be… compared to median ?

a smaller value than the median

why does the mean sit more towards the tail of the distribution?

because of potential outliers, further away values that are having a disproportionate impact on the mean.

in an asymmetrical distribution that has a pretty significant skew to it, what is the best measure of central tendancy?

median

what do measures of central tendancy try and tell you?

where most of the data is.

what is variability?

• quatifies the amount of difference among the scores

• concerned with the spread of the scores

• indicates the amount of difference among the scores

why does variability matter

you can have three different distributions with the same modality ad symmetry but they can be completely different distributions

• leptokurtic

• meso kurtic

• platykurtic

in kin we want to know why people are different. we want to:

• describe the variability

  • how much do 14 year olds vary in bmi

• understand variability

  • why do 14 year olds vary in bmi

• explain variability

  • do genetic markers explain variability in 14 -15 year olds bmi scores

• predict variability

• does parents bmi scores predict their 14 year old daughters bmi score?

what are the different ways that variability is measured?

• range

• variance

• standard deviation

range

highest score - lowest score

• examines the two endpoints of the distribution

• you report, you state the range and then the lowest and highest values

strengths of the range

• easy to compute

• provides some information about the sample

weaknesses of the range

• only focuses on two scores out of the whole distribution

• may not accurately reflect the variability of the whole distribution

• cannot be used to test hypotheses about distributions

• affected by outliers (extreme scores)

the interquartile range

• the range of the middle 50% of the scores

• removes the highest and lowest 25% of the distribution — minimizing the effect of outliers

strengths of the interquartile range

• reduces the influence of outliers by focusing on the middle 50%

• can be reported with the median (both compensating for outliers)

weaknesses of the interquartile range

• ignores the top 25% and bottom 25%

• may not accurately reflect the variability of the whole distribution

• can not be used to test hypotheses about distributions

population parameter

any value that refers to a population value

sample statistic

any value thats based on samples

the variance

Average squared deviation of a score from the mean

• includes all the scores in the distribution

• measures the variability by examining the extent to which each score differs from the mean

sum of squared scores

1. square the scores

2. sum the scores

sum of scores squares

1. sum the scores

2. square the sum

why n-1?

• because it corrects for the bias when using a sample to estimate a population variability

  • populations generally have more variability than there is in samples

  • n-1 corrects for this

• if you divide by smaller it makes the variance larger

what is bias

systematic underrepresentation of the true score

standard deviation

the average deviation of a score from the mean

whats the difference between the formula for the population standard deviation and the formula for the sample standard deviation?

theres no n-1

• you dont have to correct because youre just genuinely dealing with population data

• important to distinguish when youre working with population vs. sample data

what is standard deviation impacted by?

• unit of measurement

the larger the standard deviation is, what does that mean in terms of variability?

the larger the standard deviation the more variability in the data

when can you compare standard deviations?

only when you have the same unit of measurement

what are z scores

indicate distance from the mean in standard deviation units

• measured in standard deviation units

normal distribution

• unimodal

• perfectly symmetrical

• mesokurtic ; neither peaked nor flat

to be a normal distribution, it has to be based on a population of an infinite number of scores

• generated from mathematical formulas — not collected data

frequency distributions are based…

data that we have collected, which typically means its based on samples

characteristics of normal distributions?

• the let and right tails continue to infinity without touching the x axis

• bell shaped curve

  • unimodal

  • symmetric

  • mesokurtic

• the mean is the population mean (mew)

• the standard deviation is the population standard deviation

why do we care about normal distributions?

researchers beleive that many variables are normally distributed — we expect variables such as height, broad jump, vert, age, to be normally distributed throughout the population

• many inferential tests are based mathematically on the assumption of normal distributions

• AND we can determine the proportion of the distribution associated with any given score; the proportion of peaople that are going to likely fall between various scores

what are the three reasons why you mightg not be able to directly compare scores on a normal distribution

• even if they have the same population standard deviation, that doesnt mean they could have very different population means

• they could have the same population means but different population standard deviations

• they could also just be completly different units of measurement

research hypothesis

a statement regarding an expected or predicted relationship between variables

the standard normal distribution

you can take all those different normal distributions and put them all into the same metric on a distribution; standardising those distributions

• to avoid confusion that may have come from different units of measurement, different population means or different population standard deviations

• theres only one

describinng z scores

• positive = above the mean

• negative = below the mean

how much of the data will fall within ± 1 s from the mean?

68.26% of all observations