# Contingency Tables Example 1

## Data

Load the birth weight data with `data(birthwt)`.

```low   - indicator of birth weight less than 2.5 kg.
race  - mother's race (1 = white, 2 = black, 3 = other).
smoke - smoking status during pregnancy.```

## Analysis

We wish to know if either smoking or race is associated with higher rates of low birth weight. So `race` and `smoke` are entered into the row list, and `low` is entered into the column list.

## R Code

Clicking run yeilds the following code:

```tables<-contingency.tables(
row.vars=d(race,smoke),
col.vars=d(low),data=birthwt)
print(tables,prop.r=T,prop.c=T,prop.t=F)
remove(tables)```

### Output

```================================================================================================================

==================================================================================
========== Table: race by low ==========
| low
race |        0  |        1  | Row Total |
-----------------------|-----------|-----------|-----------|
1  Count    |       73  |       23  |       96  |
Row %    |   76.042% |   23.958% |   50.794% |
Column % |   56.154% |   38.983% |           |
-----------------------|-----------|-----------|-----------|
2  Count    |       15  |       11  |       26  |
Row %    |   57.692% |   42.308% |   13.757% |
Column % |   11.538% |   18.644% |           |
-----------------------|-----------|-----------|-----------|
3  Count    |       42  |       25  |       67  |
Row %    |   62.687% |   37.313% |   35.450% |
Column % |   32.308% |   42.373% |           |
-----------------------|-----------|-----------|-----------|
Column Total |      130  |       59  |      189  |
Column % |   68.783% |   31.217% |           |

Large Sample
Test Statistic    DF p-value | Effect Size est.  Lower (%) Upper (%)
Chi Squared 5.005        2  0.082   | Cramer's V  0.163 0 (2.5)   0.293 (97.5)
-----------

==================================================================================
========== Table: smoke by low ==========
| low
smoke |        0  |        1  | Row Total |
-----------------------|-----------|-----------|-----------|
0  Count    |       86  |       29  |      115  |
Row %    |   74.783% |   25.217% |   60.847% |
Column % |   66.154% |   49.153% |           |
-----------------------|-----------|-----------|-----------|
1  Count    |       44  |       30  |       74  |
Row %    |   59.459% |   40.541% |   39.153% |
Column % |   33.846% |   50.847% |           |
-----------------------|-----------|-----------|-----------|
Column Total |      130  |       59  |      189  |
Column % |   68.783% |   31.217% |           |

Large Sample
Test Statistic    DF p-value | Effect Size est.  Lower (%) Upper (%)
Chi Squared 4.924        1  0.026   | Cramer's V  0.161 0 (2.5)   0.304 (97.5)
-----------

================================================================================================================```

From the output we can see that 42% of African Americans had a low birth rate versus 24% of Caucasians and 37% for Others. The differences between the races did not pass the bar of statistical significance at the 0.05 level, with a chi squared p-value of 0.082. Smoking on the other hand seems to be fairly strongly related to low birth weight. 41% of babies with mothers who were smokers were born underweight compared to 25% of those with non-smoking mothers. This passed the bar of statistical significance with a p-value of 0.026