Inference

SET SCENE: CHILDREN ACROSS A NUMBER OF SCHOOLS WHERE ASKED TO TEST “HOW PERFECT THEY ARE” ACORDING TO DE VINCIS VITRUVIAN MAN THE PERFECT RATIO BETWEEN HEIGHT AND ARMSPAN IS 1. ie. Armspan = height

DATA COLLECTED FROM SCHOOL CHILDREN TESTING IF ARM SPAN = HEIGHT DATA COLLECTED FROM SCHOOL CHILDREN TESTING IF ARM SPAN = HEIGHT. WHAT DO YOU NOTICE. WHY ARE THRE TWO GROUPINGS? WHY ARE THE DISTINCT LINES AT X=100 and y=100

WHAT DOES THIS SHOW? LET STUDENTS MAKE THE JUDGMENT HERE THAT GIRLS ARE TALLER THAN BOYS

SAMPLING ERROR NHANES 1000, MARIJANA USE COMPARE WHAT HAPPENS WHEN WE CHANGE SAMPLE SIZE CENSUS AT SCHOOL, ARM SPAN LOOKING AT WHAT HAPPENS TO THE SAMPLING ERROR FOR A BOX PLOT USING VIT SAMPLING ERROR COMPARE WHAT HAPPENS TO SAMPLES TAKEN FROM THESE TWO SETS

"Whenever I see I remember " WHENEVER I SEE THE BOX PLOT I MUST REMEMBER..

HOW CONFIDENT ARE YOU NOW?

HOW CONFIDENT ARE YOU NOW?

HOW CONFIDENT ARE YOU NOW?

To summarise Our sample gives us this: But we need to see this So we need an idea of how “wrong” we could be: - We could take another sample or an even larger sample - Even better we could take another 1000 samples and find the average of our results - In 202 we will be using a formula to find an interval that has a high probability of containing our statistic (the median that is)

Writing questions PROPLEM AND PLAN STAGE

What you are comparing (you must include the median) I wonder what the difference is between the median weight of forward and back rugby players from ……….. data set. What you are comparing (you must include the median) The characteristic you are grouping by Where the data set is sourced from DEFINE YOUR VARIABLES

JUSTIFY/PURPOSE FOR EXCELLENCE I am doing this investigation as I play rugby and it has often been commented that I would better be suited to playing back due to my size and weight. I also wonder how my weight compares to the median weights of both backs and forwards. I would expect that the median weights for backs to be less than forwards. In addition have a hypothesis back it up with research I think this is because forwards have more physically demanding roles where weight would be an advantage; playing in the scrum for example

Make up where the sample comes from Make up where the sample comes from. Focus here on clearly defining the population and the sample

Features

SUCCOS S SPREAD Discuss the Inter Quartile Range (IQR) – which is UQ – LQ This is the spread of the middle 50% U UNUSUAL FEATURES This is usually seen by looking at the raw data (dot plot) OR a long whisker C CLUSTERS Where does most of the data lie between OR any groupings? CENTRE Compare the middle 50% of the data and which is higher up the scale O OVERLAP Is there a visible overlap of the boxes? SHAPE Is there an even distribution? – median in the middle of the box and whiskers even in length

Comparing the sizes of the spreads What do you see? The inter quartile range for the forwards is 12.2 kg whereas the interquartile range for the backs is 7.5 kg. The range is also greater for the forwards than the backs. The standard deviation is also higher for the forwards. What does this mean for the sample? This indicates that the forwards have more variation in their weights than the backs. What does this mean for the population? Overall visually forwards seem to be slightly more spread out than backs.

Describing any unusual features What do you see? Looking at the graphs I can see that the forwards have one player that weighs more than most of the other forwards. What does this mean for the sample? He is a New Zealander weighing 137 kg and is 1.81 m tall. What does this mean for the population? This could be because he is a stockier player that is quite large with more muscles causing him to weigh more, which is what I would expect are characteristics a forward is more likely to have.

CENTRE Comparing the middle 50% What do you see? The forwards’ median weight is 18.50 kg higher than the backs’ median weight. The middle 50% of the forward’s weights are between 104.8 kg and 117.0 kg whereas the middle 50% of the back’s weights are between 88.0 kg and 95.5 kg. What does this mean for the sample? Remember this structure is only a guide What does this mean for the population?

Where does most of the data lie between and are there any groupings? CLUSTERS Where does most of the data lie between and are there any groupings? What do you see? There are two discernable groups for the forwards, one between 97kg-105kg and the other between 115kg and 120kg. What does this mean for the sample? This could be due to the heavier group being props and the lighter group being flankers. (If we have access to the raw data we could actually find this out!) What does this mean for the population?

Where does most of the data lie between and are there any groupings? OVERLAP Where does most of the data lie between and are there any groupings? What do you see? The lower quartile for the forwards weight is higher than the upper quartile of the weight of the backs What does this mean for the sample? Therefore the middle 50% do not overlap. What does this mean for the population? This suggests that weights for forwards will be higher on average than the weights for backs

What is the distribution like? SHAPE What is the distribution like? What do you see? The forwards weights appear to have two distinct groupings and be skewed to the right whereas the backs weights seem reasonably symmetrical. What does this mean for the sample? This means that the weights of the backs are more evenly spread out but cluster around the median following an almost normal distribution. The forwards however have weights that are more variable with two distinct groupings and a particularly heavier player who skews the data to the right. However there is only one player skewing the data to the right so this could be down to sampling variability. What does this mean for the population? Backs appear to be unimodal whereas the forwards are potentially bimodal.

Making an Inference

Writing a Conclusion

Conclusion Make a formal statistical inference. Conclude your investigation, reflecting on your hypothesis and justifying your informal inference This may include: - Discussing sampling variability, including the variability of estimates. - Reflecting on the process you have used to make the informal inference Empahsis on difference between an inference and conclusion

Conclusion women equality in workplace

Putting it all TOGETHER